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a8249acc18
* feat(run_eval): add checkpoint resume functionality and update example documentation; - update new bootcamp benchmark dataset * refactor(data_pipeline): optimize data generation pipeline; add multiple preset configurations for data generation * docs: update bootcamp list and add new scripts - Update Fulllist_InternBootcamp.md with new bootcamps and categories - Add new scripts to .gitignore: - examples/pipelines/filter_autogen_configs.py - examples/pipelines/quickgen_data_configs_from_eval_meta.py - Update dependencies in setup.py: - Add scipy and scikit-learn * refactor(internbootcamp): update bootcamp modules and improve error handling - Update import statements in __init__.py files - Add timestamp to target directory name in verl_data_preprocess.py - Improve error handling and scoring logic in bootcamp_judger.py - Remove unnecessary comments and update puzzle descriptions in multiple files
100 lines
469 KiB
JSON
100 lines
469 KiB
JSON
{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 1.00), (0.06, 0.97), (0.12, 0.95), (0.17, 0.92), (0.23, 0.90), (0.29, 0.87), (0.35, 0.85), (0.41, 0.83), (0.46, 0.81), (0.52, 0.79), (0.58, 0.76), (0.64, 0.74), (0.70, 0.72), (0.75, 0.71), (0.81, 0.69), (0.87, 0.67), (0.93, 0.65), (0.99, 0.63), (1.04, 0.62), (1.10, 0.60), (1.16, 0.58), (1.22, 0.57), (1.28, 0.55), (1.33, 0.54), (1.39, 0.52), (1.45, 0.51), (1.51, 0.50), (1.57, 0.48), (1.62, 0.47), (1.68, 0.46), (1.74, 0.45), (1.80, 0.43), (1.86, 0.42), (1.91, 0.41), (1.97, 0.40), (2.03, 0.39), (2.09, 0.38), (2.14, 0.37), (2.20, 0.36), (2.26, 0.35), (2.32, 0.34), (2.38, 0.33), (2.43, 0.32), (2.49, 0.32), (2.55, 0.31), (2.61, 0.30), (2.67, 0.29), (2.72, 0.28), (2.78, 0.28), (2.84, 0.27), (2.90, 0.26), (2.96, 0.25), (3.01, 0.25), (3.07, 0.24), (3.13, 0.23), (3.19, 0.23), (3.25, 0.22), (3.30, 0.22), (3.36, 0.21), (3.42, 0.20), (3.48, 0.20), (3.54, 0.19), (3.59, 0.19), (3.65, 0.18), (3.71, 0.18), (3.77, 0.17), (3.83, 0.17), (3.88, 0.17), (3.94, 0.16), (4.00, 0.16)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.057971014492753624, 0.11594202898550725, 0.17391304347826086, 0.2318840579710145, 0.2898550724637681, 0.34782608695652173, 0.4057971014492754, 0.463768115942029, 0.5217391304347826, 0.5797101449275363, 0.6376811594202899, 0.6956521739130435, 0.7536231884057971, 0.8115942028985508, 0.8695652173913043, 0.927536231884058, 0.9855072463768116, 1.0434782608695652, 1.1014492753623188, 1.1594202898550725, 1.2173913043478262, 1.2753623188405798, 1.3333333333333333, 1.391304347826087, 1.4492753623188406, 1.5072463768115942, 1.565217391304348, 1.6231884057971016, 1.681159420289855, 1.7391304347826086, 1.7971014492753623, 1.855072463768116, 1.9130434782608696, 1.9710144927536233, 2.028985507246377, 2.0869565217391304, 2.1449275362318843, 2.2028985507246377, 2.260869565217391, 2.318840579710145, 2.3768115942028984, 2.4347826086956523, 2.4927536231884058, 2.5507246376811596, 2.608695652173913, 2.6666666666666665, 2.7246376811594204, 2.782608695652174, 2.8405797101449277, 2.898550724637681, 2.956521739130435, 3.0144927536231885, 3.072463768115942, 3.130434782608696, 3.1884057971014492, 3.246376811594203, 3.3043478260869565, 3.36231884057971, 3.420289855072464, 3.4782608695652173, 3.536231884057971, 3.5942028985507246, 3.6521739130434785, 3.710144927536232, 3.7681159420289854, 3.8260869565217392, 3.8840579710144927, 3.9420289855072466, 4.0], "x": [1.0005204308523323, 0.9739916609321732, 0.948166299630469, 0.9230256891255513, 0.8985516768483367, 0.87472658712449, 0.8515332238945623, 0.8289548333545694, 0.8069751084693789, 0.785578175292917, 0.7647485727759129, 0.7444712573215461, 0.7247315971163825, 0.7055153509707964, 0.6868086387208452, 0.6685979441724836, 0.6508700965621821, 0.6336122819953057, 0.6168120528048361, 0.6004572873253387, 0.5845361746328033, 0.5690372115941895, 0.5539491996574953, 0.5392612456768955, 0.5249627425130937, 0.5110433638131319, 0.49749305769121555, 0.4843020374378969, 0.4714607769937057, 0.4589600027047443, 0.4467906856921117, 0.4349440381829923, 0.4234115044107645, 0.41218475587260184, 0.40125568655398347, 0.39061640293531463, 0.3802592194095434, 0.37017665293764457, 0.36036142279657657, 0.3508064410826619, 0.34150480830912805, 0.3324498100208271, 0.32363490790819105, 0.3150537317382566, 0.3067000844309884, 0.2985679341107404, 0.2906514097004781, 0.28294479232233155, 0.2754425155065034, 0.26813916122620635, 0.2610294553932865, 0.25410826351883115, 0.24737058656276073, 0.24081155868648854, 0.23442644331514306, 0.22821062971241696, 0.2221596283799057, 0.21626906909510957, 0.21053469780219822, 0.2049523733986819, 0.19951806442500447, 0.19422784587983594, 0.18907789722052826, 0.18406449935431526, 0.17918403193143434, 0.17443296969673483, 0.16980788120686938, 0.16530542636683032, 0.16092235392417753, 0.15665549924514988], "k": 0.46355660110720165}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 1.19), (0.11, 1.00), (0.22, 0.85), (0.33, 0.72), (0.44, 0.61), (0.55, 0.51), (0.66, 0.44), (0.77, 0.37), (0.88, 0.31), (0.99, 0.26), (1.10, 0.22), (1.21, 0.19), (1.32, 0.16), (1.43, 0.14), (1.54, 0.11), (1.65, 0.10), (1.76, 0.08), (1.87, 0.07), (1.98, 0.06), (2.09, 0.05), (2.20, 0.04), (2.31, 0.04), (2.42, 0.03), (2.53, 0.03), (2.64, 0.02), (2.75, 0.02), (2.86, 0.02), (2.97, 0.01), (3.08, 0.01), (3.19, 0.01), (3.30, 0.01), (3.41, 0.01), (3.52, 0.01), (3.63, 0.00), (3.74, 0.00), (3.85, 0.00), (3.96, 0.00), (4.07, 0.00), (4.18, 0.00), (4.29, 0.00), (4.40, 0.00), (4.51, 0.00), (4.62, 0.00), (4.73, 0.00), (4.84, 0.00), (4.95, 0.00), (5.06, 0.00), (5.17, 0.00), (5.28, 0.00), (5.39, 0.00), (5.50, 0.00), (5.61, 0.00), (5.72, 0.00), (5.83, 0.00), (5.94, 0.00), (6.06, 0.00), (6.17, 0.00), (6.28, 0.00), (6.39, 0.00), (6.50, 0.00), (6.61, 0.00), (6.72, 0.00), (6.83, 0.00), (6.94, 0.00), (7.05, 0.00), (7.16, 0.00), (7.27, 0.00), (7.38, 0.00), (7.49, 0.00), (7.60, 0.00), (7.71, 0.00), (7.82, 0.00), (7.93, 0.00), (8.04, 0.00), (8.15, 0.00), (8.26, 0.00), (8.37, 0.00), (8.48, 0.00), (8.59, 0.00), (8.70, 0.00), (8.81, 0.00), (8.92, 0.00), (9.03, 0.00), (9.14, 0.00), (9.25, 0.00), (9.36, 0.00), (9.47, 0.00), (9.58, 0.00), (9.69, 0.00), (9.80, 0.00), (9.91, 0.00), (10.02, 0.00), (10.13, 0.00), (10.24, 0.00), (10.35, 0.00), (10.46, 0.00), (10.57, 0.00), (10.68, 0.00), (10.79, 0.00), (10.90, 0.00), (11.01, 0.00), (11.12, 0.00), (11.23, 0.00), (11.34, 0.00), (11.45, 0.00), (11.56, 0.00), (11.67, 0.00), (11.78, 0.00), (11.89, 0.00), (12.00, 0.00)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.11009174311926606, 0.22018348623853212, 0.3302752293577982, 0.44036697247706424, 0.5504587155963303, 0.6605504587155964, 0.7706422018348624, 0.8807339449541285, 0.9908256880733946, 1.1009174311926606, 1.2110091743119267, 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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 0.49), (0.10, 0.49), (0.20, 0.48), (0.30, 0.47), (0.41, 0.47), (0.51, 0.46), (0.61, 0.45), (0.71, 0.45), (0.81, 0.44), (0.91, 0.43), (1.01, 0.43), (1.11, 0.42), (1.22, 0.42), (1.32, 0.41), (1.42, 0.40), (1.52, 0.40), (1.62, 0.39), (1.72, 0.39), (1.82, 0.38), (1.92, 0.38), (2.03, 0.37), (2.13, 0.37), (2.23, 0.36), (2.33, 0.36), (2.43, 0.35), (2.53, 0.35), (2.63, 0.34), (2.73, 0.34), (2.84, 0.33), (2.94, 0.33), (3.04, 0.32), (3.14, 0.32), (3.24, 0.31), (3.34, 0.31), (3.44, 0.31), (3.54, 0.30), (3.65, 0.30), (3.75, 0.29), (3.85, 0.29), (3.95, 0.29), (4.05, 0.28), (4.15, 0.28), (4.25, 0.27), (4.35, 0.27), (4.46, 0.27), (4.56, 0.26), (4.66, 0.26), (4.76, 0.26), (4.86, 0.25), (4.96, 0.25), (5.06, 0.24), (5.16, 0.24), (5.27, 0.24), (5.37, 0.23), (5.47, 0.23), (5.57, 0.23), (5.67, 0.23), (5.77, 0.22), (5.87, 0.22), (5.97, 0.22), (6.08, 0.21), (6.18, 0.21), (6.28, 0.21), (6.38, 0.20), (6.48, 0.20), (6.58, 0.20), (6.68, 0.20), (6.78, 0.19), (6.89, 0.19), (6.99, 0.19), (7.09, 0.19), (7.19, 0.18), (7.29, 0.18), (7.39, 0.18), (7.49, 0.18), (7.59, 0.17), (7.70, 0.17), (7.80, 0.17), (7.90, 0.17), (8.00, 0.16)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.10126582278481013, 0.20253164556962025, 0.3037974683544304, 0.4050632911392405, 0.5063291139240507, 0.6075949367088608, 0.7088607594936709, 0.810126582278481, 0.9113924050632911, 1.0126582278481013, 1.1139240506329113, 1.2151898734177216, 1.3164556962025316, 1.4177215189873418, 1.5189873417721518, 1.620253164556962, 1.7215189873417722, 1.8227848101265822, 1.9240506329113924, 2.0253164556962027, 2.1265822784810124, 2.2278481012658227, 2.329113924050633, 2.430379746835443, 2.5316455696202533, 2.632911392405063, 2.7341772151898733, 2.8354430379746836, 2.9367088607594938, 3.0379746835443036, 3.1392405063291138, 3.240506329113924, 3.3417721518987342, 3.4430379746835444, 3.5443037974683542, 3.6455696202531644, 3.7468354430379747, 3.848101265822785, 3.9493670886075947, 4.050632911392405, 4.151898734177215, 4.253164556962025, 4.3544303797468356, 4.455696202531645, 4.556962025316456, 4.658227848101266, 4.7594936708860756, 4.860759493670886, 4.962025316455696, 5.063291139240507, 5.1645569620253164, 5.265822784810126, 5.367088607594937, 5.468354430379747, 5.5696202531645564, 5.670886075949367, 5.772151898734177, 5.8734177215189876, 5.974683544303797, 6.075949367088607, 6.177215189873418, 6.2784810126582276, 6.379746835443038, 6.481012658227848, 6.582278481012658, 6.6835443037974684, 6.784810126582278, 6.886075949367089, 6.987341772151899, 7.0886075949367084, 7.189873417721519, 7.291139240506329, 7.3924050632911396, 7.493670886075949, 7.594936708860759, 7.69620253164557, 7.7974683544303796, 7.898734177215189, 8.0], "x": [0.49236427251430115, 0.4855362843700358, 0.47880301689019555, 0.472163122900883, 0.4656152956550819, 0.45915827217938415, 0.45279079262319333, 0.4465116147623934, 0.4403195139493074, 0.4342132827995142, 0.4281917301331454, 0.42225368125140667, 0.4163979821887997, 0.41062348882444233, 0.4049290745564817, 0.3993136289969692, 0.393776056674873, 0.38831527818794026, 0.3829302279989106, 0.3776198562357651, 0.37238312663265033, 0.3672190158923464, 0.36212651711540284, 0.3571046378046786, 0.35215239957247296, 0.3472688378971852, 0.34245300187997507, 0.3377039540014224, 0.3330207689311987, 0.3284025320689679, 0.32384834274567237, 0.31935731247222354, 0.31492856458202506, 0.31056123396475205, 0.3062544668001308, 0.30200742029171856, 0.2978192642889973, 0.293689185893692, 0.2896163805519022, 0.28560005489739604, 0.28163942701598105, 0.2777337263355183, 0.2738821914013559, 0.27008406942147667, 0.26633861953373156, 0.26264511090353376, 0.2590028225234912, 0.25541104307920254, 0.2518690728140672, 0.2483762216339638, 0.24493180836851403, 0.24153516128038868, 0.2381856179247887, 0.23488252503923562, 0.23162523859787662, 0.22841312341138836, 0.2252455530432351, 0.22212190970156911, 0.21904158410365446, 0.21600397548751035, 0.21300849170397662, 0.21005454858613062, 0.20714157001816078, 0.20426898782131606, 0.20143624171445254, 0.19864277910241096, 0.19588805559490716, 0.1931715339399548, 0.1904926843149535, 0.18785098420504595, 0.18524591831043696, 0.1826769788821217, 0.180143665071597, 0.17764548282551923, 0.1751819449060515, 0.1727525707904537, 0.1703568865730094, 0.16799442486928842, 0.16566472472274518, 0.16336733166192388], "k": 0.13790221402304292}}
|
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 2.37), (0.10, 2.22), (0.20, 2.08), (0.30, 1.95), (0.40, 1.83), (0.51, 1.71), (0.61, 1.60), (0.71, 1.50), (0.81, 1.41), (0.91, 1.32), (1.01, 1.24), (1.11, 1.16), (1.21, 1.09), (1.31, 1.02), (1.42, 0.95), (1.52, 0.89), (1.62, 0.84), (1.72, 0.79), (1.82, 0.74), (1.92, 0.69), (2.02, 0.65), (2.12, 0.61), (2.22, 0.57), (2.33, 0.53), (2.43, 0.50), (2.53, 0.47), (2.63, 0.44), (2.73, 0.41), (2.83, 0.38), (2.93, 0.36), (3.03, 0.34), (3.13, 0.32), (3.24, 0.30), (3.34, 0.28), (3.44, 0.26), (3.54, 0.24), (3.64, 0.23), (3.74, 0.21), (3.84, 0.20), (3.94, 0.19), (4.04, 0.18), (4.15, 0.17), (4.25, 0.16), (4.35, 0.15), (4.45, 0.14), (4.55, 0.13), (4.65, 0.12), (4.75, 0.11), (4.85, 0.11), (4.96, 0.10), (5.06, 0.09), (5.16, 0.09), (5.26, 0.08), (5.36, 0.08), (5.46, 0.07), (5.56, 0.07), (5.66, 0.06), (5.76, 0.06), (5.87, 0.05), (5.97, 0.05), (6.07, 0.05), (6.17, 0.05), (6.27, 0.04), (6.37, 0.04), (6.47, 0.04), (6.57, 0.03), (6.67, 0.03), (6.78, 0.03), (6.88, 0.03), (6.98, 0.03), (7.08, 0.03), (7.18, 0.02), (7.28, 0.02), (7.38, 0.02), (7.48, 0.02), (7.58, 0.02), (7.69, 0.02), (7.79, 0.02), (7.89, 0.01), (7.99, 0.01), (8.09, 0.01), (8.19, 0.01), (8.29, 0.01), (8.39, 0.01), (8.49, 0.01), (8.60, 0.01), (8.70, 0.01), (8.80, 0.01), (8.90, 0.01), (9.00, 0.01)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.10112359550561797, 0.20224719101123595, 0.3033707865168539, 0.4044943820224719, 0.5056179775280899, 0.6067415730337078, 0.7078651685393258, 0.8089887640449438, 0.9101123595505618, 1.0112359550561798, 1.1123595505617978, 1.2134831460674156, 1.3146067415730336, 1.4157303370786516, 1.5168539325842696, 1.6179775280898876, 1.7191011235955056, 1.8202247191011236, 1.9213483146067416, 2.0224719101123596, 2.1235955056179776, 2.2247191011235956, 2.3258426966292136, 2.426966292134831, 2.528089887640449, 2.629213483146067, 2.730337078651685, 2.831460674157303, 2.932584269662921, 3.033707865168539, 3.134831460674157, 3.235955056179775, 3.337078651685393, 3.438202247191011, 3.539325842696629, 3.640449438202247, 3.741573033707865, 3.842696629213483, 3.943820224719101, 4.044943820224719, 4.146067415730337, 4.247191011235955, 4.348314606741573, 4.449438202247191, 4.550561797752809, 4.651685393258427, 4.752808988764045, 4.853932584269662, 4.955056179775281, 5.056179775280898, 5.157303370786517, 5.258426966292134, 5.359550561797753, 5.46067415730337, 5.561797752808989, 5.662921348314606, 5.764044943820225, 5.865168539325842, 5.966292134831461, 6.067415730337078, 6.168539325842697, 6.269662921348314, 6.370786516853933, 6.47191011235955, 6.573033707865168, 6.674157303370786, 6.775280898876404, 6.876404494382022, 6.97752808988764, 7.078651685393258, 7.179775280898876, 7.280898876404494, 7.382022471910112, 7.48314606741573, 7.584269662921348, 7.685393258426966, 7.786516853932584, 7.887640449438202, 7.98876404494382, 8.089887640449438, 8.191011235955056, 8.292134831460674, 8.393258426966291, 8.49438202247191, 8.595505617977528, 8.696629213483146, 8.797752808988763, 8.898876404494382, 9.0], "x": [2.368723308562644, 2.219848088548843, 2.0803296800649624, 1.9495800717988216, 1.8270481009676247, 1.7122173274955548, 1.6046038096403423, 1.5037537547621143, 1.4092422015199815, 1.320670730244797, 1.237666014232364, 1.1598781802588778, 1.086979344468243, 1.0186622430748724, 0.9546389089453057, 0.8946394309319883, 0.8384109413570979, 0.7857164640540619, 0.7363338503675834, 0.6900549490267609, 0.6466847018071266, 0.6060402931501198, 0.5679504023082718, 0.5322544768407685, 0.4988020558437436, 0.4674521338323218, 0.43807256777696446, 0.41053951966157964, 0.38473693214308785, 0.3605560498023204, 0.3378949461429238, 0.3166581029716211, 0.29675600460159474, 0.2781047611448666, 0.26062575720839765, 0.24424531508874975, 0.22889439228519826, 0.21450828017255275, 0.2010263428800983, 0.18839174965307096, 0.17655124751773277, 0.16545492475076773, 0.15505601171956884, 0.145310673318489, 0.1361778342447625, 0.12761900135298793, 0.11959809671825382, 0.11208130656443102, 0.10503695056198158, 0.09843533476953334, 0.09224863187637208, 0.0864507665120207, 0.08101729895040237, 0.07592532753462232, 0.07115338868084606, 0.06668136776948376, 0.06249041531876979, 0.05856286607373742, 0.05488216525304193, 0.05143279805263651, 0.048200224871332714, 0.04517082041244692, 0.04233181518807151, 0.03967124309206985, 0.037177889436245094, 0.03484124343046445, 0.032651456679954186, 0.03059929922019839, 0.028676120268516847, 0.02687381398403886, 0.02518478372536629, 0.023601909431233137, 0.022118519475569077, 0.020728361495124636, 0.019425575271479076, 0.018204669588612794, 0.017060498539360855, 0.015988239012577583, 0.014983371401446642, 0.014041660365412094, 0.0131591361809928, 0.012332078868410123, 0.011557002612023833, 0.010830640187548394, 0.010149929813164234, 0.009512002503614, 0.008914169200187253, 0.008353909857571767, 0.007828863172577676, 0.007336815910445478], "k": 0.6419112989657589}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 2.39), (0.11, 2.17), (0.22, 1.97), (0.33, 1.79), (0.44, 1.62), (0.55, 1.47), (0.66, 1.34), (0.77, 1.21), (0.88, 1.10), (0.99, 1.00), (1.10, 0.91), (1.21, 0.82), (1.32, 0.75), (1.43, 0.68), (1.54, 0.62), (1.65, 0.56), (1.76, 0.51), (1.87, 0.46), (1.98, 0.42), (2.09, 0.38), (2.20, 0.34), (2.31, 0.31), (2.42, 0.28), (2.53, 0.26), (2.64, 0.23), (2.75, 0.21), (2.86, 0.19), (2.97, 0.17), (3.08, 0.16), (3.19, 0.14), (3.30, 0.13), (3.41, 0.12), (3.52, 0.11), (3.63, 0.10), (3.74, 0.09), (3.85, 0.08), (3.96, 0.07), (4.07, 0.07), (4.18, 0.06), (4.29, 0.05), (4.40, 0.05), (4.51, 0.04), (4.62, 0.04), (4.73, 0.04), (4.84, 0.03), (4.95, 0.03), (5.06, 0.03), (5.17, 0.03), (5.28, 0.02), (5.39, 0.02), (5.50, 0.02), (5.61, 0.02), (5.72, 0.02), (5.83, 0.01), (5.94, 0.01), (6.06, 0.01), (6.17, 0.01), (6.28, 0.01), (6.39, 0.01), (6.50, 0.01), (6.61, 0.01), (6.72, 0.01), (6.83, 0.01), (6.94, 0.01), (7.05, 0.00), (7.16, 0.00), (7.27, 0.00), (7.38, 0.00), (7.49, 0.00), (7.60, 0.00), (7.71, 0.00), (7.82, 0.00), (7.93, 0.00), (8.04, 0.00), (8.15, 0.00), (8.26, 0.00), (8.37, 0.00), (8.48, 0.00), (8.59, 0.00), (8.70, 0.00), (8.81, 0.00), (8.92, 0.00), (9.03, 0.00), (9.14, 0.00), (9.25, 0.00), (9.36, 0.00), (9.47, 0.00), (9.58, 0.00), (9.69, 0.00), (9.80, 0.00), (9.91, 0.00), (10.02, 0.00), (10.13, 0.00), (10.24, 0.00), (10.35, 0.00), (10.46, 0.00), (10.57, 0.00), (10.68, 0.00), (10.79, 0.00), (10.90, 0.00), (11.01, 0.00), (11.12, 0.00), (11.23, 0.00), (11.34, 0.00), (11.45, 0.00), (11.56, 0.00), (11.67, 0.00), (11.78, 0.00), (11.89, 0.00), (12.00, 0.00)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.11009174311926606, 0.22018348623853212, 0.3302752293577982, 0.44036697247706424, 0.5504587155963303, 0.6605504587155964, 0.7706422018348624, 0.8807339449541285, 0.9908256880733946, 1.1009174311926606, 1.2110091743119267, 1.3211009174311927, 1.4311926605504588, 1.5412844036697249, 1.651376146788991, 1.761467889908257, 1.871559633027523, 1.981651376146789, 2.091743119266055, 2.2018348623853212, 2.3119266055045875, 2.4220183486238533, 2.532110091743119, 2.6422018348623855, 2.7522935779816518, 2.8623853211009176, 2.9724770642201834, 3.0825688073394497, 3.192660550458716, 3.302752293577982, 3.4128440366972477, 3.522935779816514, 3.6330275229357802, 3.743119266055046, 3.853211009174312, 3.963302752293578, 4.0733944954128445, 4.18348623853211, 4.293577981651376, 4.4036697247706424, 4.513761467889909, 4.623853211009175, 4.73394495412844, 4.844036697247707, 4.954128440366973, 5.064220183486238, 5.174311926605505, 5.284403669724771, 5.394495412844037, 5.5045871559633035, 5.614678899082569, 5.724770642201835, 5.8348623853211015, 5.944954128440367, 6.055045871559633, 6.165137614678899, 6.275229357798166, 6.385321100917432, 6.495412844036697, 6.605504587155964, 6.71559633027523, 6.825688073394495, 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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 1.05), (0.06, 1.01), (0.12, 0.96), (0.17, 0.92), (0.23, 0.89), (0.29, 0.85), (0.35, 0.81), (0.41, 0.78), (0.46, 0.75), (0.52, 0.71), (0.58, 0.68), (0.64, 0.66), (0.70, 0.63), (0.75, 0.60), (0.81, 0.58), (0.87, 0.55), (0.93, 0.53), (0.99, 0.51), (1.04, 0.49), (1.10, 0.46), (1.16, 0.45), (1.22, 0.43), (1.28, 0.41), (1.33, 0.39), (1.39, 0.38), (1.45, 0.36), (1.51, 0.34), (1.57, 0.33), (1.62, 0.32), (1.68, 0.30), (1.74, 0.29), (1.80, 0.28), (1.86, 0.27), (1.91, 0.25), (1.97, 0.24), (2.03, 0.23), (2.09, 0.22), (2.14, 0.21), (2.20, 0.21), (2.26, 0.20), (2.32, 0.19), (2.38, 0.18), (2.43, 0.17), (2.49, 0.17), (2.55, 0.16), (2.61, 0.15), (2.67, 0.15), (2.72, 0.14), (2.78, 0.13), (2.84, 0.13), (2.90, 0.12), (2.96, 0.12), (3.01, 0.11), (3.07, 0.11), (3.13, 0.10), (3.19, 0.10), (3.25, 0.09), (3.30, 0.09), (3.36, 0.09), (3.42, 0.08), (3.48, 0.08), (3.54, 0.08), (3.59, 0.07), (3.65, 0.07), (3.71, 0.07), (3.77, 0.06), (3.83, 0.06), (3.88, 0.06), (3.94, 0.06), (4.00, 0.05)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.057971014492753624, 0.11594202898550725, 0.17391304347826086, 0.2318840579710145, 0.2898550724637681, 0.34782608695652173, 0.4057971014492754, 0.463768115942029, 0.5217391304347826, 0.5797101449275363, 0.6376811594202899, 0.6956521739130435, 0.7536231884057971, 0.8115942028985508, 0.8695652173913043, 0.927536231884058, 0.9855072463768116, 1.0434782608695652, 1.1014492753623188, 1.1594202898550725, 1.2173913043478262, 1.2753623188405798, 1.3333333333333333, 1.391304347826087, 1.4492753623188406, 1.5072463768115942, 1.565217391304348, 1.6231884057971016, 1.681159420289855, 1.7391304347826086, 1.7971014492753623, 1.855072463768116, 1.9130434782608696, 1.9710144927536233, 2.028985507246377, 2.0869565217391304, 2.1449275362318843, 2.2028985507246377, 2.260869565217391, 2.318840579710145, 2.3768115942028984, 2.4347826086956523, 2.4927536231884058, 2.5507246376811596, 2.608695652173913, 2.6666666666666665, 2.7246376811594204, 2.782608695652174, 2.8405797101449277, 2.898550724637681, 2.956521739130435, 3.0144927536231885, 3.072463768115942, 3.130434782608696, 3.1884057971014492, 3.246376811594203, 3.3043478260869565, 3.36231884057971, 3.420289855072464, 3.4782608695652173, 3.536231884057971, 3.5942028985507246, 3.6521739130434785, 3.710144927536232, 3.7681159420289854, 3.8260869565217392, 3.8840579710144927, 3.9420289855072466, 4.0], "x": [1.050976344563714, 1.0068084771517756, 0.9644967705842454, 0.9239632267220038, 0.8851331310786623, 0.8479348952875494, 0.812299932077731, 0.7781625254136122, 0.7454597810942285, 0.7141314293543184, 0.6841196701302011, 0.6553691319159717, 0.6278268569307597, 0.6014420743821705, 0.5761661223473128, 0.5519524061887902, 0.5287562857093803, 0.50653499568708, 0.48524756883858633, 0.4648547578328783, 0.4453189669367734, 0.426604181294979, 0.40867589987635095, 0.39150106074464674, 0.37504799644166137, 0.3592863773123217, 0.34418715484549717, 0.3297224864390745, 0.3158657027819962, 0.3025912624787119, 0.2898746884724039, 0.27769253549228834, 0.26602234501913996, 0.2548426002093205, 0.24413269068397006, 0.23387287217938946, 0.22404422813624666, 0.21462863875471722, 0.20560874507763258, 0.19696791724303025, 0.18869022555647222, 0.18076040788613737, 0.17316384407980148, 0.1658865306735477, 0.15891505247476512, 0.15223655386444868, 0.1458387225706752, 0.13970976506657892, 0.13383838033743098, 0.12821374309505154, 0.12282548484702882, 0.1176636722233601, 0.1127187869590362, 0.10798171304063436, 0.10344371849339307, 0.09909643558532927, 0.09493184920135565, 0.09094228236114228, 0.08712037988426649, 0.08345909447057394, 0.07995167652190913, 0.07659166067814975, 0.07337285116016141, 0.07028931358925228, 0.06733536386981015, 0.06450555570539922, 0.061794671138252606, 0.059197712650956254, 0.05670989344108044, 0.05432662769578813], "k": 0.7406150346494319}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 0.49), (0.10, 0.48), (0.20, 0.46), (0.30, 0.45), (0.41, 0.44), (0.51, 0.43), (0.61, 0.42), (0.71, 0.40), (0.81, 0.39), (0.91, 0.38), (1.01, 0.37), (1.11, 0.36), (1.22, 0.35), (1.32, 0.34), (1.42, 0.33), (1.52, 0.32), (1.62, 0.32), (1.72, 0.31), (1.82, 0.30), (1.92, 0.29), (2.03, 0.28), (2.13, 0.28), (2.23, 0.27), (2.33, 0.26), (2.43, 0.25), (2.53, 0.25), (2.63, 0.24), (2.73, 0.23), (2.84, 0.23), (2.94, 0.22), (3.04, 0.22), (3.14, 0.21), (3.24, 0.20), (3.34, 0.20), (3.44, 0.19), (3.54, 0.19), (3.65, 0.18), (3.75, 0.18), (3.85, 0.17), (3.95, 0.17), (4.05, 0.16), (4.15, 0.16), (4.25, 0.16), (4.35, 0.15), (4.46, 0.15), (4.56, 0.14), (4.66, 0.14), (4.76, 0.14), (4.86, 0.13), (4.96, 0.13), (5.06, 0.12), (5.16, 0.12), (5.27, 0.12), (5.37, 0.12), (5.47, 0.11), (5.57, 0.11), (5.67, 0.11), (5.77, 0.10), (5.87, 0.10), (5.97, 0.10), (6.08, 0.10), (6.18, 0.09), (6.28, 0.09), (6.38, 0.09), (6.48, 0.09), (6.58, 0.08), (6.68, 0.08), (6.78, 0.08), (6.89, 0.08), (6.99, 0.07), (7.09, 0.07), (7.19, 0.07), (7.29, 0.07), (7.39, 0.07), (7.49, 0.06), (7.59, 0.06), (7.70, 0.06), (7.80, 0.06), (7.90, 0.06), (8.00, 0.06)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.10126582278481013, 0.20253164556962025, 0.3037974683544304, 0.4050632911392405, 0.5063291139240507, 0.6075949367088608, 0.7088607594936709, 0.810126582278481, 0.9113924050632911, 1.0126582278481013, 1.1139240506329113, 1.2151898734177216, 1.3164556962025316, 1.4177215189873418, 1.5189873417721518, 1.620253164556962, 1.7215189873417722, 1.8227848101265822, 1.9240506329113924, 2.0253164556962027, 2.1265822784810124, 2.2278481012658227, 2.329113924050633, 2.430379746835443, 2.5316455696202533, 2.632911392405063, 2.7341772151898733, 2.8354430379746836, 2.9367088607594938, 3.0379746835443036, 3.1392405063291138, 3.240506329113924, 3.3417721518987342, 3.4430379746835444, 3.5443037974683542, 3.6455696202531644, 3.7468354430379747, 3.848101265822785, 3.9493670886075947, 4.050632911392405, 4.151898734177215, 4.253164556962025, 4.3544303797468356, 4.455696202531645, 4.556962025316456, 4.658227848101266, 4.7594936708860756, 4.860759493670886, 4.962025316455696, 5.063291139240507, 5.1645569620253164, 5.265822784810126, 5.367088607594937, 5.468354430379747, 5.5696202531645564, 5.670886075949367, 5.772151898734177, 5.8734177215189876, 5.974683544303797, 6.075949367088607, 6.177215189873418, 6.2784810126582276, 6.379746835443038, 6.481012658227848, 6.582278481012658, 6.6835443037974684, 6.784810126582278, 6.886075949367089, 6.987341772151899, 7.0886075949367084, 7.189873417721519, 7.291139240506329, 7.3924050632911396, 7.493670886075949, 7.594936708860759, 7.69620253164557, 7.7974683544303796, 7.898734177215189, 8.0], "x": [0.48907547125368905, 0.4759079731053281, 0.46309500621397093, 0.45062699047824956, 0.4384946521090317, 0.42668895245928007, 0.4152010979424977, 0.4040225378753158, 0.3931449410009487, 0.38256020431548504, 0.37226044279525583, 0.36223797793371365, 0.35248534206801113, 0.3429952772625556, 0.3337607249384383, 0.32477481068482067, 0.3160308375553088, 0.3075222865255073, 0.29924280503755873, 0.2911862156444645, 0.2833465296422932, 0.2757179159023679, 0.2682946971448852, 0.2610713382759334, 0.25404245445195345, 0.24720280818479046, 0.24054730740513652, 0.2340709941568503, 0.22776904429967693, 0.22163676368437357, 0.21566958377796536, 0.20986305972121883, 0.2042128664603626, 0.198714794441104, 0.19336474816626328, 0.18815874278371386, 0.18309289969319525, 0.17816344605564466, 0.17336671022327757, 0.1686991184573007, 0.164157192557981, 0.15973754830149542, 0.15543689401683322, 0.15125202630021342, 0.1471798288762448, 0.1432172701351443, 0.13936139642393364, 0.1356093348752813, 0.1319582908345203, 0.12840554539827523, 0.12494845197611326, 0.1215844345913142, 0.11831098733758208, 0.11512567189230173, 0.11202611561059879, 0.10901000929402814, 0.1060751061828763, 0.10321922013795885, 0.10044022401589013, 0.09773604755848632, 0.09510467623223204, 0.09254414990743857, 0.09005256129311144, 0.0876280544039344, 0.08526882301722306, 0.08297310970809788, 0.08073920443833521, 0.0785654432519362, 0.07645020649528353, 0.07439191834973331, 0.07238904561148497, 0.07044009650949229, 0.06854361966066119, 0.06669820296082371, 0.06490247097876577, 0.06315508563233031, 0.06145474528077627, 0.05980018344087805, 0.0581901678964714, 0.05662349980481868], "k": 0.2695115781731208}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 0.54), (0.10, 0.53), (0.20, 0.51), (0.30, 0.50), (0.41, 0.49), (0.51, 0.47), (0.61, 0.46), (0.71, 0.45), (0.81, 0.44), (0.91, 0.42), (1.01, 0.41), (1.11, 0.40), (1.22, 0.39), (1.32, 0.38), (1.42, 0.37), (1.52, 0.36), (1.62, 0.35), (1.72, 0.34), (1.82, 0.33), (1.92, 0.32), (2.03, 0.31), (2.13, 0.30), (2.23, 0.30), (2.33, 0.29), (2.43, 0.28), (2.53, 0.27), (2.63, 0.27), (2.73, 0.26), (2.84, 0.25), (2.94, 0.24), (3.04, 0.24), (3.14, 0.23), (3.24, 0.23), (3.34, 0.22), (3.44, 0.21), (3.54, 0.21), (3.65, 0.20), (3.75, 0.20), (3.85, 0.19), (3.95, 0.19), (4.05, 0.18), (4.15, 0.18), (4.25, 0.17), (4.35, 0.17), (4.46, 0.16), (4.56, 0.16), (4.66, 0.15), (4.76, 0.15), (4.86, 0.15), (4.96, 0.14), (5.06, 0.14), (5.16, 0.13), (5.27, 0.13), (5.37, 0.13), (5.47, 0.12), (5.57, 0.12), (5.67, 0.12), (5.77, 0.11), (5.87, 0.11), (5.97, 0.11), (6.08, 0.10), (6.18, 0.10), (6.28, 0.10), (6.38, 0.10), (6.48, 0.09), (6.58, 0.09), (6.68, 0.09), (6.78, 0.09), (6.89, 0.08), (6.99, 0.08), (7.09, 0.08), (7.19, 0.08), (7.29, 0.08), (7.39, 0.07), (7.49, 0.07), (7.59, 0.07), (7.70, 0.07), (7.80, 0.07), (7.90, 0.06), (8.00, 0.06)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.10126582278481013, 0.20253164556962025, 0.3037974683544304, 0.4050632911392405, 0.5063291139240507, 0.6075949367088608, 0.7088607594936709, 0.810126582278481, 0.9113924050632911, 1.0126582278481013, 1.1139240506329113, 1.2151898734177216, 1.3164556962025316, 1.4177215189873418, 1.5189873417721518, 1.620253164556962, 1.7215189873417722, 1.8227848101265822, 1.9240506329113924, 2.0253164556962027, 2.1265822784810124, 2.2278481012658227, 2.329113924050633, 2.430379746835443, 2.5316455696202533, 2.632911392405063, 2.7341772151898733, 2.8354430379746836, 2.9367088607594938, 3.0379746835443036, 3.1392405063291138, 3.240506329113924, 3.3417721518987342, 3.4430379746835444, 3.5443037974683542, 3.6455696202531644, 3.7468354430379747, 3.848101265822785, 3.9493670886075947, 4.050632911392405, 4.151898734177215, 4.253164556962025, 4.3544303797468356, 4.455696202531645, 4.556962025316456, 4.658227848101266, 4.7594936708860756, 4.860759493670886, 4.962025316455696, 5.063291139240507, 5.1645569620253164, 5.265822784810126, 5.367088607594937, 5.468354430379747, 5.5696202531645564, 5.670886075949367, 5.772151898734177, 5.8734177215189876, 5.974683544303797, 6.075949367088607, 6.177215189873418, 6.2784810126582276, 6.379746835443038, 6.481012658227848, 6.582278481012658, 6.6835443037974684, 6.784810126582278, 6.886075949367089, 6.987341772151899, 7.0886075949367084, 7.189873417721519, 7.291139240506329, 7.3924050632911396, 7.493670886075949, 7.594936708860759, 7.69620253164557, 7.7974683544303796, 7.898734177215189, 8.0], "x": [0.5417523940676484, 0.5271022073192414, 0.5128482095860217, 0.4989796580871786, 0.48548614026898895, 0.47235751378805435, 0.4595839131889965, 0.44715574266210173, 0.43506365751657805, 0.4232985693136271, 0.4118516343662917, 0.4007142415599642, 0.38987802149117834, 0.37933483845834987, 0.36907677954220486, 0.3590961345479802, 0.3493853986630152, 0.33993726367060295, 0.3307446101903012, 0.3218005344231347, 0.3130983239341732, 0.3046314481775096, 0.29639354024281545, 0.28837840462873054, 0.2805800125748375, 0.27299250592799656, 0.26561018228700756, 0.2584274929350492, 0.2514390398100227, 0.24463957001443148, 0.23802397275979323, 0.23158727636935378, 0.2253246424751523, 0.2192313636791845, 0.21330286106183255, 0.20753467813511914, 0.20192248011873948, 0.19646204950299156, 0.19114928162958048, 0.18598018207020786, 0.1809508644514466, 0.17605754941442964, 0.17129655932288007, 0.16666431687955996, 0.1621573426127631, 0.15777224729393768, 0.15350573415982735, 0.14935459679131358, 0.1453157160470385, 0.1413860564097063, 0.13756266336254885, 0.13384266321526733, 0.13022326011626684, 0.12670173388795733, 0.1232754374106548, 0.11994179542184343, 0.11669830246024593, 0.11354252098158137, 0.11047207895611207, 0.10748466842867326, 0.10457804406441501, 0.10175002132151993, 0.09899847469711462, 0.09632133591486405, 0.09371659282096288, 0.09118228775730981, 0.08871651606262429, 0.08631742403635298, 0.08398320833997176, 0.08171211461820413, 0.07950243613068748, 0.07735251254470236, 0.0752607285733479, 0.0732255111067338, 0.07124533013510433, 0.0693186973714903, 0.06744416490722885, 0.06562032418451948, 0.06384580483273525, 0.0621192723671692], "k": 0.27071908487348145}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 1.56), (0.10, 1.45), (0.20, 1.34), (0.30, 1.24), (0.40, 1.15), (0.51, 1.07), (0.61, 0.99), (0.71, 0.92), (0.81, 0.85), (0.91, 0.79), (1.01, 0.73), (1.11, 0.68), (1.21, 0.63), (1.31, 0.58), (1.42, 0.54), (1.52, 0.50), (1.62, 0.47), (1.72, 0.43), (1.82, 0.40), (1.92, 0.37), (2.02, 0.34), (2.12, 0.32), (2.22, 0.30), (2.33, 0.27), (2.43, 0.25), (2.53, 0.24), (2.63, 0.22), (2.73, 0.20), (2.83, 0.19), (2.93, 0.17), (3.03, 0.16), (3.13, 0.15), (3.24, 0.14), (3.34, 0.13), (3.44, 0.12), (3.54, 0.11), (3.64, 0.10), (3.74, 0.10), (3.84, 0.09), (3.94, 0.08), (4.04, 0.08), (4.15, 0.07), (4.25, 0.07), (4.35, 0.06), (4.45, 0.06), (4.55, 0.05), (4.65, 0.05), (4.75, 0.04), (4.85, 0.04), (4.96, 0.04), (5.06, 0.04), (5.16, 0.03), (5.26, 0.03), (5.36, 0.03), (5.46, 0.03), (5.56, 0.02), (5.66, 0.02), (5.76, 0.02), (5.87, 0.02), (5.97, 0.02), (6.07, 0.02), (6.17, 0.02), (6.27, 0.01), (6.37, 0.01), (6.47, 0.01), (6.57, 0.01), (6.67, 0.01), (6.78, 0.01), (6.88, 0.01), (6.98, 0.01), (7.08, 0.01), (7.18, 0.01), (7.28, 0.01), (7.38, 0.01), (7.48, 0.01), (7.58, 0.01), (7.69, 0.00), (7.79, 0.00), (7.89, 0.00), (7.99, 0.00), (8.09, 0.00), (8.19, 0.00), (8.29, 0.00), (8.39, 0.00), (8.49, 0.00), (8.60, 0.00), (8.70, 0.00), (8.80, 0.00), (8.90, 0.00), (9.00, 0.00)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.10112359550561797, 0.20224719101123595, 0.3033707865168539, 0.4044943820224719, 0.5056179775280899, 0.6067415730337078, 0.7078651685393258, 0.8089887640449438, 0.9101123595505618, 1.0112359550561798, 1.1123595505617978, 1.2134831460674156, 1.3146067415730336, 1.4157303370786516, 1.5168539325842696, 1.6179775280898876, 1.7191011235955056, 1.8202247191011236, 1.9213483146067416, 2.0224719101123596, 2.1235955056179776, 2.2247191011235956, 2.3258426966292136, 2.426966292134831, 2.528089887640449, 2.629213483146067, 2.730337078651685, 2.831460674157303, 2.932584269662921, 3.033707865168539, 3.134831460674157, 3.235955056179775, 3.337078651685393, 3.438202247191011, 3.539325842696629, 3.640449438202247, 3.741573033707865, 3.842696629213483, 3.943820224719101, 4.044943820224719, 4.146067415730337, 4.247191011235955, 4.348314606741573, 4.449438202247191, 4.550561797752809, 4.651685393258427, 4.752808988764045, 4.853932584269662, 4.955056179775281, 5.056179775280898, 5.157303370786517, 5.258426966292134, 5.359550561797753, 5.46067415730337, 5.561797752808989, 5.662921348314606, 5.764044943820225, 5.865168539325842, 5.966292134831461, 6.067415730337078, 6.168539325842697, 6.269662921348314, 6.370786516853933, 6.47191011235955, 6.573033707865168, 6.674157303370786, 6.775280898876404, 6.876404494382022, 6.97752808988764, 7.078651685393258, 7.179775280898876, 7.280898876404494, 7.382022471910112, 7.48314606741573, 7.584269662921348, 7.685393258426966, 7.786516853932584, 7.887640449438202, 7.98876404494382, 8.089887640449438, 8.191011235955056, 8.292134831460674, 8.393258426966291, 8.49438202247191, 8.595505617977528, 8.696629213483146, 8.797752808988763, 8.898876404494382, 9.0], "x": [1.5614632214679294, 1.4477584133349737, 1.342333475998916, 1.2445855292467338, 1.153955482805744, 1.0699251603864457, 0.9920138351066738, 0.9197759667534909, 0.8527984166357659, 0.7906981322633052, 0.7331199548904674, 0.679734587118582, 0.630236725717777, 0.584343252735742, 0.5417916973119777, 0.5023387327749961, 0.4657587129954287, 0.4318424329403381, 0.40039591673907265, 0.37123931629524, 0.34420588370323485, 0.3191410103896137, 0.2959013456717938, 0.27435397909405584, 0.2543756777624439, 0.23585218702148958, 0.21867756596099047, 0.20275359058244727, 0.18798919034562228, 0.17429992458826685, 0.16160750432500115, 0.14983933783623854, 0.13892812359377593, 0.1288114564864782, 0.11943148049351122, 0.11073454793729498, 0.10267092155299155, 0.09519448193520388, 0.08826247548057464, 0.08183525705001377, 0.07587606325763746, 0.07035081417743382, 0.06522791016458279, 0.06047805135812785, 0.05607407509269493, 0.05199079339486778, 0.04820485454949389, 0.04469460501520882, 0.041439969639752605, 0.03842233499271513, 0.03562444306276051, 0.03303029209093715, 0.03062504549417211, 0.028394947667963685, 0.02632724414295652, 0.02441011002488849, 0.02263258032676934, 0.020984489066937683, 0.019456411113785984, 0.018039606556571813, 0.016725973008638234, 0.01550799761330863, 0.014378714215897101, 0.013331664837359158, 0.0123608608584347, 0.011460750161010082, 0.01062618514157515, 0.009852392497389836, 0.009134947103944696, 0.008469745713149499, 0.007852983739293724, 0.007281134139744242, 0.006750926215118167, 0.0062593277062589865, 0.005803527194155725, 0.005380917708681541, 0.004989082472901387, 0.004625780458585742, 0.004288933804878258, 0.003976616193286358, 0.003687041316743743, 0.0034185531339832797, 0.0031696161414576755, 0.0029388065696042418, 0.002724804616037955, 0.0025263862197505292, 0.0023424162335618903, 0.0021718428101578633, 0.0020136904154485257, 0.0018670545006838032], "k": 0.7476685452102361}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 0.79), (0.10, 0.78), (0.20, 0.76), (0.30, 0.74), (0.41, 0.72), (0.51, 0.70), (0.61, 0.68), (0.71, 0.67), (0.81, 0.65), (0.91, 0.63), (1.01, 0.62), (1.11, 0.60), (1.22, 0.59), (1.32, 0.57), (1.42, 0.56), (1.52, 0.55), (1.62, 0.53), (1.72, 0.52), (1.82, 0.51), (1.92, 0.49), (2.03, 0.48), (2.13, 0.47), (2.23, 0.46), (2.33, 0.45), (2.43, 0.43), (2.53, 0.42), (2.63, 0.41), (2.73, 0.40), (2.84, 0.39), (2.94, 0.38), (3.04, 0.37), (3.14, 0.36), (3.24, 0.36), (3.34, 0.35), (3.44, 0.34), (3.54, 0.33), (3.65, 0.32), (3.75, 0.31), (3.85, 0.31), (3.95, 0.30), (4.05, 0.29), (4.15, 0.28), (4.25, 0.28), (4.35, 0.27), (4.46, 0.26), (4.56, 0.26), (4.66, 0.25), (4.76, 0.24), (4.86, 0.24), (4.96, 0.23), (5.06, 0.23), (5.16, 0.22), (5.27, 0.22), (5.37, 0.21), (5.47, 0.20), (5.57, 0.20), (5.67, 0.19), (5.77, 0.19), (5.87, 0.19), (5.97, 0.18), (6.08, 0.18), (6.18, 0.17), (6.28, 0.17), (6.38, 0.16), (6.48, 0.16), (6.58, 0.16), (6.68, 0.15), (6.78, 0.15), (6.89, 0.14), (6.99, 0.14), (7.09, 0.14), (7.19, 0.13), (7.29, 0.13), (7.39, 0.13), (7.49, 0.12), (7.59, 0.12), (7.70, 0.12), (7.80, 0.11), (7.90, 0.11), (8.00, 0.11)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.10126582278481013, 0.20253164556962025, 0.3037974683544304, 0.4050632911392405, 0.5063291139240507, 0.6075949367088608, 0.7088607594936709, 0.810126582278481, 0.9113924050632911, 1.0126582278481013, 1.1139240506329113, 1.2151898734177216, 1.3164556962025316, 1.4177215189873418, 1.5189873417721518, 1.620253164556962, 1.7215189873417722, 1.8227848101265822, 1.9240506329113924, 2.0253164556962027, 2.1265822784810124, 2.2278481012658227, 2.329113924050633, 2.430379746835443, 2.5316455696202533, 2.632911392405063, 2.7341772151898733, 2.8354430379746836, 2.9367088607594938, 3.0379746835443036, 3.1392405063291138, 3.240506329113924, 3.3417721518987342, 3.4430379746835444, 3.5443037974683542, 3.6455696202531644, 3.7468354430379747, 3.848101265822785, 3.9493670886075947, 4.050632911392405, 4.151898734177215, 4.253164556962025, 4.3544303797468356, 4.455696202531645, 4.556962025316456, 4.658227848101266, 4.7594936708860756, 4.860759493670886, 4.962025316455696, 5.063291139240507, 5.1645569620253164, 5.265822784810126, 5.367088607594937, 5.468354430379747, 5.5696202531645564, 5.670886075949367, 5.772151898734177, 5.8734177215189876, 5.974683544303797, 6.075949367088607, 6.177215189873418, 6.2784810126582276, 6.379746835443038, 6.481012658227848, 6.582278481012658, 6.6835443037974684, 6.784810126582278, 6.886075949367089, 6.987341772151899, 7.0886075949367084, 7.189873417721519, 7.291139240506329, 7.3924050632911396, 7.493670886075949, 7.594936708860759, 7.69620253164557, 7.7974683544303796, 7.898734177215189, 8.0], "x": [0.794888547803525, 0.7751664168238488, 0.755933635968691, 0.7371780256850247, 0.7188877618852713, 0.7010512976784251, 0.6836573748544272, 0.6666950205026719, 0.6501535224852973, 0.6340224387774348, 0.6182915860931344, 0.6029510275125806, 0.5879910784149261, 0.573402303120211, 0.5591755039008222, 0.5453017020700588, 0.5317721364488184, 0.5185782589133295, 0.5057117237422702, 0.493164408659421, 0.48092840359089645, 0.4689959933979447, 0.4573596462622818, 0.4460120127464677, 0.43494592519604475, 0.42415439892634504, 0.41363062336770884, 0.403367955001761, 0.3933599158344881, 0.3836001883388462, 0.3740826109780973, 0.36480117622609126, 0.35575002521222326, 0.34692344361386546, 0.33831586004628245, 0.3299218411392524, 0.32173608756565036, 0.3137534333843319, 0.3059688397608155, 0.2983773918600347, 0.29097429590657437, 0.28375487690532275, 0.2767145786022196, 0.2698489569350974, 0.2631536787462818, 0.25662451971896255, 0.25025735928045884, 0.24404817502849546, 0.23799304737987612, 0.23208815453052017, 0.2263297701858942, 0.2207142591988225, 0.21523807555693844, 0.2098977623664392, 0.20468994863076306, 0.19961134717153428, 0.1946587518332811, 0.18982903602642365, 0.18511915103094123, 0.1805261239231717, 0.1760470556736725, 0.1716791184795357, 0.16741955490573282, 0.16326567610482276, 0.15921486002789167, 0.15526454969658965, 0.15141225118056936, 0.1476555326473875, 0.14399202270189473, 0.1404194088992531, 0.13693543599060687, 0.13353790417837832, 0.13022466871513694, 0.12699363820680004, 0.1238427733399863, 0.12077008566837319, 0.11777363592657855, 0.11485153151673029, 0.1120019277013207, 0.10922302569053312], "k": 0.24810124387561894}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 0.97), (0.10, 0.93), (0.20, 0.89), (0.30, 0.85), (0.40, 0.82), (0.51, 0.78), (0.61, 0.75), (0.71, 0.72), (0.81, 0.69), (0.91, 0.66), (1.01, 0.63), (1.11, 0.61), (1.21, 0.58), (1.31, 0.56), (1.42, 0.53), (1.52, 0.51), (1.62, 0.49), (1.72, 0.47), (1.82, 0.45), (1.92, 0.43), (2.02, 0.41), (2.12, 0.40), (2.22, 0.38), (2.33, 0.36), (2.43, 0.35), (2.53, 0.34), (2.63, 0.32), (2.73, 0.31), (2.83, 0.30), (2.93, 0.28), (3.03, 0.27), (3.13, 0.26), (3.24, 0.25), (3.34, 0.24), (3.44, 0.23), (3.54, 0.22), (3.64, 0.21), (3.74, 0.20), (3.84, 0.19), (3.94, 0.19), (4.04, 0.18), (4.15, 0.17), (4.25, 0.16), (4.35, 0.16), (4.45, 0.15), (4.55, 0.14), (4.65, 0.14), (4.75, 0.13), (4.85, 0.13), (4.96, 0.12), (5.06, 0.12), (5.16, 0.11), (5.26, 0.11), (5.36, 0.10), (5.46, 0.10), (5.56, 0.09), (5.66, 0.09), (5.76, 0.09), (5.87, 0.08), (5.97, 0.08), (6.07, 0.08), (6.17, 0.07), (6.27, 0.07), (6.37, 0.07), (6.47, 0.06), (6.57, 0.06), (6.67, 0.06), (6.78, 0.06), (6.88, 0.05), (6.98, 0.05), (7.08, 0.05), (7.18, 0.05), (7.28, 0.05), (7.38, 0.04), (7.48, 0.04), (7.58, 0.04), (7.69, 0.04), (7.79, 0.04), (7.89, 0.04), (7.99, 0.03), (8.09, 0.03), (8.19, 0.03), (8.29, 0.03), (8.39, 0.03), (8.49, 0.03), (8.60, 0.03), (8.70, 0.03), (8.80, 0.02), (8.90, 0.02), (9.00, 0.02)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.10112359550561797, 0.20224719101123595, 0.3033707865168539, 0.4044943820224719, 0.5056179775280899, 0.6067415730337078, 0.7078651685393258, 0.8089887640449438, 0.9101123595505618, 1.0112359550561798, 1.1123595505617978, 1.2134831460674156, 1.3146067415730336, 1.4157303370786516, 1.5168539325842696, 1.6179775280898876, 1.7191011235955056, 1.8202247191011236, 1.9213483146067416, 2.0224719101123596, 2.1235955056179776, 2.2247191011235956, 2.3258426966292136, 2.426966292134831, 2.528089887640449, 2.629213483146067, 2.730337078651685, 2.831460674157303, 2.932584269662921, 3.033707865168539, 3.134831460674157, 3.235955056179775, 3.337078651685393, 3.438202247191011, 3.539325842696629, 3.640449438202247, 3.741573033707865, 3.842696629213483, 3.943820224719101, 4.044943820224719, 4.146067415730337, 4.247191011235955, 4.348314606741573, 4.449438202247191, 4.550561797752809, 4.651685393258427, 4.752808988764045, 4.853932584269662, 4.955056179775281, 5.056179775280898, 5.157303370786517, 5.258426966292134, 5.359550561797753, 5.46067415730337, 5.561797752808989, 5.662921348314606, 5.764044943820225, 5.865168539325842, 5.966292134831461, 6.067415730337078, 6.168539325842697, 6.269662921348314, 6.370786516853933, 6.47191011235955, 6.573033707865168, 6.674157303370786, 6.775280898876404, 6.876404494382022, 6.97752808988764, 7.078651685393258, 7.179775280898876, 7.280898876404494, 7.382022471910112, 7.48314606741573, 7.584269662921348, 7.685393258426966, 7.786516853932584, 7.887640449438202, 7.98876404494382, 8.089887640449438, 8.191011235955056, 8.292134831460674, 8.393258426966291, 8.49438202247191, 8.595505617977528, 8.696629213483146, 8.797752808988763, 8.898876404494382, 9.0], "x": [0.9687998437677967, 0.9285425221704687, 0.8899580282396872, 0.8529768579400683, 0.8175323971557009, 0.783560793022475, 0.7510008364309191, 0.7197938484278696, 0.6898836383198499, 0.6612163516736022, 0.63374031511974, 0.6074059720371718, 0.5821659161469748, 0.5579746966989607, 0.5347887133100343, 0.5125661937812739, 0.491267104842749, 0.47085307523022146, 0.4512873266039326, 0.4325346098509708, 0.4145611403778944, 0.3973345377123356, 0.3808237706886058, 0.36499909028704497, 0.34983197858515414, 0.33529511296952247, 0.3213623093942931, 0.30800847277679333, 0.29520953701174796, 0.28294244715203704, 0.2711851046678351, 0.25991632419501237, 0.24911580487107277, 0.23876408835896196, 0.22884252463071467, 0.21933324053117567, 0.21021910380355396, 0.2014836941191436, 0.19311127453640411, 0.18508676082214298, 0.17739569615338902, 0.1700242249877858, 0.162959065483766, 0.1561874894093974, 0.1496972994313654, 0.1434768027582208, 0.13751479069811554, 0.13180052286095342, 0.12632370601581425, 0.12107447137878835, 0.11604336179036438, 0.11122131461396853, 0.10659964267641919, 0.10217001813462671, 0.09792446118113765, 0.09385532443515487, 0.08995527570278847, 0.0862172883884793, 0.08263462903884704, 0.07920084351434939, 0.07590974435806964, 0.07275540270978424, 0.06973213678547219, 0.06683449903039765, 0.06405726880301783, 0.06139544326920821, 0.05884422722487652, 0.056399023302639635, 0.054055426437325, 0.05180921517703751, 0.04965634391099156, 0.04759293363190755, 0.04561526680295313, 0.0437197799117542, 0.041903056501003594, 0.04016182442638997, 0.038492947692746235, 0.036893419453559964, 0.035360357148087634, 0.033890998515073, 0.03248269753702865, 0.031132917077635044, 0.02983922520860625, 0.028599290922262315, 0.027410880834780098, 0.026271853971437272, 0.02518015811273209, 0.024133826112951142, 0.02313097305955695, 0.022169792375468865], "k": 0.4197030380855957}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 2.94), (0.11, 2.40), (0.22, 1.97), (0.33, 1.61), (0.44, 1.32), (0.55, 1.08), (0.66, 0.88), (0.77, 0.72), (0.88, 0.59), (0.99, 0.48), (1.10, 0.39), (1.21, 0.32), (1.32, 0.26), (1.43, 0.22), (1.54, 0.18), (1.65, 0.14), (1.76, 0.12), (1.87, 0.10), (1.98, 0.08), (2.09, 0.06), (2.20, 0.05), (2.31, 0.04), (2.42, 0.04), (2.53, 0.03), (2.64, 0.02), (2.75, 0.02), (2.86, 0.02), (2.97, 0.01), (3.08, 0.01), (3.19, 0.01), (3.30, 0.01), (3.41, 0.01), (3.52, 0.00), (3.63, 0.00), (3.74, 0.00), (3.85, 0.00), (3.96, 0.00), (4.07, 0.00), (4.18, 0.00), (4.29, 0.00), (4.40, 0.00), (4.51, 0.00), (4.62, 0.00), (4.73, 0.00), (4.84, 0.00), (4.95, 0.00), (5.06, 0.00), (5.17, 0.00), (5.28, 0.00), (5.39, 0.00), (5.50, 0.00), (5.61, 0.00), (5.72, 0.00), (5.83, 0.00), (5.94, 0.00), (6.06, 0.00), (6.17, 0.00), (6.28, 0.00), (6.39, 0.00), (6.50, 0.00), (6.61, 0.00), (6.72, 0.00), (6.83, 0.00), (6.94, 0.00), (7.05, 0.00), (7.16, 0.00), (7.27, 0.00), (7.38, 0.00), (7.49, 0.00), (7.60, 0.00), (7.71, 0.00), (7.82, 0.00), (7.93, 0.00), (8.04, 0.00), (8.15, 0.00), (8.26, 0.00), (8.37, 0.00), (8.48, 0.00), (8.59, 0.00), (8.70, 0.00), (8.81, 0.00), (8.92, 0.00), (9.03, 0.00), (9.14, 0.00), (9.25, 0.00), (9.36, 0.00), (9.47, 0.00), (9.58, 0.00), (9.69, 0.00), (9.80, 0.00), (9.91, 0.00), (10.02, 0.00), (10.13, 0.00), (10.24, 0.00), (10.35, 0.00), (10.46, 0.00), (10.57, 0.00), (10.68, 0.00), (10.79, 0.00), (10.90, 0.00), (11.01, 0.00), (11.12, 0.00), (11.23, 0.00), (11.34, 0.00), (11.45, 0.00), (11.56, 0.00), (11.67, 0.00), (11.78, 0.00), (11.89, 0.00), (12.00, 0.00)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.11009174311926606, 0.22018348623853212, 0.3302752293577982, 0.44036697247706424, 0.5504587155963303, 0.6605504587155964, 0.7706422018348624, 0.8807339449541285, 0.9908256880733946, 1.1009174311926606, 1.2110091743119267, 1.3211009174311927, 1.4311926605504588, 1.5412844036697249, 1.651376146788991, 1.761467889908257, 1.871559633027523, 1.981651376146789, 2.091743119266055, 2.2018348623853212, 2.3119266055045875, 2.4220183486238533, 2.532110091743119, 2.6422018348623855, 2.7522935779816518, 2.8623853211009176, 2.9724770642201834, 3.0825688073394497, 3.192660550458716, 3.302752293577982, 3.4128440366972477, 3.522935779816514, 3.6330275229357802, 3.743119266055046, 3.853211009174312, 3.963302752293578, 4.0733944954128445, 4.18348623853211, 4.293577981651376, 4.4036697247706424, 4.513761467889909, 4.623853211009175, 4.73394495412844, 4.844036697247707, 4.954128440366973, 5.064220183486238, 5.174311926605505, 5.284403669724771, 5.394495412844037, 5.5045871559633035, 5.614678899082569, 5.724770642201835, 5.8348623853211015, 5.944954128440367, 6.055045871559633, 6.165137614678899, 6.275229357798166, 6.385321100917432, 6.495412844036697, 6.605504587155964, 6.71559633027523, 6.825688073394495, 6.935779816513762, 7.045871559633028, 7.155963302752294, 7.2660550458715605, 7.376146788990826, 7.486238532110092, 7.596330275229358, 7.706422018348624, 7.81651376146789, 7.926605504587156, 8.036697247706423, 8.146788990825689, 8.256880733944955, 8.36697247706422, 8.477064220183486, 8.587155963302752, 8.697247706422019, 8.807339449541285, 8.917431192660551, 9.027522935779817, 9.137614678899084, 9.24770642201835, 9.357798165137615, 9.46788990825688, 9.577981651376147, 9.688073394495413, 9.79816513761468, 9.908256880733946, 10.018348623853212, 10.128440366972477, 10.238532110091743, 10.34862385321101, 10.458715596330276, 10.568807339449542, 10.678899082568808, 10.788990825688074, 10.89908256880734, 11.009174311926607, 11.119266055045872, 11.229357798165138, 11.339449541284404, 11.44954128440367, 11.559633027522937, 11.669724770642203, 11.77981651376147, 11.889908256880734, 12.0], "x": [2.939625016210126, 2.4047450042147656, 1.9671891708896259, 1.6092488736687434, 1.3164376883690898, 1.0769050016958575, 0.8809565411440741, 0.7206619202863488, 0.5895337368720212, 0.4822650031771871, 0.39451437341563006, 0.32273042617089454, 0.26400794390745097, 0.215970322114935, 0.17667339528484777, 0.1445267600129817, 0.11822936773118811, 0.09671692071255292, 0.07911877420435914, 0.06472270262699868, 0.05294607144628651, 0.04331226010143365, 0.035431370027410675, 0.028984448846696546, 0.023710578270190234, 0.019396315723405614, 0.015867055691549996, 0.012979962703176338, 0.010618191315883221, 0.008686156437080587, 0.007105665281808761, 0.005812752711779102, 0.004755092246169342, 0.0038898785956134477, 0.0031820950471908253, 0.00260309637206829, 0.0021294497333774203, 0.0017419855358786498, 0.0014250219673419765, 0.0011657310654070896, 0.0009536197784949404, 0.0007801034270263243, 0.0006381593836440305, 0.0005220428841514293, 0.0004270543281532695, 0.0003493492981414719, 0.0002857832748724847, 0.0002337834511669746, 0.0001912452821786473, 0.000156447181710017, 0.00012798078673419486, 0.00010469391235929648, 8.564430577516419e-05, 7.006064026594469e-05, 5.7312467133520894e-05, 4.688481391987664e-05, 3.835440383990951e-05, 3.137623386812118e-05, 2.5667097873239454e-05, 2.0996680069424054e-05, 1.717636797544345e-05, 1.4050964707124083e-05, 1.1494330398563311e-05, 9.403017967747762e-06, 7.691775334840206e-06, 6.291024972398921e-06, 5.1460193641658676e-06, 4.209309817904146e-06, 3.4437521568600057e-06, 2.817255577806087e-06, 2.3047486914359885e-06, 1.8853752171057582e-06, 1.5420753022705987e-06, 1.2612302319232805e-06, 1.0321668756526936e-06, 8.446561884831614e-07, 6.914692068623861e-07, 5.658936403269619e-07, 4.631334399367811e-07, 3.788909841482175e-07, 3.0956318459900077e-07, 2.536979180527191e-07, 2.0765772136740103e-07, 1.7006496429774083e-07, 1.3937988732770165e-07, 1.1419650505759917e-07, 9.360126528584678e-08, 7.67197566261258e-08, 6.263425979132792e-08, 5.1086290047539855e-08, 4.163588466043726e-08, 3.345286046448384e-08, 2.752376358824806e-08, 2.2469263295488988e-08, 1.8230650401069674e-08, 1.4752838717502725e-08, 1.2031652025720645e-08, 9.842744789911205e-09, 8.058346590506004e-09, 6.669400880276527e-09, 5.523977786431455e-09, 4.5678490027761734e-09, 3.793382117846561e-09, 3.1382621881133697e-09, 2.5887571464809805e-09, 2.13861192241231e-09, 1.7585029406059085e-09, 1.444695335181092e-09, 1.1906158438196428e-09, 9.772871918021517e-10], "k": 1.8242800647774746}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 1.23), (0.10, 1.14), (0.20, 1.06), (0.31, 0.99), (0.41, 0.92), (0.51, 0.85), (0.61, 0.79), (0.71, 0.74), (0.81, 0.69), (0.92, 0.64), (1.02, 0.60), (1.12, 0.55), (1.22, 0.52), (1.32, 0.48), (1.42, 0.45), (1.53, 0.41), (1.63, 0.39), (1.73, 0.36), (1.83, 0.33), (1.93, 0.31), (2.03, 0.29), (2.14, 0.27), (2.24, 0.25), (2.34, 0.23), (2.44, 0.22), (2.54, 0.20), (2.64, 0.19), (2.75, 0.17), (2.85, 0.16), (2.95, 0.15), (3.05, 0.14), (3.15, 0.13), (3.25, 0.12), (3.36, 0.11), (3.46, 0.11), (3.56, 0.10), (3.66, 0.09), (3.76, 0.08), (3.86, 0.08), (3.97, 0.07), (4.07, 0.07), (4.17, 0.06), (4.27, 0.06), (4.37, 0.05), (4.47, 0.05), (4.58, 0.05), (4.68, 0.04), (4.78, 0.04), (4.88, 0.04), (4.98, 0.04), (5.08, 0.03), (5.19, 0.03), (5.29, 0.03), (5.39, 0.03), (5.49, 0.02), (5.59, 0.02), (5.69, 0.02), (5.80, 0.02), (5.90, 0.02), (6.00, 0.02)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.1016949152542373, 0.2033898305084746, 0.3050847457627119, 0.4067796610169492, 0.5084745762711864, 0.6101694915254238, 0.7118644067796611, 0.8135593220338984, 0.9152542372881356, 1.0169491525423728, 1.1186440677966103, 1.2203389830508475, 1.3220338983050848, 1.4237288135593222, 1.5254237288135595, 1.6271186440677967, 1.728813559322034, 1.8305084745762712, 1.9322033898305087, 2.0338983050847457, 2.135593220338983, 2.2372881355932206, 2.3389830508474576, 2.440677966101695, 2.5423728813559325, 2.6440677966101696, 2.745762711864407, 2.8474576271186445, 2.9491525423728815, 3.050847457627119, 3.152542372881356, 3.2542372881355934, 3.355932203389831, 3.457627118644068, 3.5593220338983054, 3.6610169491525424, 3.76271186440678, 3.8644067796610173, 3.9661016949152543, 4.067796610169491, 4.169491525423729, 4.271186440677966, 4.372881355932203, 4.474576271186441, 4.576271186440678, 4.677966101694915, 4.779661016949153, 4.88135593220339, 4.983050847457627, 5.084745762711865, 5.186440677966102, 5.288135593220339, 5.389830508474577, 5.491525423728814, 5.593220338983051, 5.694915254237289, 5.796610169491526, 5.898305084745763, 6.0], "x": [1.226315205305363, 1.1408461723417624, 1.061333935201297, 0.9873633763937447, 0.9185482271290467, 0.8545292387856152, 0.7949721519413996, 0.7395658873973844, 0.6880212311914197, 0.6400690162658071, 0.5954588716571411, 0.5539578685630185, 0.5153493134908584, 0.4794316251408678, 0.4460172336968296, 0.41493167529253905, 0.38601265927094114, 0.3591091801061036, 0.33408076461328545, 0.3107967255646671, 0.28913548566446906, 0.268983945444416, 0.250236883607602, 0.2327964134485563, 0.21657147144958214, 0.20147733722617547, 0.18743520439945968, 0.17437174857614188, 0.16221876292534076, 0.15091278809714434, 0.14039479426137066, 0.13060985951285886, 0.12150689542538007, 0.11303836902814561, 0.10516006475149581, 0.09783084451991848, 0.09101244143280716, 0.08466925190160837, 0.0787681569672283, 0.07327834233554234, 0.068171145403259, 0.0634199022535216, 0.058999802882359724, 0.054887763349730584, 0.051062316613785366, 0.047503486662502516, 0.04419269113690792, 0.041112644793991744, 0.03824726445698661, 0.03558158979284677, 0.03310170129794656, 0.030794650324787412, 0.028648391218506465, 0.02665171760772457, 0.024794204145921702, 0.023066151479702906, 0.021458536888668264, 0.01996296635822932, 0.018571630759151903, 0.01727726574348932], "k": 0.7103962798433598}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 0.64), (0.10, 0.60), (0.20, 0.56), (0.31, 0.52), (0.41, 0.48), (0.51, 0.45), (0.61, 0.42), (0.71, 0.39), (0.81, 0.37), (0.92, 0.34), (1.02, 0.32), (1.12, 0.30), (1.22, 0.28), (1.32, 0.26), (1.42, 0.24), (1.53, 0.23), (1.63, 0.21), (1.73, 0.20), (1.83, 0.19), (1.93, 0.17), (2.03, 0.16), (2.14, 0.15), (2.24, 0.14), (2.34, 0.13), (2.44, 0.12), (2.54, 0.11), (2.64, 0.11), (2.75, 0.10), (2.85, 0.09), (2.95, 0.09), (3.05, 0.08), (3.15, 0.08), (3.25, 0.07), (3.36, 0.07), (3.46, 0.06), (3.56, 0.06), (3.66, 0.05), (3.76, 0.05), (3.86, 0.05), (3.97, 0.04), (4.07, 0.04), (4.17, 0.04), (4.27, 0.04), (4.37, 0.03), (4.47, 0.03), (4.58, 0.03), (4.68, 0.03), (4.78, 0.03), (4.88, 0.02), (4.98, 0.02), (5.08, 0.02), (5.19, 0.02), (5.29, 0.02), (5.39, 0.02), (5.49, 0.02), (5.59, 0.01), (5.69, 0.01), (5.80, 0.01), (5.90, 0.01), (6.00, 0.01)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.1016949152542373, 0.2033898305084746, 0.3050847457627119, 0.4067796610169492, 0.5084745762711864, 0.6101694915254238, 0.7118644067796611, 0.8135593220338984, 0.9152542372881356, 1.0169491525423728, 1.1186440677966103, 1.2203389830508475, 1.3220338983050848, 1.4237288135593222, 1.5254237288135595, 1.6271186440677967, 1.728813559322034, 1.8305084745762712, 1.9322033898305087, 2.0338983050847457, 2.135593220338983, 2.2372881355932206, 2.3389830508474576, 2.440677966101695, 2.5423728813559325, 2.6440677966101696, 2.745762711864407, 2.8474576271186445, 2.9491525423728815, 3.050847457627119, 3.152542372881356, 3.2542372881355934, 3.355932203389831, 3.457627118644068, 3.5593220338983054, 3.6610169491525424, 3.76271186440678, 3.8644067796610173, 3.9661016949152543, 4.067796610169491, 4.169491525423729, 4.271186440677966, 4.372881355932203, 4.474576271186441, 4.576271186440678, 4.677966101694915, 4.779661016949153, 4.88135593220339, 4.983050847457627, 5.084745762711865, 5.186440677966102, 5.288135593220339, 5.389830508474577, 5.491525423728814, 5.593220338983051, 5.694915254237289, 5.796610169491526, 5.898305084745763, 6.0], "x": [0.637330407463284, 0.5950319536357787, 0.5555407460100692, 0.5186704986735278, 0.4842472633654331, 0.4521086027871667, 0.42210298357627174, 0.3940888007156933, 0.3679338172114795, 0.34351471701627256, 0.3207162615056071, 0.2994308987819101, 0.2795582077256994, 0.261004431447438, 0.2436820367235939, 0.2275093030283892, 0.21240991627743733, 0.19831264356828227, 0.1851509866622025, 0.17286284550556338, 0.16139024816304, 0.15067906647514345, 0.1406787659911665, 0.13134216823640155, 0.12262522357310689, 0.11448680701627116, 0.10688852240732748, 0.09979452078550013, 0.09317133425858028, 0.08698771921548676, 0.08121449816044696, 0.07582443707014776, 0.07079210358117785, 0.06609375756278814, 0.06170723245613879, 0.05761183254333672, 0.05378823824093004, 0.05021840800734326, 0.04688550201593487, 0.043773794297886755, 0.04086860545800193, 0.0381562288245459, 0.035623867450013044, 0.033259574792086105, 0.031052194753009646, 0.028991315274400083, 0.02706721500696126, 0.02527081542270694, 0.023593638334913916, 0.022027771776542873, 0.020565829636225805, 0.019200912463219803, 0.017926582035864558, 0.01673682700404647, 0.015626033608063243, 0.014588961995586269, 0.013620719183271473, 0.01271673633863885, 0.011872749108590038, 0.01108477582282024], "k": 0.6752859263725348}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 0.95), (0.10, 0.90), (0.20, 0.86), (0.31, 0.82), (0.41, 0.78), (0.51, 0.74), (0.61, 0.70), (0.71, 0.67), (0.81, 0.64), (0.92, 0.61), (1.02, 0.58), (1.12, 0.55), (1.22, 0.52), (1.32, 0.50), (1.42, 0.47), (1.53, 0.45), (1.63, 0.43), (1.73, 0.41), (1.83, 0.39), (1.93, 0.37), (2.03, 0.35), (2.14, 0.34), (2.24, 0.32), (2.34, 0.30), (2.44, 0.29), (2.54, 0.28), (2.64, 0.26), (2.75, 0.25), (2.85, 0.24), (2.95, 0.23), (3.05, 0.22), (3.15, 0.21), (3.25, 0.20), (3.36, 0.19), (3.46, 0.18), (3.56, 0.17), (3.66, 0.16), (3.76, 0.15), (3.86, 0.15), (3.97, 0.14), (4.07, 0.13), (4.17, 0.13), (4.27, 0.12), (4.37, 0.11), (4.47, 0.11), (4.58, 0.10), (4.68, 0.10), (4.78, 0.09), (4.88, 0.09), (4.98, 0.08), (5.08, 0.08), (5.19, 0.08), (5.29, 0.07), (5.39, 0.07), (5.49, 0.07), (5.59, 0.06), (5.69, 0.06), (5.80, 0.06), (5.90, 0.05), (6.00, 0.05)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.1016949152542373, 0.2033898305084746, 0.3050847457627119, 0.4067796610169492, 0.5084745762711864, 0.6101694915254238, 0.7118644067796611, 0.8135593220338984, 0.9152542372881356, 1.0169491525423728, 1.1186440677966103, 1.2203389830508475, 1.3220338983050848, 1.4237288135593222, 1.5254237288135595, 1.6271186440677967, 1.728813559322034, 1.8305084745762712, 1.9322033898305087, 2.0338983050847457, 2.135593220338983, 2.2372881355932206, 2.3389830508474576, 2.440677966101695, 2.5423728813559325, 2.6440677966101696, 2.745762711864407, 2.8474576271186445, 2.9491525423728815, 3.050847457627119, 3.152542372881356, 3.2542372881355934, 3.355932203389831, 3.457627118644068, 3.5593220338983054, 3.6610169491525424, 3.76271186440678, 3.8644067796610173, 3.9661016949152543, 4.067796610169491, 4.169491525423729, 4.271186440677966, 4.372881355932203, 4.474576271186441, 4.576271186440678, 4.677966101694915, 4.779661016949153, 4.88135593220339, 4.983050847457627, 5.084745762711865, 5.186440677966102, 5.288135593220339, 5.389830508474577, 5.491525423728814, 5.593220338983051, 5.694915254237289, 5.796610169491526, 5.898305084745763, 6.0], "x": [0.9456225109314602, 0.900146824842962, 0.8568580801431526, 0.8156511114529514, 0.776425824330812, 0.7390869109159566, 0.7035436299108263, 0.6697096595154958, 0.6375028406898622, 0.6068448685500719, 0.5776612200073372, 0.5498810506980342, 0.5234368552616365, 0.4982643769624239, 0.47430246227370265, 0.45149289470594633, 0.42978025715284074, 0.40911179634466005, 0.38943729801844923, 0.3707089659757093, 0.35288129475857666, 0.33591096042141577, 0.3197567365363382, 0.30437938694578104, 0.28974154592900103, 0.27580765003566327, 0.26254384939172, 0.24991791433133514, 0.23789917051861884, 0.2264584164991523, 0.21556785716153487, 0.20520103378734342, 0.1953327585428657, 0.18593905660380278, 0.17699710454393533, 0.16848517793190718, 0.1603825956370336, 0.15266967112597266, 0.14532766819623397, 0.13833874893642686, 0.13168593109582535, 0.1253530529273783, 0.11932472838528932, 0.11358630943716833, 0.10812385578442577, 0.1029240965640677, 0.09797439675531597, 0.09326273199326986, 0.08877765572109741, 0.08450826939401931, 0.08044420115576575, 0.07657557785783857, 0.07289299888379289, 0.0693875179020596, 0.06605061899364315, 0.06287419351306682, 0.05985052466174645, 0.05697226695638672, 0.0542324260178857, 0.051624345554690726], "k": 0.48464163764519785}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 0.93), (0.11, 0.77), (0.22, 0.65), (0.33, 0.54), (0.44, 0.45), (0.55, 0.38), (0.66, 0.32), (0.77, 0.26), (0.88, 0.22), (0.99, 0.18), (1.10, 0.15), (1.21, 0.13), (1.32, 0.11), (1.43, 0.09), (1.54, 0.08), (1.65, 0.06), (1.76, 0.05), (1.87, 0.04), (1.98, 0.04), (2.09, 0.03), (2.20, 0.03), (2.31, 0.02), (2.42, 0.02), (2.53, 0.02), (2.64, 0.01), (2.75, 0.01), (2.86, 0.01), (2.97, 0.01), (3.08, 0.01), (3.19, 0.01), (3.30, 0.00), (3.41, 0.00), (3.52, 0.00), (3.63, 0.00), (3.74, 0.00), (3.85, 0.00), (3.96, 0.00), (4.07, 0.00), (4.18, 0.00), (4.29, 0.00), (4.40, 0.00), (4.51, 0.00), (4.62, 0.00), (4.73, 0.00), (4.84, 0.00), (4.95, 0.00), (5.06, 0.00), (5.17, 0.00), (5.28, 0.00), (5.39, 0.00), (5.50, 0.00), (5.61, 0.00), (5.72, 0.00), (5.83, 0.00), (5.94, 0.00), (6.06, 0.00), (6.17, 0.00), (6.28, 0.00), (6.39, 0.00), (6.50, 0.00), (6.61, 0.00), (6.72, 0.00), (6.83, 0.00), (6.94, 0.00), (7.05, 0.00), (7.16, 0.00), (7.27, 0.00), (7.38, 0.00), (7.49, 0.00), (7.60, 0.00), (7.71, 0.00), (7.82, 0.00), (7.93, 0.00), (8.04, 0.00), (8.15, 0.00), (8.26, 0.00), (8.37, 0.00), (8.48, 0.00), (8.59, 0.00), (8.70, 0.00), (8.81, 0.00), (8.92, 0.00), (9.03, 0.00), (9.14, 0.00), (9.25, 0.00), (9.36, 0.00), (9.47, 0.00), (9.58, 0.00), (9.69, 0.00), (9.80, 0.00), (9.91, 0.00), (10.02, 0.00), (10.13, 0.00), (10.24, 0.00), (10.35, 0.00), (10.46, 0.00), (10.57, 0.00), (10.68, 0.00), (10.79, 0.00), (10.90, 0.00), (11.01, 0.00), (11.12, 0.00), (11.23, 0.00), (11.34, 0.00), (11.45, 0.00), (11.56, 0.00), (11.67, 0.00), (11.78, 0.00), (11.89, 0.00), (12.00, 0.00)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.11009174311926606, 0.22018348623853212, 0.3302752293577982, 0.44036697247706424, 0.5504587155963303, 0.6605504587155964, 0.7706422018348624, 0.8807339449541285, 0.9908256880733946, 1.1009174311926606, 1.2110091743119267, 1.3211009174311927, 1.4311926605504588, 1.5412844036697249, 1.651376146788991, 1.761467889908257, 1.871559633027523, 1.981651376146789, 2.091743119266055, 2.2018348623853212, 2.3119266055045875, 2.4220183486238533, 2.532110091743119, 2.6422018348623855, 2.7522935779816518, 2.8623853211009176, 2.9724770642201834, 3.0825688073394497, 3.192660550458716, 3.302752293577982, 3.4128440366972477, 3.522935779816514, 3.6330275229357802, 3.743119266055046, 3.853211009174312, 3.963302752293578, 4.0733944954128445, 4.18348623853211, 4.293577981651376, 4.4036697247706424, 4.513761467889909, 4.623853211009175, 4.73394495412844, 4.844036697247707, 4.954128440366973, 5.064220183486238, 5.174311926605505, 5.284403669724771, 5.394495412844037, 5.5045871559633035, 5.614678899082569, 5.724770642201835, 5.8348623853211015, 5.944954128440367, 6.055045871559633, 6.165137614678899, 6.275229357798166, 6.385321100917432, 6.495412844036697, 6.605504587155964, 6.71559633027523, 6.825688073394495, 6.935779816513762, 7.045871559633028, 7.155963302752294, 7.2660550458715605, 7.376146788990826, 7.486238532110092, 7.596330275229358, 7.706422018348624, 7.81651376146789, 7.926605504587156, 8.036697247706423, 8.146788990825689, 8.256880733944955, 8.36697247706422, 8.477064220183486, 8.587155963302752, 8.697247706422019, 8.807339449541285, 8.917431192660551, 9.027522935779817, 9.137614678899084, 9.24770642201835, 9.357798165137615, 9.46788990825688, 9.577981651376147, 9.688073394495413, 9.79816513761468, 9.908256880733946, 10.018348623853212, 10.128440366972477, 10.238532110091743, 10.34862385321101, 10.458715596330276, 10.568807339449542, 10.678899082568808, 10.788990825688074, 10.89908256880734, 11.009174311926607, 11.119266055045872, 11.229357798165138, 11.339449541284404, 11.44954128440367, 11.559633027522937, 11.669724770642203, 11.77981651376147, 11.889908256880734, 12.0], "x": [0.9267778877046486, 0.7748119109013989, 0.6477641016765278, 0.5415487022027541, 0.45274966884675344, 0.37851122235760754, 0.31644583035705415, 0.26455743718954094, 0.22117731809882896, 0.18491034112780852, 0.15459014604114935, 0.12924162368477607, 0.10804956096591589, 0.09033241250937868, 0.07552038820100113, 0.06313712700926503, 0.052784378460835474, 0.04412919714146852, 0.03689323167878246, 0.030843761531228447, 0.02578623597829248, 0.021558005430545705, 0.01802308724052741, 0.015067798827563964, 0.012597095934864893, 0.010531520140971525, 0.008804641827462593, 0.007360923695935385, 0.006153935513252903, 0.005144860043657806, 0.004301245057554776, 0.003595959651822441, 0.003006321587451186, 0.002513367908629298, 0.002101245409073779, 0.0017566990729427812, 0.001468648350955992, 0.0012278300693344475, 0.001026499475506924, 0.0008581815583537998, 0.0007174633150508261, 0.0005998190614856899, 0.0005014651762095786, 0.00041923826595188486, 0.0003504947095033459, 0.00029302326238487305, 0.0002449754336764452, 0.00020480609541048935, 0.00017122356024723147, 0.00014314761217618452, 0.00011967527363165105, 0.00010005181021354038, 8.364597344557209e-05, 6.992985918800507e-05, 5.84636035672183e-05, 4.887778331064733e-05, 4.086380039140773e-05, 3.416351600326591e-05, 2.8561683503761944e-05, 2.387819728063046e-05, 1.9962995055187708e-05, 1.6689516360852008e-05, 1.3952972641792397e-05, 1.166513999865636e-05, 9.752354760223931e-06, 8.152369927323643e-06, 6.814834525964808e-06, 5.697079214271527e-06, 4.762823394803559e-06, 3.982060998182809e-06, 3.3292274088317615e-06, 2.7833603651584278e-06, 2.326941642887226e-06, 1.945138097020731e-06, 1.6257042301354904e-06, 1.3595030212992285e-06, 1.1368928126267839e-06, 9.509201937370954e-07, 7.954757661060528e-07, 6.652617143678604e-07, 5.564115583962472e-07, 4.6519610694833255e-07, 3.8826770338451167e-07, 3.2525303604475937e-07, 2.720752898899473e-07, 2.2763652622112403e-07, 1.9056481841285637e-07, 1.5960298219123605e-07, 1.3359866433113703e-07, 1.1191101528836596e-07, 9.371896874203696e-08, 7.821721761036313e-08, 6.521926668998201e-08, 5.436582639559906e-08, 4.434328008335991e-08, 3.7412952380702555e-08, 3.133535040992765e-08, 2.6105266176748125e-08, 2.1643233960725665e-08, 1.792234683358688e-08, 1.4941040718417963e-08, 1.2495893483059138e-08, 1.044470169278206e-08, 8.787465347586772e-09, 7.442241933315356e-09, 6.282805859199479e-09, 5.307754658290316e-09, 4.498595959691917e-09, 3.796672788968392e-09, 3.1976470725420943e-09], "k": 1.6267673344855487}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 1.20), (0.06, 1.13), (0.12, 1.06), (0.17, 1.00), (0.23, 0.94), (0.29, 0.89), (0.35, 0.84), (0.41, 0.79), (0.46, 0.74), (0.52, 0.70), (0.58, 0.66), (0.64, 0.62), (0.70, 0.59), (0.75, 0.55), (0.81, 0.52), (0.87, 0.49), (0.93, 0.46), (0.99, 0.44), (1.04, 0.41), (1.10, 0.39), (1.16, 0.36), (1.22, 0.34), (1.28, 0.32), (1.33, 0.31), (1.39, 0.29), (1.45, 0.27), (1.51, 0.26), (1.57, 0.24), (1.62, 0.23), (1.68, 0.21), (1.74, 0.20), (1.80, 0.19), (1.86, 0.18), (1.91, 0.17), (1.97, 0.16), (2.03, 0.15), (2.09, 0.14), (2.14, 0.13), (2.20, 0.13), (2.26, 0.12), (2.32, 0.11), (2.38, 0.10), (2.43, 0.10), (2.49, 0.09), (2.55, 0.09), (2.61, 0.08), (2.67, 0.08), (2.72, 0.07), (2.78, 0.07), (2.84, 0.07), (2.90, 0.06), (2.96, 0.06), (3.01, 0.05), (3.07, 0.05), (3.13, 0.05), (3.19, 0.05), (3.25, 0.04), (3.30, 0.04), (3.36, 0.04), (3.42, 0.04), (3.48, 0.03), (3.54, 0.03), (3.59, 0.03), (3.65, 0.03), (3.71, 0.03), (3.77, 0.03), (3.83, 0.02), (3.88, 0.02), (3.94, 0.02), (4.00, 0.02)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.057971014492753624, 0.11594202898550725, 0.17391304347826086, 0.2318840579710145, 0.2898550724637681, 0.34782608695652173, 0.4057971014492754, 0.463768115942029, 0.5217391304347826, 0.5797101449275363, 0.6376811594202899, 0.6956521739130435, 0.7536231884057971, 0.8115942028985508, 0.8695652173913043, 0.927536231884058, 0.9855072463768116, 1.0434782608695652, 1.1014492753623188, 1.1594202898550725, 1.2173913043478262, 1.2753623188405798, 1.3333333333333333, 1.391304347826087, 1.4492753623188406, 1.5072463768115942, 1.565217391304348, 1.6231884057971016, 1.681159420289855, 1.7391304347826086, 1.7971014492753623, 1.855072463768116, 1.9130434782608696, 1.9710144927536233, 2.028985507246377, 2.0869565217391304, 2.1449275362318843, 2.2028985507246377, 2.260869565217391, 2.318840579710145, 2.3768115942028984, 2.4347826086956523, 2.4927536231884058, 2.5507246376811596, 2.608695652173913, 2.6666666666666665, 2.7246376811594204, 2.782608695652174, 2.8405797101449277, 2.898550724637681, 2.956521739130435, 3.0144927536231885, 3.072463768115942, 3.130434782608696, 3.1884057971014492, 3.246376811594203, 3.3043478260869565, 3.36231884057971, 3.420289855072464, 3.4782608695652173, 3.536231884057971, 3.5942028985507246, 3.6521739130434785, 3.710144927536232, 3.7681159420289854, 3.8260869565217392, 3.8840579710144927, 3.9420289855072466, 4.0], "x": [1.196804320083257, 1.1277437324376123, 1.0626681998537597, 1.001347791780628, 0.9435658322266048, 0.8891180988511288, 0.8378122641644672, 0.7894670409491606, 0.7439114741285795, 0.7009846720204239, 0.6605349266317223, 0.6224192979802666, 0.5865031011027212, 0.552659419484152, 0.5207686594366996, 0.4907181331268701, 0.462401654872568, 0.4357191409980887, 0.4105763102853538, 0.3868843356597521, 0.3645594839706743, 0.34352287601999676, 0.32370016795982753, 0.3050213135141503, 0.2874203056471946, 0.27083495091001375, 0.2552066401676603, 0.24048014886502206, 0.22660343703499022, 0.21352746984898346, 0.20120603835651796, 0.1895956055503018, 0.1786551449349789, 0.16834599343282858, 0.1586317248217242, 0.1494780087757579, 0.1408525010044394, 0.13272472146279965, 0.12506594787862224, 0.117849119098315, 0.11104873050214725, 0.10464075341602268, 0.0986025433559815, 0.09291276274414186, 0.0875513073390268, 0.0824992294872004, 0.077738678280937, 0.07325283012833585, 0.06902583325365821, 0.06504275352866502, 0.061289516341313084, 0.05775285799356981, 0.054420277714281116, 0.05128000106551815, 0.04832093219462503, 0.04553261240734888, 0.04290518995296268, 0.04042938117460253, 0.03809643660908906, 0.03589811292620933, 0.03382664206245367, 0.031874703314831235, 0.030035399397026916, 0.028302231014142424, 0.02666907377024879, 0.025130156733968456, 0.02368004182281626, 0.022313604413811396, 0.0210260161755275, 0.019812727233620556], "k": 1.025271421736372}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 2.08), (0.06, 1.98), (0.12, 1.88), (0.17, 1.79), (0.23, 1.70), (0.29, 1.62), (0.35, 1.54), (0.41, 1.46), (0.46, 1.39), (0.52, 1.32), (0.58, 1.26), (0.64, 1.19), (0.70, 1.14), (0.75, 1.08), (0.81, 1.03), (0.87, 0.98), (0.93, 0.93), (0.99, 0.88), (1.04, 0.84), (1.10, 0.80), (1.16, 0.76), (1.22, 0.72), (1.28, 0.69), (1.33, 0.65), (1.39, 0.62), (1.45, 0.59), (1.51, 0.56), (1.57, 0.53), (1.62, 0.51), (1.68, 0.48), (1.74, 0.46), (1.80, 0.44), (1.86, 0.41), (1.91, 0.39), (1.97, 0.37), (2.03, 0.36), (2.09, 0.34), (2.14, 0.32), (2.20, 0.31), (2.26, 0.29), (2.32, 0.28), (2.38, 0.26), (2.43, 0.25), (2.49, 0.24), (2.55, 0.23), (2.61, 0.22), (2.67, 0.20), (2.72, 0.19), (2.78, 0.19), (2.84, 0.18), (2.90, 0.17), (2.96, 0.16), (3.01, 0.15), (3.07, 0.14), (3.13, 0.14), (3.19, 0.13), (3.25, 0.12), (3.30, 0.12), (3.36, 0.11), (3.42, 0.11), (3.48, 0.10), (3.54, 0.10), (3.59, 0.09), (3.65, 0.09), (3.71, 0.08), (3.77, 0.08), (3.83, 0.07), (3.88, 0.07), (3.94, 0.07), (4.00, 0.06)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.057971014492753624, 0.11594202898550725, 0.17391304347826086, 0.2318840579710145, 0.2898550724637681, 0.34782608695652173, 0.4057971014492754, 0.463768115942029, 0.5217391304347826, 0.5797101449275363, 0.6376811594202899, 0.6956521739130435, 0.7536231884057971, 0.8115942028985508, 0.8695652173913043, 0.927536231884058, 0.9855072463768116, 1.0434782608695652, 1.1014492753623188, 1.1594202898550725, 1.2173913043478262, 1.2753623188405798, 1.3333333333333333, 1.391304347826087, 1.4492753623188406, 1.5072463768115942, 1.565217391304348, 1.6231884057971016, 1.681159420289855, 1.7391304347826086, 1.7971014492753623, 1.855072463768116, 1.9130434782608696, 1.9710144927536233, 2.028985507246377, 2.0869565217391304, 2.1449275362318843, 2.2028985507246377, 2.260869565217391, 2.318840579710145, 2.3768115942028984, 2.4347826086956523, 2.4927536231884058, 2.5507246376811596, 2.608695652173913, 2.6666666666666665, 2.7246376811594204, 2.782608695652174, 2.8405797101449277, 2.898550724637681, 2.956521739130435, 3.0144927536231885, 3.072463768115942, 3.130434782608696, 3.1884057971014492, 3.246376811594203, 3.3043478260869565, 3.36231884057971, 3.420289855072464, 3.4782608695652173, 3.536231884057971, 3.5942028985507246, 3.6521739130434785, 3.710144927536232, 3.7681159420289854, 3.8260869565217392, 3.8840579710144927, 3.9420289855072466, 4.0], "x": [2.080072216462231, 1.9778459018387855, 1.8806435220742608, 1.7882181945109998, 1.7003351727373572, 1.6167711950186738, 1.5373139944359493, 1.461761843190046, 1.3899227480334377, 1.321614168968333, 1.2566626803559018, 1.1949032676725724, 1.1361790542995218, 1.0803408772456624, 1.0272468995965445, 0.9767622559984148, 0.928758710091547, 0.8831143370240229, 0.8397131877013174, 0.7984449907670196, 0.7592049294217666, 0.7218933559349575, 0.686415493522406, 0.6526812079871411, 0.6206048076113139, 0.5901048226507957, 0.5611037789713355, 0.5335280084766154, 0.5073074648505368, 0.48237554502645785, 0.45866891830759293, 0.4361273679917299, 0.4146936352362309, 0.39431327586131837, 0.3749345207726613, 0.3565081458558731, 0.33898734385276247, 0.32232761097057133, 0.30648663299158874, 0.2914241676046879, 0.277101956044799, 0.2634836192062598, 0.25053456180268036, 0.2382218943765882, 0.2265143403579234, 0.21538215970817048, 0.20479707804512112, 0.19473220587460105, 0.18516197708591395, 0.17606208409783988, 0.16740940968812226, 0.15918197596858263, 0.15135888518406904, 0.14392026379952672, 0.13684721829847582, 0.13012178171634875, 0.12372686955937572, 0.11764623948930826, 0.1118644476641377, 0.10636680690092432, 0.10113935138187155, 0.0961687999916759, 0.09144252965033349, 0.08694853515126837, 0.08267539926324768, 0.0786122686737727, 0.07474882339740867, 0.07107524925932421, 0.06758221484438759, 0.06426084798835774], "k": 0.8693018322331005}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 1.69), (0.06, 1.60), (0.12, 1.51), (0.17, 1.43), (0.23, 1.35), (0.29, 1.28), (0.35, 1.21), (0.41, 1.14), (0.46, 1.08), (0.52, 1.02), (0.58, 0.96), (0.64, 0.91), (0.70, 0.86), (0.75, 0.82), (0.81, 0.77), (0.87, 0.73), (0.93, 0.69), (0.99, 0.65), (1.04, 0.62), (1.10, 0.58), (1.16, 0.55), (1.22, 0.52), (1.28, 0.49), (1.33, 0.47), (1.39, 0.44), (1.45, 0.42), (1.51, 0.39), (1.57, 0.37), (1.62, 0.35), (1.68, 0.33), (1.74, 0.31), (1.80, 0.30), (1.86, 0.28), (1.91, 0.27), (1.97, 0.25), (2.03, 0.24), (2.09, 0.22), (2.14, 0.21), (2.20, 0.20), (2.26, 0.19), (2.32, 0.18), (2.38, 0.17), (2.43, 0.16), (2.49, 0.15), (2.55, 0.14), (2.61, 0.14), (2.67, 0.13), (2.72, 0.12), (2.78, 0.11), (2.84, 0.11), (2.90, 0.10), (2.96, 0.10), (3.01, 0.09), (3.07, 0.09), (3.13, 0.08), (3.19, 0.08), (3.25, 0.07), (3.30, 0.07), (3.36, 0.07), (3.42, 0.06), (3.48, 0.06), (3.54, 0.06), (3.59, 0.05), (3.65, 0.05), (3.71, 0.05), (3.77, 0.04), (3.83, 0.04), (3.88, 0.04), (3.94, 0.04), (4.00, 0.04)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.057971014492753624, 0.11594202898550725, 0.17391304347826086, 0.2318840579710145, 0.2898550724637681, 0.34782608695652173, 0.4057971014492754, 0.463768115942029, 0.5217391304347826, 0.5797101449275363, 0.6376811594202899, 0.6956521739130435, 0.7536231884057971, 0.8115942028985508, 0.8695652173913043, 0.927536231884058, 0.9855072463768116, 1.0434782608695652, 1.1014492753623188, 1.1594202898550725, 1.2173913043478262, 1.2753623188405798, 1.3333333333333333, 1.391304347826087, 1.4492753623188406, 1.5072463768115942, 1.565217391304348, 1.6231884057971016, 1.681159420289855, 1.7391304347826086, 1.7971014492753623, 1.855072463768116, 1.9130434782608696, 1.9710144927536233, 2.028985507246377, 2.0869565217391304, 2.1449275362318843, 2.2028985507246377, 2.260869565217391, 2.318840579710145, 2.3768115942028984, 2.4347826086956523, 2.4927536231884058, 2.5507246376811596, 2.608695652173913, 2.6666666666666665, 2.7246376811594204, 2.782608695652174, 2.8405797101449277, 2.898550724637681, 2.956521739130435, 3.0144927536231885, 3.072463768115942, 3.130434782608696, 3.1884057971014492, 3.246376811594203, 3.3043478260869565, 3.36231884057971, 3.420289855072464, 3.4782608695652173, 3.536231884057971, 3.5942028985507246, 3.6521739130434785, 3.710144927536232, 3.7681159420289854, 3.8260869565217392, 3.8840579710144927, 3.9420289855072466, 4.0], "x": [1.6908925075345986, 1.598650135007292, 1.5114397781854407, 1.4289869555697854, 1.351032146613632, 1.2773299304878525, 1.2076483853929245, 1.1417682077680487, 1.0794818884103148, 1.0205934546185214, 0.9649175381013678, 0.9122788773292665, 0.8625117876171905, 0.8154596170700308, 0.7709742595031153, 0.72891569145041, 0.6891515355029223, 0.6515566026871036, 0.616012548635799, 0.5824075147904249, 0.5506357234236541, 0.520597162696723, 0.49219728761390685, 0.4653466953569725, 0.4399608704188997, 0.4159599036548072, 0.3932682516620892, 0.37181448522022226, 0.35153107610431694, 0.33235417671469336, 0.31422342556005417, 0.29708175029420536, 0.280875195429375, 0.26555275153070224, 0.25106618362273825, 0.23736989556309032, 0.22442077351358572, 0.21217805783225843, 0.2006032144292787, 0.1896598061867585, 0.1793133894651863, 0.16953139521736993, 0.16028303284247475, 0.15153919276868902, 0.14327234989747661, 0.13545648494033707, 0.12806699455144396, 0.1210806191156544, 0.11447536843641193, 0.1082304492675933, 0.10232620639135423, 0.09674405732709856, 0.09146643025986174, 0.08647671080634028, 0.08175919090904435, 0.07729902450484014, 0.07308217105557327, 0.06909535578228604, 0.06532603167980176, 0.061762333748107225, 0.058393044071722175, 0.05520755801374037, 0.05219584822292437, 0.04934843422639322, 0.046656353765882716, 0.044111133047148934, 0.04170476056940431, 0.03942966194428115, 0.0372786756767812, 0.035245030857200196], "k": 0.9676717988347026}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 1.25), (0.10, 1.24), (0.20, 1.23), (0.30, 1.21), (0.41, 1.20), (0.51, 1.19), (0.61, 1.18), (0.71, 1.16), (0.81, 1.15), (0.91, 1.14), (1.01, 1.13), (1.11, 1.12), (1.22, 1.11), (1.32, 1.09), (1.42, 1.08), (1.52, 1.07), (1.62, 1.06), (1.72, 1.05), (1.82, 1.04), (1.92, 1.03), (2.03, 1.02), (2.13, 1.01), (2.23, 1.00), (2.33, 0.98), (2.43, 0.97), (2.53, 0.96), (2.63, 0.95), (2.73, 0.94), (2.84, 0.93), (2.94, 0.92), (3.04, 0.92), (3.14, 0.91), (3.24, 0.90), (3.34, 0.89), (3.44, 0.88), (3.54, 0.87), (3.65, 0.86), (3.75, 0.85), (3.85, 0.84), (3.95, 0.83), (4.05, 0.82), (4.15, 0.82), (4.25, 0.81), (4.35, 0.80), (4.46, 0.79), (4.56, 0.78), (4.66, 0.77), (4.76, 0.77), (4.86, 0.76), (4.96, 0.75), (5.06, 0.74), (5.16, 0.73), (5.27, 0.73), (5.37, 0.72), (5.47, 0.71), (5.57, 0.70), (5.67, 0.70), (5.77, 0.69), (5.87, 0.68), (5.97, 0.67), (6.08, 0.67), (6.18, 0.66), (6.28, 0.65), (6.38, 0.65), (6.48, 0.64), (6.58, 0.63), (6.68, 0.63), (6.78, 0.62), (6.89, 0.61), (6.99, 0.61), (7.09, 0.60), (7.19, 0.60), (7.29, 0.59), (7.39, 0.58), (7.49, 0.58), (7.59, 0.57), (7.70, 0.56), (7.80, 0.56), (7.90, 0.55), (8.00, 0.55)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.10126582278481013, 0.20253164556962025, 0.3037974683544304, 0.4050632911392405, 0.5063291139240507, 0.6075949367088608, 0.7088607594936709, 0.810126582278481, 0.9113924050632911, 1.0126582278481013, 1.1139240506329113, 1.2151898734177216, 1.3164556962025316, 1.4177215189873418, 1.5189873417721518, 1.620253164556962, 1.7215189873417722, 1.8227848101265822, 1.9240506329113924, 2.0253164556962027, 2.1265822784810124, 2.2278481012658227, 2.329113924050633, 2.430379746835443, 2.5316455696202533, 2.632911392405063, 2.7341772151898733, 2.8354430379746836, 2.9367088607594938, 3.0379746835443036, 3.1392405063291138, 3.240506329113924, 3.3417721518987342, 3.4430379746835444, 3.5443037974683542, 3.6455696202531644, 3.7468354430379747, 3.848101265822785, 3.9493670886075947, 4.050632911392405, 4.151898734177215, 4.253164556962025, 4.3544303797468356, 4.455696202531645, 4.556962025316456, 4.658227848101266, 4.7594936708860756, 4.860759493670886, 4.962025316455696, 5.063291139240507, 5.1645569620253164, 5.265822784810126, 5.367088607594937, 5.468354430379747, 5.5696202531645564, 5.670886075949367, 5.772151898734177, 5.8734177215189876, 5.974683544303797, 6.075949367088607, 6.177215189873418, 6.2784810126582276, 6.379746835443038, 6.481012658227848, 6.582278481012658, 6.6835443037974684, 6.784810126582278, 6.886075949367089, 6.987341772151899, 7.0886075949367084, 7.189873417721519, 7.291139240506329, 7.3924050632911396, 7.493670886075949, 7.594936708860759, 7.69620253164557, 7.7974683544303796, 7.898734177215189, 8.0], "x": [1.253831322716117, 1.240737397462621, 1.2277802218406417, 1.2149584001688098, 1.202270442186787, 1.1897149853128823, 1.1772906482750851, 1.1649960580049679, 1.1528298613414771, 1.1407907170300522, 1.1288772979407116, 1.1170882918922738, 1.1054223973854744, 1.0938783322704908, 1.0824548259710811, 1.071150616537869, 1.0599644584585397, 1.048895118899267, 1.0379413775885786, 1.0271020278963607, 1.0163758745491887, 1.0057617356954658, 0.9952584417665564, 0.984864833606525, 0.9745797647781471, 0.9644021020251213, 0.954330724200655, 0.9443645221134329, 0.9345023983735866, 0.9247432672386631, 0.9150860544595941, 0.9055296970211809, 0.8960731408380886, 0.88671534321697, 0.8774552727873104, 0.8682919086543839, 0.8592242402294151, 0.8502512670597407, 0.8413719986589704, 0.8325854543371488, 0.8238906634400177, 0.8152866704909386, 0.8067725286675939, 0.7983473000300139, 0.7900100566480818, 0.7817598805176059, 0.7735958634763946, 0.7655171064419308, 0.7575227176728003, 0.749611815934483, 0.7417835292155739, 0.7340369944635151, 0.7263713574641337, 0.7187857727211812, 0.7112794044141799, 0.7038514260746335, 0.6965010190693004, 0.6892273733022469, 0.6820296871197561, 0.6749071672149787, 0.6678590285464642, 0.6608844944807555, 0.6539827964322421, 0.6471531737629044, 0.6403948737525043, 0.633707151507103, 0.6270892698675795, 0.6205404994112049, 0.6140601186483093, 0.6076474134112457, 0.6013016769397428, 0.5950222098242706, 0.5888083199203585, 0.5826593222629144, 0.5765745392609862, 0.570553300411456, 0.5645949422122887, 0.5586988079617606, 0.5528642477941239, 0.547090618597043], "k": 0.10366809791933604}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 0.80), (0.10, 0.75), (0.20, 0.70), (0.31, 0.66), (0.41, 0.62), (0.51, 0.58), (0.61, 0.54), (0.71, 0.51), (0.81, 0.48), (0.92, 0.45), (1.02, 0.42), (1.12, 0.39), (1.22, 0.37), (1.32, 0.35), (1.42, 0.32), (1.53, 0.30), (1.63, 0.29), (1.73, 0.27), (1.83, 0.25), (1.93, 0.24), (2.03, 0.22), (2.14, 0.21), (2.24, 0.19), (2.34, 0.18), (2.44, 0.17), (2.54, 0.16), (2.64, 0.15), (2.75, 0.14), (2.85, 0.13), (2.95, 0.12), (3.05, 0.12), (3.15, 0.11), (3.25, 0.10), (3.36, 0.10), (3.46, 0.09), (3.56, 0.08), (3.66, 0.08), (3.76, 0.07), (3.86, 0.07), (3.97, 0.07), (4.07, 0.06), (4.17, 0.06), (4.27, 0.05), (4.37, 0.05), (4.47, 0.05), (4.58, 0.04), (4.68, 0.04), (4.78, 0.04), (4.88, 0.04), (4.98, 0.03), (5.08, 0.03), (5.19, 0.03), (5.29, 0.03), (5.39, 0.03), (5.49, 0.02), (5.59, 0.02), (5.69, 0.02), (5.80, 0.02), (5.90, 0.02), (6.00, 0.02)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.1016949152542373, 0.2033898305084746, 0.3050847457627119, 0.4067796610169492, 0.5084745762711864, 0.6101694915254238, 0.7118644067796611, 0.8135593220338984, 0.9152542372881356, 1.0169491525423728, 1.1186440677966103, 1.2203389830508475, 1.3220338983050848, 1.4237288135593222, 1.5254237288135595, 1.6271186440677967, 1.728813559322034, 1.8305084745762712, 1.9322033898305087, 2.0338983050847457, 2.135593220338983, 2.2372881355932206, 2.3389830508474576, 2.440677966101695, 2.5423728813559325, 2.6440677966101696, 2.745762711864407, 2.8474576271186445, 2.9491525423728815, 3.050847457627119, 3.152542372881356, 3.2542372881355934, 3.355932203389831, 3.457627118644068, 3.5593220338983054, 3.6610169491525424, 3.76271186440678, 3.8644067796610173, 3.9661016949152543, 4.067796610169491, 4.169491525423729, 4.271186440677966, 4.372881355932203, 4.474576271186441, 4.576271186440678, 4.677966101694915, 4.779661016949153, 4.88135593220339, 4.983050847457627, 5.084745762711865, 5.186440677966102, 5.288135593220339, 5.389830508474577, 5.491525423728814, 5.593220338983051, 5.694915254237289, 5.796610169491526, 5.898305084745763, 6.0], "x": [0.7956086869233511, 0.7461742909934231, 0.6998114315828301, 0.6563292819983013, 0.615548858803152, 0.5773022567653693, 0.5414321135794978, 0.5077907679013274, 0.47623963575996037, 0.44664892588095556, 0.4188968045755121, 0.39286903442496934, 0.3684584764276114, 0.3455646463966081, 0.3240933034405073, 0.3039560670616654, 0.28507003903806516, 0.2673574653778158, 0.2507454477500127, 0.23516560438534595, 0.22055380278308742, 0.20684989323001504, 0.19399746369325213, 0.18194360720093686, 0.1706387069431072, 0.1600362261086107, 0.15009252104781035, 0.1407666585750579, 0.13202024962219727, 0.12381728852998827, 0.11612401328006564, 0.10890875216582561, 0.10214180490502975, 0.09579531643533187, 0.08984315995220458, 0.08426083685868758, 0.07902536517102433, 0.07411519544385167, 0.06951011473596234, 0.06519116598244529, 0.06114057216031424, 0.05734165732274146, 0.05377878542544851, 0.05043728895557101, 0.04730341330230083, 0.04436425830135212, 0.0416077238100612, 0.0390224649019237, 0.03659784099574193, 0.03432387047612173, 0.032191189961542244, 0.030191020584954296, 0.028315130696313723, 0.02655579637160265, 0.02490577586924337, 0.023358278299799907, 0.02190693290230868, 0.020545765676329236, 0.01926917373597626, 0.018071901297079536], "k": 0.63079152321013}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 0.86), (0.11, 0.79), (0.22, 0.72), (0.33, 0.66), (0.44, 0.61), (0.55, 0.56), (0.66, 0.51), (0.77, 0.47), (0.88, 0.43), (0.99, 0.39), (1.10, 0.36), (1.21, 0.33), (1.32, 0.30), (1.43, 0.28), (1.54, 0.25), (1.65, 0.23), (1.76, 0.21), (1.87, 0.19), (1.98, 0.18), (2.09, 0.16), (2.20, 0.15), (2.31, 0.14), (2.42, 0.12), (2.53, 0.11), (2.64, 0.10), (2.75, 0.10), (2.86, 0.09), (2.97, 0.08), (3.08, 0.07), (3.19, 0.07), (3.30, 0.06), (3.41, 0.06), (3.52, 0.05), (3.63, 0.05), (3.74, 0.04), (3.85, 0.04), (3.96, 0.04), (4.07, 0.03), (4.18, 0.03), (4.29, 0.03), (4.40, 0.03), (4.51, 0.02), (4.62, 0.02), (4.73, 0.02), (4.84, 0.02), (4.95, 0.02), (5.06, 0.02), (5.17, 0.01), (5.28, 0.01), (5.39, 0.01), (5.50, 0.01), (5.61, 0.01), (5.72, 0.01), (5.83, 0.01), (5.94, 0.01), (6.06, 0.01), (6.17, 0.01), (6.28, 0.01), (6.39, 0.01), (6.50, 0.00), (6.61, 0.00), (6.72, 0.00), (6.83, 0.00), (6.94, 0.00), (7.05, 0.00), (7.16, 0.00), (7.27, 0.00), (7.38, 0.00), (7.49, 0.00), (7.60, 0.00), (7.71, 0.00), (7.82, 0.00), (7.93, 0.00), (8.04, 0.00), (8.15, 0.00), (8.26, 0.00), (8.37, 0.00), (8.48, 0.00), (8.59, 0.00), (8.70, 0.00), (8.81, 0.00), (8.92, 0.00), (9.03, 0.00), (9.14, 0.00), (9.25, 0.00), (9.36, 0.00), (9.47, 0.00), (9.58, 0.00), (9.69, 0.00), (9.80, 0.00), (9.91, 0.00), (10.02, 0.00), (10.13, 0.00), (10.24, 0.00), (10.35, 0.00), (10.46, 0.00), (10.57, 0.00), (10.68, 0.00), (10.79, 0.00), (10.90, 0.00), (11.01, 0.00), (11.12, 0.00), (11.23, 0.00), (11.34, 0.00), (11.45, 0.00), (11.56, 0.00), (11.67, 0.00), (11.78, 0.00), (11.89, 0.00), (12.00, 0.00)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.11009174311926606, 0.22018348623853212, 0.3302752293577982, 0.44036697247706424, 0.5504587155963303, 0.6605504587155964, 0.7706422018348624, 0.8807339449541285, 0.9908256880733946, 1.1009174311926606, 1.2110091743119267, 1.3211009174311927, 1.4311926605504588, 1.5412844036697249, 1.651376146788991, 1.761467889908257, 1.871559633027523, 1.981651376146789, 2.091743119266055, 2.2018348623853212, 2.3119266055045875, 2.4220183486238533, 2.532110091743119, 2.6422018348623855, 2.7522935779816518, 2.8623853211009176, 2.9724770642201834, 3.0825688073394497, 3.192660550458716, 3.302752293577982, 3.4128440366972477, 3.522935779816514, 3.6330275229357802, 3.743119266055046, 3.853211009174312, 3.963302752293578, 4.0733944954128445, 4.18348623853211, 4.293577981651376, 4.4036697247706424, 4.513761467889909, 4.623853211009175, 4.73394495412844, 4.844036697247707, 4.954128440366973, 5.064220183486238, 5.174311926605505, 5.284403669724771, 5.394495412844037, 5.5045871559633035, 5.614678899082569, 5.724770642201835, 5.8348623853211015, 5.944954128440367, 6.055045871559633, 6.165137614678899, 6.275229357798166, 6.385321100917432, 6.495412844036697, 6.605504587155964, 6.71559633027523, 6.825688073394495, 6.935779816513762, 7.045871559633028, 7.155963302752294, 7.2660550458715605, 7.376146788990826, 7.486238532110092, 7.596330275229358, 7.706422018348624, 7.81651376146789, 7.926605504587156, 8.036697247706423, 8.146788990825689, 8.256880733944955, 8.36697247706422, 8.477064220183486, 8.587155963302752, 8.697247706422019, 8.807339449541285, 8.917431192660551, 9.027522935779817, 9.137614678899084, 9.24770642201835, 9.357798165137615, 9.46788990825688, 9.577981651376147, 9.688073394495413, 9.79816513761468, 9.908256880733946, 10.018348623853212, 10.128440366972477, 10.238532110091743, 10.34862385321101, 10.458715596330276, 10.568807339449542, 10.678899082568808, 10.788990825688074, 10.89908256880734, 11.009174311926607, 11.119266055045872, 11.229357798165138, 11.339449541284404, 11.44954128440367, 11.559633027522937, 11.669724770642203, 11.77981651376147, 11.889908256880734, 12.0], "x": [0.8641050778330363, 0.7912644899399652, 0.7245640383776969, 0.6634861715277496, 0.607556892306128, 0.5563423242905361, 0.5094448670307371, 0.4665007022253588, 0.4271765528920113, 0.3911672733607327, 0.35819343225509503, 0.3279991617113054, 0.30035013818196976, 0.2750318088258482, 0.2518477175713988, 0.23061795847145897, 0.21117778308742347, 0.19337633617615024, 0.17707548102167903, 0.1621487231424631, 0.14848023103680272, 0.1359639350417607, 0.12450271574919151, 0.11400763047759391, 0.10439724056967987, 0.09559696745000741, 0.08753852241606268, 0.0801593728779326, 0.07340225554049983, 0.06721473736151277, 0.06154880140480162, 0.05636048207754134, 0.05160951717431729, 0.0472590387662526, 0.04327528858976175, 0.03962735675963571, 0.03628693197089125, 0.033228089458861576, 0.030427095843881157, 0.027862212447057094, 0.025513539123798373, 0.023362849322143414, 0.02139345481255189, 0.019590071726458255, 0.017938706473127876, 0.01642654490058046, 0.015041852926642075, 0.013773884829757707, 0.012612801426206974, 0.011549592593788268, 0.010576008047238197, 0.00968449283971458, 0.00886812876054013, 0.008120581081114006, 0.007436048443391663, 0.006809219279436535, 0.006235229224686858, 0.0057096243414936415, 0.005228325824071194, 0.004787598837428813, 0.004384023413524645, 0.0040144677030728645, 0.003676064133505832, 0.0033661865757433343, 0.003082430533465785, 0.002822593937887911, 0.0025846605446047796, 0.0023667839835151833, 0.002167273663015234, 0.0019845814477983032, 0.0018172891897391416, 0.0016640989192639487, 0.0015238219400732157, 0.001395369616774983, 0.0012777450188053618, 0.0011700359355749123, 0.001071406423609229, 0.0009810908123191818, 0.0008983887786641795, 0.0008226580478700331, 0.000753311053361597, 0.0006898099641543826, 0.0006316615532431956, 0.0005784149480645687, 0.0005296568676068728, 0.00048500878594599843, 0.0004441244890352159, 0.0004066864009087922, 0.00037240412188094675, 0.00034101197040853473, 0.0003122659578463182, 0.00028594311844086436, 0.0002618393077544947, 0.00023976723151364929, 0.00021955576547768067, 0.000201048096295191, 0.0001841004570422347, 0.00016858150382237163, 0.00015437076893769181, 0.00014135789061882237, 0.0001294419959644767, 0.00011853054121062133, 0.000108538836237153, 9.938943864193089e-05, 9.101130187971239e-05, 8.333937912398008e-05, 7.631417922248825e-05, 6.988101284064221e-05, 6.399004414552959e-05, 5.8595832936569574e-05], "k": 0.7998976548006262}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 0.32), (0.10, 0.31), (0.20, 0.30), (0.30, 0.29), (0.41, 0.29), (0.51, 0.28), (0.61, 0.27), (0.71, 0.27), (0.81, 0.26), (0.91, 0.25), (1.01, 0.25), (1.11, 0.24), (1.22, 0.23), (1.32, 0.23), (1.42, 0.22), (1.52, 0.22), (1.62, 0.21), (1.72, 0.21), (1.82, 0.20), (1.92, 0.20), (2.03, 0.19), (2.13, 0.19), (2.23, 0.18), (2.33, 0.18), (2.43, 0.17), (2.53, 0.17), (2.63, 0.16), (2.73, 0.16), (2.84, 0.16), (2.94, 0.15), (3.04, 0.15), (3.14, 0.14), (3.24, 0.14), (3.34, 0.14), (3.44, 0.13), (3.54, 0.13), (3.65, 0.13), (3.75, 0.12), (3.85, 0.12), (3.95, 0.12), (4.05, 0.12), (4.15, 0.11), (4.25, 0.11), (4.35, 0.11), (4.46, 0.10), (4.56, 0.10), (4.66, 0.10), (4.76, 0.10), (4.86, 0.09), (4.96, 0.09), (5.06, 0.09), (5.16, 0.09), (5.27, 0.09), (5.37, 0.08), (5.47, 0.08), (5.57, 0.08), (5.67, 0.08), (5.77, 0.08), (5.87, 0.07), (5.97, 0.07), (6.08, 0.07), (6.18, 0.07), (6.28, 0.07), (6.38, 0.06), (6.48, 0.06), (6.58, 0.06), (6.68, 0.06), (6.78, 0.06), (6.89, 0.06), (6.99, 0.06), (7.09, 0.05), (7.19, 0.05), (7.29, 0.05), (7.39, 0.05), (7.49, 0.05), (7.59, 0.05), (7.70, 0.05), (7.80, 0.05), (7.90, 0.04), (8.00, 0.04)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.10126582278481013, 0.20253164556962025, 0.3037974683544304, 0.4050632911392405, 0.5063291139240507, 0.6075949367088608, 0.7088607594936709, 0.810126582278481, 0.9113924050632911, 1.0126582278481013, 1.1139240506329113, 1.2151898734177216, 1.3164556962025316, 1.4177215189873418, 1.5189873417721518, 1.620253164556962, 1.7215189873417722, 1.8227848101265822, 1.9240506329113924, 2.0253164556962027, 2.1265822784810124, 2.2278481012658227, 2.329113924050633, 2.430379746835443, 2.5316455696202533, 2.632911392405063, 2.7341772151898733, 2.8354430379746836, 2.9367088607594938, 3.0379746835443036, 3.1392405063291138, 3.240506329113924, 3.3417721518987342, 3.4430379746835444, 3.5443037974683542, 3.6455696202531644, 3.7468354430379747, 3.848101265822785, 3.9493670886075947, 4.050632911392405, 4.151898734177215, 4.253164556962025, 4.3544303797468356, 4.455696202531645, 4.556962025316456, 4.658227848101266, 4.7594936708860756, 4.860759493670886, 4.962025316455696, 5.063291139240507, 5.1645569620253164, 5.265822784810126, 5.367088607594937, 5.468354430379747, 5.5696202531645564, 5.670886075949367, 5.772151898734177, 5.8734177215189876, 5.974683544303797, 6.075949367088607, 6.177215189873418, 6.2784810126582276, 6.379746835443038, 6.481012658227848, 6.582278481012658, 6.6835443037974684, 6.784810126582278, 6.886075949367089, 6.987341772151899, 7.0886075949367084, 7.189873417721519, 7.291139240506329, 7.3924050632911396, 7.493670886075949, 7.594936708860759, 7.69620253164557, 7.7974683544303796, 7.898734177215189, 8.0], "x": [0.31694596479391246, 0.30904198407956057, 0.3013351529570996, 0.2938204890304276, 0.2864932245128705, 0.2793486845378969, 0.2723823125943319, 0.265589665136613, 0.2589664158330718, 0.25250833653987914, 0.24621130796377994, 0.24007131426316142, 0.23408443883565486, 0.2282468596981854, 0.22255485375097012, 0.2170047944155659, 0.21159314720022726, 0.20631646201203424, 0.20117137189468887, 0.19615459222323464, 0.19126291579562657, 0.18649321878962885, 0.1818424656005623, 0.17730769259382953, 0.17288601057942451, 0.16857459766195582, 0.16437070293035985, 0.1602716431723413, 0.15627480490122234, 0.15237763950375455, 0.1485776610763871, 0.14487244606477676, 0.14125963156006782, 0.13773691306682775, 0.13430204357029635, 0.130952832759258, 0.12768714432320927, 0.12450289500601053, 0.12139805424820063, 0.11837064186636931, 0.11541872661445393, 0.11254042639643605, 0.10973390584684867, 0.10699737472038677, 0.10432908703704633, 0.10172733990480334, 0.09919047320258981, 0.09671686964674621, 0.09430495159014582, 0.09195318107466229, 0.0896600590908856, 0.08742412457321862, 0.08524394987986181, 0.08311814370859671, 0.08104535032108734, 0.07902424803788595, 0.07705354849585488, 0.0751319948910913, 0.073258360716729, 0.0714314509242668, 0.06965010032574276, 0.06791317287313897, 0.06621956090237612, 0.06456818395311083, 0.06295798869373151, 0.061387948181866735, 0.0598570611668253, 0.058364351483029854, 0.056908867034168746, 0.055489679254470736, 0.054105882980195294, 0.052756595647756754, 0.051440956747687734, 0.05015812723558694, 0.048907288748473485, 0.047687643461161174, 0.04649841349872678, 0.04533884043275006, 0.04420818481413912, 0.04310572529448932], "k": 0.24938442868772764}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 2.02), (0.10, 1.92), (0.20, 1.83), (0.30, 1.74), (0.40, 1.66), (0.51, 1.58), (0.61, 1.50), (0.71, 1.43), (0.81, 1.36), (0.91, 1.29), (1.01, 1.23), (1.11, 1.17), (1.21, 1.12), (1.31, 1.06), (1.42, 1.01), (1.52, 0.96), (1.62, 0.91), (1.72, 0.87), (1.82, 0.83), (1.92, 0.79), (2.02, 0.75), (2.12, 0.71), (2.22, 0.68), (2.33, 0.65), (2.43, 0.62), (2.53, 0.59), (2.63, 0.56), (2.73, 0.53), (2.83, 0.51), (2.93, 0.48), (3.03, 0.46), (3.13, 0.44), (3.24, 0.41), (3.34, 0.39), (3.44, 0.38), (3.54, 0.36), (3.64, 0.34), (3.74, 0.32), (3.84, 0.31), (3.94, 0.29), (4.04, 0.28), (4.15, 0.27), (4.25, 0.25), (4.35, 0.24), (4.45, 0.23), (4.55, 0.22), (4.65, 0.21), (4.75, 0.20), (4.85, 0.19), (4.96, 0.18), (5.06, 0.17), (5.16, 0.16), (5.26, 0.15), (5.36, 0.15), (5.46, 0.14), (5.56, 0.13), (5.66, 0.13), (5.76, 0.12), (5.87, 0.11), (5.97, 0.11), (6.07, 0.10), (6.17, 0.10), (6.27, 0.09), (6.37, 0.09), (6.47, 0.09), (6.57, 0.08), (6.67, 0.08), (6.78, 0.07), (6.88, 0.07), (6.98, 0.07), (7.08, 0.06), (7.18, 0.06), (7.28, 0.06), (7.38, 0.05), (7.48, 0.05), (7.58, 0.05), (7.69, 0.05), (7.79, 0.04), (7.89, 0.04), (7.99, 0.04), (8.09, 0.04), (8.19, 0.04), (8.29, 0.03), (8.39, 0.03), (8.49, 0.03), (8.60, 0.03), (8.70, 0.03), (8.80, 0.03), (8.90, 0.03), (9.00, 0.02)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.10112359550561797, 0.20224719101123595, 0.3033707865168539, 0.4044943820224719, 0.5056179775280899, 0.6067415730337078, 0.7078651685393258, 0.8089887640449438, 0.9101123595505618, 1.0112359550561798, 1.1123595505617978, 1.2134831460674156, 1.3146067415730336, 1.4157303370786516, 1.5168539325842696, 1.6179775280898876, 1.7191011235955056, 1.8202247191011236, 1.9213483146067416, 2.0224719101123596, 2.1235955056179776, 2.2247191011235956, 2.3258426966292136, 2.426966292134831, 2.528089887640449, 2.629213483146067, 2.730337078651685, 2.831460674157303, 2.932584269662921, 3.033707865168539, 3.134831460674157, 3.235955056179775, 3.337078651685393, 3.438202247191011, 3.539325842696629, 3.640449438202247, 3.741573033707865, 3.842696629213483, 3.943820224719101, 4.044943820224719, 4.146067415730337, 4.247191011235955, 4.348314606741573, 4.449438202247191, 4.550561797752809, 4.651685393258427, 4.752808988764045, 4.853932584269662, 4.955056179775281, 5.056179775280898, 5.157303370786517, 5.258426966292134, 5.359550561797753, 5.46067415730337, 5.561797752808989, 5.662921348314606, 5.764044943820225, 5.865168539325842, 5.966292134831461, 6.067415730337078, 6.168539325842697, 6.269662921348314, 6.370786516853933, 6.47191011235955, 6.573033707865168, 6.674157303370786, 6.775280898876404, 6.876404494382022, 6.97752808988764, 7.078651685393258, 7.179775280898876, 7.280898876404494, 7.382022471910112, 7.48314606741573, 7.584269662921348, 7.685393258426966, 7.786516853932584, 7.887640449438202, 7.98876404494382, 8.089887640449438, 8.191011235955056, 8.292134831460674, 8.393258426966291, 8.49438202247191, 8.595505617977528, 8.696629213483146, 8.797752808988763, 8.898876404494382, 9.0], "x": [2.0189480277078977, 1.9215030809562719, 1.828761301676991, 1.7404957102176306, 1.6564902869444673, 1.5765393914120966, 1.500447313406284, 1.428027907030686, 1.3591038634941586, 1.2935063884444762, 1.231075008850171, 1.1716568989577074, 1.1151066127482585, 1.0612857392584891, 1.0100625423815828, 0.9613116450569064, 0.9149137209839631, 0.8707552084878916, 0.8287280278307183, 0.7887292841230636, 0.750661071419599, 0.7144302283342487, 0.679948093346114, 0.64713024854212, 0.6158963580188053, 0.5861699761602357, 0.5578783486685701, 0.5309522232388417, 0.5053256932768093, 0.48093603329821294, 0.45772354576942775, 0.4356314137880129, 0.4146055642538596, 0.39459453193029115, 0.37554933681877745, 0.3574233620684633, 0.340172241380834, 0.32375374781929805, 0.3081276968850952, 0.29325584276571615, 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0.027290510782364507, 0.025973328272425916, 0.024719719982601928], "k": 0.4891922935314488}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 0.49), (0.10, 0.47), (0.20, 0.44), (0.30, 0.42), (0.40, 0.40), (0.51, 0.38), (0.61, 0.36), (0.71, 0.34), (0.81, 0.32), (0.91, 0.31), (1.01, 0.29), (1.11, 0.27), (1.21, 0.26), (1.31, 0.25), (1.42, 0.23), (1.52, 0.22), (1.62, 0.21), (1.72, 0.20), (1.82, 0.19), (1.92, 0.18), (2.02, 0.17), (2.12, 0.16), (2.22, 0.15), (2.33, 0.15), (2.43, 0.14), (2.53, 0.13), (2.63, 0.12), (2.73, 0.12), (2.83, 0.11), (2.93, 0.11), (3.03, 0.10), (3.13, 0.09), (3.24, 0.09), (3.34, 0.09), (3.44, 0.08), (3.54, 0.08), (3.64, 0.07), (3.74, 0.07), (3.84, 0.07), (3.94, 0.06), (4.04, 0.06), (4.15, 0.06), (4.25, 0.05), (4.35, 0.05), (4.45, 0.05), (4.55, 0.05), (4.65, 0.04), (4.75, 0.04), (4.85, 0.04), (4.96, 0.04), (5.06, 0.03), (5.16, 0.03), (5.26, 0.03), (5.36, 0.03), (5.46, 0.03), (5.56, 0.03), (5.66, 0.03), (5.76, 0.02), (5.87, 0.02), (5.97, 0.02), (6.07, 0.02), (6.17, 0.02), (6.27, 0.02), (6.37, 0.02), (6.47, 0.02), (6.57, 0.02), (6.67, 0.01), (6.78, 0.01), (6.88, 0.01), (6.98, 0.01), (7.08, 0.01), (7.18, 0.01), (7.28, 0.01), (7.38, 0.01), (7.48, 0.01), (7.58, 0.01), (7.69, 0.01), (7.79, 0.01), (7.89, 0.01), (7.99, 0.01), (8.09, 0.01), (8.19, 0.01), (8.29, 0.01), (8.39, 0.01), (8.49, 0.01), (8.60, 0.01), (8.70, 0.01), (8.80, 0.00), (8.90, 0.00), (9.00, 0.00)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.10112359550561797, 0.20224719101123595, 0.3033707865168539, 0.4044943820224719, 0.5056179775280899, 0.6067415730337078, 0.7078651685393258, 0.8089887640449438, 0.9101123595505618, 1.0112359550561798, 1.1123595505617978, 1.2134831460674156, 1.3146067415730336, 1.4157303370786516, 1.5168539325842696, 1.6179775280898876, 1.7191011235955056, 1.8202247191011236, 1.9213483146067416, 2.0224719101123596, 2.1235955056179776, 2.2247191011235956, 2.3258426966292136, 2.426966292134831, 2.528089887640449, 2.629213483146067, 2.730337078651685, 2.831460674157303, 2.932584269662921, 3.033707865168539, 3.134831460674157, 3.235955056179775, 3.337078651685393, 3.438202247191011, 3.539325842696629, 3.640449438202247, 3.741573033707865, 3.842696629213483, 3.943820224719101, 4.044943820224719, 4.146067415730337, 4.247191011235955, 4.348314606741573, 4.449438202247191, 4.550561797752809, 4.651685393258427, 4.752808988764045, 4.853932584269662, 4.955056179775281, 5.056179775280898, 5.157303370786517, 5.258426966292134, 5.359550561797753, 5.46067415730337, 5.561797752808989, 5.662921348314606, 5.764044943820225, 5.865168539325842, 5.966292134831461, 6.067415730337078, 6.168539325842697, 6.269662921348314, 6.370786516853933, 6.47191011235955, 6.573033707865168, 6.674157303370786, 6.775280898876404, 6.876404494382022, 6.97752808988764, 7.078651685393258, 7.179775280898876, 7.280898876404494, 7.382022471910112, 7.48314606741573, 7.584269662921348, 7.685393258426966, 7.786516853932584, 7.887640449438202, 7.98876404494382, 8.089887640449438, 8.191011235955056, 8.292134831460674, 8.393258426966291, 8.49438202247191, 8.595505617977528, 8.696629213483146, 8.797752808988763, 8.898876404494382, 9.0], "x": [0.493173501971457, 0.46762598312072184, 0.4434018718524472, 0.4204326149818433, 0.3986532251813287, 0.37800205832066025, 0.3584206536636006, 0.33985360083322363, 0.32224840796378096, 0.30555523158521875, 0.28972675524539554, 0.27471822353426817, 0.26048718648700364, 0.24699334463920647, 0.2341985141088145, 0.2220664861041258, 0.2105629252952664, 0.19965527602108232, 0.1893126682782637, 0.17950583205439213, 0.1702070154777575, 0.161389896207205, 0.15302951944417778, 0.14510223051079832, 0.13758559555257596, 0.13045833935309195, 0.12370029357207629, 0.11729232991874297, 0.11121631388712272, 0.10545504917727799, 0.09999223170515292, 0.09481240096656715, 0.08990089753710385, 0.08524382142624976, 0.08082799254805252, 0.07664091368853936, 0.07267073379936644, 0.06890621824727375, 0.06533671529275757, 0.06195212005959073, 0.05874285434998646, 0.05569983752532279, 0.05281445538190965, 0.05007854213705453, 0.04748435674324661, 0.04502455580461202, 0.042692177642600505, 0.04048062304856309, 0.038383632110929856, 0.03639526960520926, 0.034509909483829516, 0.03272221551962829, 0.03102712768951081, 0.029419849740651496, 0.027895832818296246, 0.026450763037480108, 0.025080551388333712, 0.023781320223696237, 0.022549391592160115, 0.02138127943739925, 0.020273679066773197, 0.019223456113951168, 0.018227638068318463, 0.01728340601181853, 0.016388085966524885, 0.015539145497949375, 0.014734182547627952, 0.013970918379890307, 0.013247191976632012, 0.012560956348656206, 0.011910269554120228, 0.011293289836816526, 0.010708270969512707, 0.010153557729954769, 0.009627580106021223, 0.009128849124396559, 0.008655953337941079, 0.008207554616248823, 0.0077823839928006676, 0.0073792382773126075, 0.006996976569259247, 0.006634517035156773, 0.006290833779088693, 0.005964953970797249, 0.005655955531372521, 0.005362963972223931, 0.005085150008213162, 0.004821727342048742, 0.00457195058648885, 0.0043351128665255565], "k": 0.5260126029413166}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 2.23), (0.10, 2.18), (0.20, 2.13), (0.30, 2.08), (0.40, 2.03), (0.51, 1.98), (0.61, 1.94), (0.71, 1.89), (0.81, 1.85), (0.91, 1.81), (1.01, 1.77), (1.11, 1.73), (1.21, 1.69), (1.31, 1.65), (1.42, 1.61), (1.52, 1.57), (1.62, 1.54), (1.72, 1.50), (1.82, 1.47), (1.92, 1.44), (2.02, 1.40), (2.12, 1.37), (2.22, 1.34), (2.33, 1.31), (2.43, 1.28), (2.53, 1.25), (2.63, 1.22), (2.73, 1.19), (2.83, 1.17), (2.93, 1.14), (3.03, 1.11), (3.13, 1.09), (3.24, 1.06), (3.34, 1.04), (3.44, 1.01), (3.54, 0.99), (3.64, 0.97), (3.74, 0.95), (3.84, 0.93), (3.94, 0.90), (4.04, 0.88), (4.15, 0.86), (4.25, 0.84), (4.35, 0.82), (4.45, 0.81), (4.55, 0.79), (4.65, 0.77), (4.75, 0.75), (4.85, 0.73), (4.96, 0.72), (5.06, 0.70), (5.16, 0.68), (5.26, 0.67), (5.36, 0.65), (5.46, 0.64), (5.56, 0.62), (5.66, 0.61), (5.76, 0.60), (5.87, 0.58), (5.97, 0.57), (6.07, 0.56), (6.17, 0.54), (6.27, 0.53), (6.37, 0.52), (6.47, 0.51), (6.57, 0.50), (6.67, 0.48), (6.78, 0.47), (6.88, 0.46), (6.98, 0.45), (7.08, 0.44), (7.18, 0.43), (7.28, 0.42), (7.38, 0.41), (7.48, 0.40), (7.58, 0.39), (7.69, 0.38), (7.79, 0.38), (7.89, 0.37), (7.99, 0.36), (8.09, 0.35), (8.19, 0.34), (8.29, 0.33), (8.39, 0.33), (8.49, 0.32), (8.60, 0.31), (8.70, 0.30), (8.80, 0.30), (8.90, 0.29), (9.00, 0.28)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.10112359550561797, 0.20224719101123595, 0.3033707865168539, 0.4044943820224719, 0.5056179775280899, 0.6067415730337078, 0.7078651685393258, 0.8089887640449438, 0.9101123595505618, 1.0112359550561798, 1.1123595505617978, 1.2134831460674156, 1.3146067415730336, 1.4157303370786516, 1.5168539325842696, 1.6179775280898876, 1.7191011235955056, 1.8202247191011236, 1.9213483146067416, 2.0224719101123596, 2.1235955056179776, 2.2247191011235956, 2.3258426966292136, 2.426966292134831, 2.528089887640449, 2.629213483146067, 2.730337078651685, 2.831460674157303, 2.932584269662921, 3.033707865168539, 3.134831460674157, 3.235955056179775, 3.337078651685393, 3.438202247191011, 3.539325842696629, 3.640449438202247, 3.741573033707865, 3.842696629213483, 3.943820224719101, 4.044943820224719, 4.146067415730337, 4.247191011235955, 4.348314606741573, 4.449438202247191, 4.550561797752809, 4.651685393258427, 4.752808988764045, 4.853932584269662, 4.955056179775281, 5.056179775280898, 5.157303370786517, 5.258426966292134, 5.359550561797753, 5.46067415730337, 5.561797752808989, 5.662921348314606, 5.764044943820225, 5.865168539325842, 5.966292134831461, 6.067415730337078, 6.168539325842697, 6.269662921348314, 6.370786516853933, 6.47191011235955, 6.573033707865168, 6.674157303370786, 6.775280898876404, 6.876404494382022, 6.97752808988764, 7.078651685393258, 7.179775280898876, 7.280898876404494, 7.382022471910112, 7.48314606741573, 7.584269662921348, 7.685393258426966, 7.786516853932584, 7.887640449438202, 7.98876404494382, 8.089887640449438, 8.191011235955056, 8.292134831460674, 8.393258426966291, 8.49438202247191, 8.595505617977528, 8.696629213483146, 8.797752808988763, 8.898876404494382, 9.0], "x": [2.22776080721529, 2.1768260941341384, 2.1270559475482624, 2.078423706672833, 2.0309033694505514, 1.984469513524469, 1.939097305870704, 1.8947624768362117, 1.8514413033317256, 1.8091106098042387, 1.7677477462691533, 1.7273305736301499, 1.6878374783150945, 1.6492473504059797, 1.611539556119075, 1.5746939164028972, 1.538690709650716, 1.5035106488767422, 1.4691349119452204, 1.4355451246842534, 1.4027233295769153, 1.3706519675466244, 1.339313875995455, 1.3086922834958454, 1.278770810917131, 1.249533452358799, 1.2209645659022548, 1.1930488687658138, 1.165771426422797, 1.1391176451314322, 1.1130732669775467, 1.0876243582614098, 1.0627573036157927, 1.038458800949869, 1.0147158505088618, 0.9915157512662867, 0.9688460946215416, 0.9466947522641317, 0.9250498715086137, 0.9038998685726133, 0.8832334245502536, 0.8630394868451846, 0.8433072524511105, 0.8240261662923158, 0.8051859169285991, 0.7867764311109553, 0.7687878569981038, 0.7512105687424674, 0.734035161781846, 0.7172524456912269, 0.7008534415660113, 0.6848293771922309, 0.6691716804878068, 0.6538719762650337, 0.6389220807512703, 0.6243139944875503, 0.610039902363841, 0.5960921680241618, 0.582463329676272, 0.5691460961458626, 0.556133342976919, 0.5434181086679221, 0.530993591010083, 0.5188531430587592, 0.5069902697692732, 0.4953986248526058, 0.48407200729632854, 0.4730043577813998, 0.4621897549849186, 0.4516224133263183, 0.44129667959231605, 0.4312070298841431, 0.4213480662553261, 0.41171451432981065, 0.40230122045083033, 0.39310314891354586, 0.38411537857406036, 0.37533310084515287, 0.3667516174386866, 0.3583663376866831, 0.35017277617845194, 0.34216655040451627, 0.3343433764028775, 0.32669906824533557, 0.31922953641157886, 0.3119307850434007, 0.3047989098854959, 0.2978300962218964, 0.2910206151666344, 0.2843668232434483], "k": 0.2287207983466507}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 1.65), (0.10, 1.60), (0.20, 1.55), (0.31, 1.50), (0.41, 1.45), (0.51, 1.40), (0.61, 1.36), (0.71, 1.32), (0.81, 1.27), (0.92, 1.23), (1.02, 1.20), (1.12, 1.16), (1.22, 1.12), (1.32, 1.08), (1.42, 1.05), (1.53, 1.02), (1.63, 0.98), (1.73, 0.95), (1.83, 0.92), (1.93, 0.89), (2.03, 0.87), (2.14, 0.84), (2.24, 0.81), (2.34, 0.79), (2.44, 0.76), (2.54, 0.74), (2.64, 0.71), (2.75, 0.69), (2.85, 0.67), (2.95, 0.65), (3.05, 0.63), (3.15, 0.61), (3.25, 0.59), (3.36, 0.57), (3.46, 0.55), (3.56, 0.53), (3.66, 0.52), (3.76, 0.50), (3.86, 0.48), (3.97, 0.47), (4.07, 0.45), (4.17, 0.44), (4.27, 0.43), (4.37, 0.41), (4.47, 0.40), (4.58, 0.39), (4.68, 0.37), (4.78, 0.36), (4.88, 0.35), (4.98, 0.34), (5.08, 0.33), (5.19, 0.32), (5.29, 0.31), (5.39, 0.30), (5.49, 0.29), (5.59, 0.28), (5.69, 0.27), (5.80, 0.26), (5.90, 0.25), (6.00, 0.25)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.1016949152542373, 0.2033898305084746, 0.3050847457627119, 0.4067796610169492, 0.5084745762711864, 0.6101694915254238, 0.7118644067796611, 0.8135593220338984, 0.9152542372881356, 1.0169491525423728, 1.1186440677966103, 1.2203389830508475, 1.3220338983050848, 1.4237288135593222, 1.5254237288135595, 1.6271186440677967, 1.728813559322034, 1.8305084745762712, 1.9322033898305087, 2.0338983050847457, 2.135593220338983, 2.2372881355932206, 2.3389830508474576, 2.440677966101695, 2.5423728813559325, 2.6440677966101696, 2.745762711864407, 2.8474576271186445, 2.9491525423728815, 3.050847457627119, 3.152542372881356, 3.2542372881355934, 3.355932203389831, 3.457627118644068, 3.5593220338983054, 3.6610169491525424, 3.76271186440678, 3.8644067796610173, 3.9661016949152543, 4.067796610169491, 4.169491525423729, 4.271186440677966, 4.372881355932203, 4.474576271186441, 4.576271186440678, 4.677966101694915, 4.779661016949153, 4.88135593220339, 4.983050847457627, 5.084745762711865, 5.186440677966102, 5.288135593220339, 5.389830508474577, 5.491525423728814, 5.593220338983051, 5.694915254237289, 5.796610169491526, 5.898305084745763, 6.0], "x": [1.6504238560846978, 1.597994200843684, 1.5472300757137842, 1.4980785895438844, 1.4504885078830547, 1.4044102478397078, 1.359795775173133, 1.3165985879992785, 1.274773648003133, 1.2342773651410341, 1.1950675663817019, 1.157103392385523, 1.120345254887483, 1.0847547957270138, 1.0502949358361606, 1.0169297854389259, 0.9846245686033562, 0.9533456021417352, 0.923060284856255, 0.8937370533963789, 0.8653453452813135, 0.8378555682177403, 0.8112390700335652, 0.7854681092716077, 0.7605158245919815, 0.7363562097559766, 0.7129640843146919, 0.6903150712384887, 0.6683855612198021, 0.6471526896369312, 0.6265943235198915, 0.6066890382135569, 0.5874160900205234, 0.5687554001714007, 0.5506875131502568, 0.5331935934875501, 0.5162554104171225, 0.49985531439776765, 0.4839762072874902, 0.4686015375795448, 0.45371528124284854, 0.4393019232603841, 0.42534643938476835, 0.411834284382313, 0.3987513761334393, 0.38608407876050427, 0.37381918816676446, 0.361943921122254, 0.3504459010148205, 0.33931314319388783, 0.32853404373789313, 0.3180973681863194, 0.3079922393627109, 0.2982081235759636, 0.2887348227455068, 0.27956246374425503, 0.27068148819129756, 0.2620826389513588, 0.2537569522089867, 0.24569575048346237], "k": 0.31744889626073525}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 1.38), (0.11, 1.15), (0.22, 0.96), (0.33, 0.80), (0.44, 0.67), (0.55, 0.56), (0.66, 0.47), (0.77, 0.39), (0.88, 0.33), (0.99, 0.27), (1.10, 0.23), (1.21, 0.19), (1.32, 0.16), (1.43, 0.13), (1.54, 0.11), (1.65, 0.09), (1.76, 0.08), (1.87, 0.06), (1.98, 0.05), (2.09, 0.05), (2.20, 0.04), (2.31, 0.03), (2.42, 0.03), (2.53, 0.02), (2.64, 0.02), (2.75, 0.02), (2.86, 0.01), (2.97, 0.01), (3.08, 0.01), (3.19, 0.01), (3.30, 0.01), (3.41, 0.01), (3.52, 0.00), (3.63, 0.00), (3.74, 0.00), (3.85, 0.00), (3.96, 0.00), (4.07, 0.00), (4.18, 0.00), (4.29, 0.00), (4.40, 0.00), (4.51, 0.00), (4.62, 0.00), (4.73, 0.00), (4.84, 0.00), (4.95, 0.00), (5.06, 0.00), (5.17, 0.00), (5.28, 0.00), (5.39, 0.00), (5.50, 0.00), (5.61, 0.00), (5.72, 0.00), (5.83, 0.00), (5.94, 0.00), (6.06, 0.00), (6.17, 0.00), (6.28, 0.00), (6.39, 0.00), (6.50, 0.00), (6.61, 0.00), (6.72, 0.00), (6.83, 0.00), (6.94, 0.00), (7.05, 0.00), (7.16, 0.00), (7.27, 0.00), (7.38, 0.00), (7.49, 0.00), (7.60, 0.00), (7.71, 0.00), (7.82, 0.00), (7.93, 0.00), (8.04, 0.00), (8.15, 0.00), (8.26, 0.00), (8.37, 0.00), (8.48, 0.00), (8.59, 0.00), (8.70, 0.00), (8.81, 0.00), (8.92, 0.00), (9.03, 0.00), (9.14, 0.00), (9.25, 0.00), (9.36, 0.00), (9.47, 0.00), (9.58, 0.00), (9.69, 0.00), (9.80, 0.00), (9.91, 0.00), (10.02, 0.00), (10.13, 0.00), (10.24, 0.00), (10.35, 0.00), (10.46, 0.00), (10.57, 0.00), (10.68, 0.00), (10.79, 0.00), (10.90, 0.00), (11.01, 0.00), (11.12, 0.00), (11.23, 0.00), (11.34, 0.00), (11.45, 0.00), (11.56, 0.00), (11.67, 0.00), (11.78, 0.00), (11.89, 0.00), (12.00, 0.00)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.11009174311926606, 0.22018348623853212, 0.3302752293577982, 0.44036697247706424, 0.5504587155963303, 0.6605504587155964, 0.7706422018348624, 0.8807339449541285, 0.9908256880733946, 1.1009174311926606, 1.2110091743119267, 1.3211009174311927, 1.4311926605504588, 1.5412844036697249, 1.651376146788991, 1.761467889908257, 1.871559633027523, 1.981651376146789, 2.091743119266055, 2.2018348623853212, 2.3119266055045875, 2.4220183486238533, 2.532110091743119, 2.6422018348623855, 2.7522935779816518, 2.8623853211009176, 2.9724770642201834, 3.0825688073394497, 3.192660550458716, 3.302752293577982, 3.4128440366972477, 3.522935779816514, 3.6330275229357802, 3.743119266055046, 3.853211009174312, 3.963302752293578, 4.0733944954128445, 4.18348623853211, 4.293577981651376, 4.4036697247706424, 4.513761467889909, 4.623853211009175, 4.73394495412844, 4.844036697247707, 4.954128440366973, 5.064220183486238, 5.174311926605505, 5.284403669724771, 5.394495412844037, 5.5045871559633035, 5.614678899082569, 5.724770642201835, 5.8348623853211015, 5.944954128440367, 6.055045871559633, 6.165137614678899, 6.275229357798166, 6.385321100917432, 6.495412844036697, 6.605504587155964, 6.71559633027523, 6.825688073394495, 6.935779816513762, 7.045871559633028, 7.155963302752294, 7.2660550458715605, 7.376146788990826, 7.486238532110092, 7.596330275229358, 7.706422018348624, 7.81651376146789, 7.926605504587156, 8.036697247706423, 8.146788990825689, 8.256880733944955, 8.36697247706422, 8.477064220183486, 8.587155963302752, 8.697247706422019, 8.807339449541285, 8.917431192660551, 9.027522935779817, 9.137614678899084, 9.24770642201835, 9.357798165137615, 9.46788990825688, 9.577981651376147, 9.688073394495413, 9.79816513761468, 9.908256880733946, 10.018348623853212, 10.128440366972477, 10.238532110091743, 10.34862385321101, 10.458715596330276, 10.568807339449542, 10.678899082568808, 10.788990825688074, 10.89908256880734, 11.009174311926607, 11.119266055045872, 11.229357798165138, 11.339449541284404, 11.44954128440367, 11.559633027522937, 11.669724770642203, 11.77981651376147, 11.889908256880734, 12.0], "x": [1.379878210935649, 1.1526104535944917, 0.9627739481962634, 0.8042038259066864, 0.6717503876956706, 0.5611122166797747, 0.4686962741756635, 0.39150136371247385, 0.3270205645031559, 0.2731598402374241, 0.22817004441774696, 0.19059013070685113, 0.15919967890540407, 0.1329792764348397, 0.11107740960040746, 0.09278281049052473, 0.0775013547159419, 0.06473678443565281, 0.05407455254312952, 0.04516840177171213, 0.037729106372878934, 0.031515072047301126, 0.02632449818640712, 0.021988818588564385, 0.018367231507029617, 0.0153421243974993, 0.012815256353089829, 0.010704566879300752, 0.008941510591726595, 0.007468832031092826, 0.006238705571532942, 0.005211182538452648, 0.004352893914200169, 0.0036359665745710826, 0.0030371180925569405, 0.002536900770336394, 0.0021190703596216556, 0.001770056598888911, 0.001478525516409715, 0.0012350098008105169, 0.0010316015986198525, 0.0008616951813749269, 0.0007197727144217126, 0.0006012250773661779, 0.0005022023841723997, 0.00041948855172648604, 0.00035039817920779696, 0.0002926871177392008, 0.00024448103827556393, 0.00020421459900533102, 0.00017058017903179659, 0.00014248537674633942, 0.00011901776940319257, 9.941537125201181e-05, 8.304145278519978e-05, 6.936392884672277e-05, 5.7939812398261614e-05, 4.839769205748703e-05, 4.0427083316688805e-05, 3.3769049530965505e-05, 2.8207244414013723e-05, 2.3561327217023544e-05, 1.9680891577726837e-05, 1.6439300837990356e-05, 1.3731848269558102e-05, 1.1470225416160845e-05, 9.581091469869836e-06, 8.00230007714193e-06, 6.683405485919247e-06, 5.5823848424246625e-06, 4.662763512756455e-06, 3.895069104862651e-06, 3.253630598979658e-06, 2.717846342501365e-06, 2.270154856132285e-06, 1.8960993998062362e-06, 1.5833187186393952e-06, 1.3228460856854157e-06, 1.1052911950599167e-06, 9.236448453859428e-07, 7.720071469457989e-07, 6.450787338018726e-07, 5.390614629103137e-07, 4.5031002896922286e-07, 3.754293279491049e-07, 3.14274630498049e-07, 2.626742527637676e-07, 2.1957343605267335e-07, 1.836495984569294e-07, 1.5367793653557895e-07, 1.2852827511826358e-07, 1.075671170165478e-07, 9.000732347939189e-08, 7.505976995984291e-08, 6.253096418094593e-08, 5.207952777829353e-08, 4.2434140547160453e-08, 3.577474478969007e-08, 2.9937933083953355e-08, 2.4918555704050894e-08, 2.0639884765922086e-08, 1.707629351898787e-08, 1.4225587253321915e-08, 1.1886332955141474e-08, 9.927201574181868e-09, 8.348193110443094e-09, 7.063835660681165e-09, 5.958039312643291e-09, 5.030147639780638e-09, 4.259531694076989e-09], "k": 1.6346905472990128}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 0.93), (0.10, 0.91), (0.20, 0.88), (0.30, 0.86), (0.41, 0.84), (0.51, 0.82), (0.61, 0.80), (0.71, 0.78), (0.81, 0.76), (0.91, 0.74), (1.01, 0.72), (1.11, 0.70), (1.22, 0.68), (1.32, 0.66), (1.42, 0.65), (1.52, 0.63), (1.62, 0.61), (1.72, 0.60), (1.82, 0.58), (1.92, 0.57), (2.03, 0.55), (2.13, 0.54), (2.23, 0.52), (2.33, 0.51), (2.43, 0.50), (2.53, 0.48), (2.63, 0.47), (2.73, 0.46), (2.84, 0.45), (2.94, 0.44), (3.04, 0.43), (3.14, 0.41), (3.24, 0.40), (3.34, 0.39), (3.44, 0.38), (3.54, 0.37), (3.65, 0.36), (3.75, 0.35), (3.85, 0.35), (3.95, 0.34), (4.05, 0.33), (4.15, 0.32), (4.25, 0.31), (4.35, 0.30), (4.46, 0.29), (4.56, 0.29), (4.66, 0.28), (4.76, 0.27), (4.86, 0.27), (4.96, 0.26), (5.06, 0.25), (5.16, 0.25), (5.27, 0.24), (5.37, 0.23), (5.47, 0.23), (5.57, 0.22), (5.67, 0.22), (5.77, 0.21), (5.87, 0.20), (5.97, 0.20), (6.08, 0.19), (6.18, 0.19), (6.28, 0.18), (6.38, 0.18), (6.48, 0.17), (6.58, 0.17), (6.68, 0.17), (6.78, 0.16), (6.89, 0.16), (6.99, 0.15), (7.09, 0.15), (7.19, 0.15), (7.29, 0.14), (7.39, 0.14), (7.49, 0.13), (7.59, 0.13), (7.70, 0.13), (7.80, 0.12), (7.90, 0.12), (8.00, 0.12)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.10126582278481013, 0.20253164556962025, 0.3037974683544304, 0.4050632911392405, 0.5063291139240507, 0.6075949367088608, 0.7088607594936709, 0.810126582278481, 0.9113924050632911, 1.0126582278481013, 1.1139240506329113, 1.2151898734177216, 1.3164556962025316, 1.4177215189873418, 1.5189873417721518, 1.620253164556962, 1.7215189873417722, 1.8227848101265822, 1.9240506329113924, 2.0253164556962027, 2.1265822784810124, 2.2278481012658227, 2.329113924050633, 2.430379746835443, 2.5316455696202533, 2.632911392405063, 2.7341772151898733, 2.8354430379746836, 2.9367088607594938, 3.0379746835443036, 3.1392405063291138, 3.240506329113924, 3.3417721518987342, 3.4430379746835444, 3.5443037974683542, 3.6455696202531644, 3.7468354430379747, 3.848101265822785, 3.9493670886075947, 4.050632911392405, 4.151898734177215, 4.253164556962025, 4.3544303797468356, 4.455696202531645, 4.556962025316456, 4.658227848101266, 4.7594936708860756, 4.860759493670886, 4.962025316455696, 5.063291139240507, 5.1645569620253164, 5.265822784810126, 5.367088607594937, 5.468354430379747, 5.5696202531645564, 5.670886075949367, 5.772151898734177, 5.8734177215189876, 5.974683544303797, 6.075949367088607, 6.177215189873418, 6.2784810126582276, 6.379746835443038, 6.481012658227848, 6.582278481012658, 6.6835443037974684, 6.784810126582278, 6.886075949367089, 6.987341772151899, 7.0886075949367084, 7.189873417721519, 7.291139240506329, 7.3924050632911396, 7.493670886075949, 7.594936708860759, 7.69620253164557, 7.7974683544303796, 7.898734177215189, 8.0], "x": [0.9320695320462442, 0.908012376648682, 0.8845761548509632, 0.8617448218612226, 0.8395027721547816, 0.8178347959497824, 0.7967260825009755, 0.776162197526247, 0.7561290763874389, 0.736613019460659, 0.717600677410727, 0.6990790422901602, 0.6810354564115552, 0.6634575949498988, 0.6463334427840335, 0.6296512856471344, 0.6133997062794808, 0.5975675706650008, 0.5821440569055185, 0.5671186291905566, 0.5524810227975547, 0.5382212245413175, 0.5243294790269767, 0.5107962826285628, 0.4976123845295147, 0.48476876909702116, 0.4722566535183759, 0.4600674821035659, 0.44819291881916556, 0.43662484381104, 0.4253553467570138, 0.41437672037843065, 0.4036814577441387, 0.39326224521338055, 0.38311195744984405, 0.3732236552447929, 0.3635905765351851, 0.3542061325843078, 0.3450639033965236, 0.336157636513899, 0.32748124266950396, 0.3190287890920552, 0.31079449758104705, 0.3027727404350618, 0.29495802896424406, 0.287345018027482, 0.2799285021086847, 0.2727034109064744, 0.26566480454136193, 0.2588078678719691, 0.25212791180016797, 0.24562036849113464, 0.23928078826071514, 0.23310483564638618, 0.22708828701316233, 0.22122702816127493, 0.21551705130075566, 0.20995445219266734, 0.20453542642854416, 0.19925626819780293, 0.1941133675155385, 0.18910320770827696, 0.18422236268966494, 0.17946749446727675, 0.1748353515325614, 0.1703227664199105, 0.16592665355152236, 0.16164400622650263, 0.15747189555156865, 0.15340746857899282, 0.14944794621836363, 0.14559062143443666, 0.14183285712675203, 0.13817208245979248, 0.1346057938137811, 0.13113155250401629, 0.12774698295730855, 0.12444977116532045, 0.12123766260130792, 0.1181084598260932], "k": 0.25822549874149925}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 1.64), (0.10, 1.54), (0.20, 1.45), (0.31, 1.36), (0.41, 1.28), (0.51, 1.20), (0.61, 1.13), (0.71, 1.06), (0.81, 0.99), (0.92, 0.93), (1.02, 0.88), (1.12, 0.82), (1.22, 0.77), (1.32, 0.73), (1.42, 0.68), (1.53, 0.64), (1.63, 0.60), (1.73, 0.57), (1.83, 0.53), (1.93, 0.50), (2.03, 0.47), (2.14, 0.44), (2.24, 0.41), (2.34, 0.39), (2.44, 0.37), (2.54, 0.34), (2.64, 0.32), (2.75, 0.30), (2.85, 0.28), (2.95, 0.27), (3.05, 0.25), (3.15, 0.24), (3.25, 0.22), (3.36, 0.21), (3.46, 0.20), (3.56, 0.18), (3.66, 0.17), (3.76, 0.16), (3.86, 0.15), (3.97, 0.14), (4.07, 0.13), (4.17, 0.13), (4.27, 0.12), (4.37, 0.11), (4.47, 0.10), (4.58, 0.10), (4.68, 0.09), (4.78, 0.09), (4.88, 0.08), (4.98, 0.08), (5.08, 0.07), (5.19, 0.07), (5.29, 0.06), (5.39, 0.06), (5.49, 0.06), (5.59, 0.05), (5.69, 0.05), (5.80, 0.05), (5.90, 0.04), (6.00, 0.04)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.1016949152542373, 0.2033898305084746, 0.3050847457627119, 0.4067796610169492, 0.5084745762711864, 0.6101694915254238, 0.7118644067796611, 0.8135593220338984, 0.9152542372881356, 1.0169491525423728, 1.1186440677966103, 1.2203389830508475, 1.3220338983050848, 1.4237288135593222, 1.5254237288135595, 1.6271186440677967, 1.728813559322034, 1.8305084745762712, 1.9322033898305087, 2.0338983050847457, 2.135593220338983, 2.2372881355932206, 2.3389830508474576, 2.440677966101695, 2.5423728813559325, 2.6440677966101696, 2.745762711864407, 2.8474576271186445, 2.9491525423728815, 3.050847457627119, 3.152542372881356, 3.2542372881355934, 3.355932203389831, 3.457627118644068, 3.5593220338983054, 3.6610169491525424, 3.76271186440678, 3.8644067796610173, 3.9661016949152543, 4.067796610169491, 4.169491525423729, 4.271186440677966, 4.372881355932203, 4.474576271186441, 4.576271186440678, 4.677966101694915, 4.779661016949153, 4.88135593220339, 4.983050847457627, 5.084745762711865, 5.186440677966102, 5.288135593220339, 5.389830508474577, 5.491525423728814, 5.593220338983051, 5.694915254237289, 5.796610169491526, 5.898305084745763, 6.0], "x": [1.63815041698907, 1.5389272979710873, 1.4457141029602214, 1.358146856276694, 1.2758835704170872, 1.1986029580896922, 1.1260033432471446, 1.0578010670189995, 0.9937297998771317, 0.9335393585356319, 0.8769946607079976, 0.8238748891011064, 0.773972594872508, 0.7270928940025225, 0.6830527161057036, 0.6416800656946298, 0.6028133422582157, 0.5663007818916518, 0.5319998033544817, 0.49977644368844054, 0.4695048668321245, 0.4410668459442142, 0.4143513215701194, 0.3892539629779123, 0.36567675794212595, 0.34352763001146114, 0.3227200794488356, 0.30317284737445843, 0.284809593497972, 0.26755860655234026, 0.2513525176659951, 0.23612803433736065, 0.22182570315875466, 0.208389665661441, 0.19576745398551382, 0.1839097713077167, 0.1727703123716289, 0.16230557266928577, 0.1524746848303551, 0.14323925651413585, 0.13456321958397227, 0.126412693357573, 0.11875584543098477, 0.11156277547910498, 0.10480539000160263, 0.09845730106799976, 0.09249372044798249, 0.08689135741914923, 0.08162832953098258, 0.07668408352985084, 0.07203931256675354, 0.06767587457803624, 0.06357673089265256, 0.05972587365237136, 0.0561082632970651, 0.05270977296039211, 0.04951712992094558, 0.046517865561694294, 0.04370026736011161, 0.04105333179814389], "k": 0.6144085075881976}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 2.04), (0.06, 1.98), (0.12, 1.93), (0.17, 1.87), (0.23, 1.82), (0.29, 1.76), (0.35, 1.71), (0.41, 1.66), (0.46, 1.62), (0.52, 1.57), (0.58, 1.52), (0.64, 1.48), (0.70, 1.44), (0.75, 1.39), (0.81, 1.35), (0.87, 1.32), (0.93, 1.28), (0.99, 1.24), (1.04, 1.20), (1.10, 1.17), (1.16, 1.14), (1.22, 1.10), (1.28, 1.07), (1.33, 1.04), (1.39, 1.01), (1.45, 0.98), (1.51, 0.95), (1.57, 0.92), (1.62, 0.90), (1.68, 0.87), (1.74, 0.85), (1.80, 0.82), (1.86, 0.80), (1.91, 0.77), (1.97, 0.75), (2.03, 0.73), (2.09, 0.71), (2.14, 0.69), (2.20, 0.67), (2.26, 0.65), (2.32, 0.63), (2.38, 0.61), (2.43, 0.59), (2.49, 0.58), (2.55, 0.56), (2.61, 0.54), (2.67, 0.53), (2.72, 0.51), (2.78, 0.50), (2.84, 0.48), (2.90, 0.47), (2.96, 0.46), (3.01, 0.44), (3.07, 0.43), (3.13, 0.42), (3.19, 0.41), (3.25, 0.39), (3.30, 0.38), (3.36, 0.37), (3.42, 0.36), (3.48, 0.35), (3.54, 0.34), (3.59, 0.33), (3.65, 0.32), (3.71, 0.31), (3.77, 0.30), (3.83, 0.29), (3.88, 0.29), (3.94, 0.28), (4.00, 0.27)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.057971014492753624, 0.11594202898550725, 0.17391304347826086, 0.2318840579710145, 0.2898550724637681, 0.34782608695652173, 0.4057971014492754, 0.463768115942029, 0.5217391304347826, 0.5797101449275363, 0.6376811594202899, 0.6956521739130435, 0.7536231884057971, 0.8115942028985508, 0.8695652173913043, 0.927536231884058, 0.9855072463768116, 1.0434782608695652, 1.1014492753623188, 1.1594202898550725, 1.2173913043478262, 1.2753623188405798, 1.3333333333333333, 1.391304347826087, 1.4492753623188406, 1.5072463768115942, 1.565217391304348, 1.6231884057971016, 1.681159420289855, 1.7391304347826086, 1.7971014492753623, 1.855072463768116, 1.9130434782608696, 1.9710144927536233, 2.028985507246377, 2.0869565217391304, 2.1449275362318843, 2.2028985507246377, 2.260869565217391, 2.318840579710145, 2.3768115942028984, 2.4347826086956523, 2.4927536231884058, 2.5507246376811596, 2.608695652173913, 2.6666666666666665, 2.7246376811594204, 2.782608695652174, 2.8405797101449277, 2.898550724637681, 2.956521739130435, 3.0144927536231885, 3.072463768115942, 3.130434782608696, 3.1884057971014492, 3.246376811594203, 3.3043478260869565, 3.36231884057971, 3.420289855072464, 3.4782608695652173, 3.536231884057971, 3.5942028985507246, 3.6521739130434785, 3.710144927536232, 3.7681159420289854, 3.8260869565217392, 3.8840579710144927, 3.9420289855072466, 4.0], "x": [2.0434483410392312, 1.984272574406885, 1.9268104399004318, 1.871012332274039, 1.8168300612974282, 1.7642168461926038, 1.7131272504053032, 1.6635171477609056, 1.6153436892173758, 1.5685652556296115, 1.5231414678703281, 1.479033128343551, 1.4362021402733316, 1.3946114926484927, 1.354225225097283, 1.315008480717867, 1.2769274143878078, 1.239949139623818, 1.2040417106057746, 1.1691741133501834, 1.1353162399209031, 1.102438849379033, 1.070513549265394, 1.0395127667427864, 1.0094097302085705, 0.9801784409972685, 0.9517936546167584, 0.9242308576884375, 0.8974662478659177, 0.8714767144222916, 0.8462398098347614, 0.8217337320916659, 0.7979373113155166, 0.774830000766052, 0.7523918456659551, 0.7306034737653512, 0.7094460763674691, 0.6889013749882178, 0.6689516244733722, 0.6495795926644932, 0.6307685491069241, 0.6125022491873428, 0.5947649196035045, 0.5775412438094096, 0.5608163450570802, 0.5445757792987366, 0.5288055207707453, 0.5134919498251675, 0.4986218412922345, 0.4841823532104231, 0.4701610153033275, 0.45654571816301504, 0.4433247035823754, 0.4304865540782726, 0.41802018187592765, 0.4059148206978109, 0.39416001631797964, 0.38274561691229125, 0.37166176459152783, 0.36089888729354486, 0.3504476899870516, 0.34029914596892025, 0.33044449076943905, 0.32087521425435106, 0.3115830535370444, 0.30255998338350903, 0.2937982098447539, 0.28529016616384945, 0.2770285051690985, 0.26900609302380385], "k": 0.5069149941772212}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 0.27), (0.10, 0.27), (0.20, 0.26), (0.30, 0.25), (0.41, 0.24), (0.51, 0.24), (0.61, 0.23), (0.71, 0.22), (0.81, 0.22), (0.91, 0.21), (1.01, 0.21), (1.11, 0.20), (1.22, 0.19), (1.32, 0.19), (1.42, 0.18), (1.52, 0.18), (1.62, 0.17), (1.72, 0.17), (1.82, 0.16), (1.92, 0.16), (2.03, 0.15), (2.13, 0.15), (2.23, 0.15), (2.33, 0.14), (2.43, 0.14), (2.53, 0.13), (2.63, 0.13), (2.73, 0.13), (2.84, 0.12), (2.94, 0.12), (3.04, 0.12), (3.14, 0.11), (3.24, 0.11), (3.34, 0.11), (3.44, 0.10), (3.54, 0.10), (3.65, 0.10), (3.75, 0.09), (3.85, 0.09), (3.95, 0.09), (4.05, 0.09), (4.15, 0.08), (4.25, 0.08), (4.35, 0.08), (4.46, 0.08), (4.56, 0.08), (4.66, 0.07), (4.76, 0.07), (4.86, 0.07), (4.96, 0.07), (5.06, 0.07), (5.16, 0.06), (5.27, 0.06), (5.37, 0.06), (5.47, 0.06), (5.57, 0.06), (5.67, 0.06), (5.77, 0.05), (5.87, 0.05), (5.97, 0.05), (6.08, 0.05), (6.18, 0.05), (6.28, 0.05), (6.38, 0.05), (6.48, 0.04), (6.58, 0.04), (6.68, 0.04), (6.78, 0.04), (6.89, 0.04), (6.99, 0.04), (7.09, 0.04), (7.19, 0.04), (7.29, 0.03), (7.39, 0.03), (7.49, 0.03), (7.59, 0.03), (7.70, 0.03), (7.80, 0.03), (7.90, 0.03), (8.00, 0.03)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.10126582278481013, 0.20253164556962025, 0.3037974683544304, 0.4050632911392405, 0.5063291139240507, 0.6075949367088608, 0.7088607594936709, 0.810126582278481, 0.9113924050632911, 1.0126582278481013, 1.1139240506329113, 1.2151898734177216, 1.3164556962025316, 1.4177215189873418, 1.5189873417721518, 1.620253164556962, 1.7215189873417722, 1.8227848101265822, 1.9240506329113924, 2.0253164556962027, 2.1265822784810124, 2.2278481012658227, 2.329113924050633, 2.430379746835443, 2.5316455696202533, 2.632911392405063, 2.7341772151898733, 2.8354430379746836, 2.9367088607594938, 3.0379746835443036, 3.1392405063291138, 3.240506329113924, 3.3417721518987342, 3.4430379746835444, 3.5443037974683542, 3.6455696202531644, 3.7468354430379747, 3.848101265822785, 3.9493670886075947, 4.050632911392405, 4.151898734177215, 4.253164556962025, 4.3544303797468356, 4.455696202531645, 4.556962025316456, 4.658227848101266, 4.7594936708860756, 4.860759493670886, 4.962025316455696, 5.063291139240507, 5.1645569620253164, 5.265822784810126, 5.367088607594937, 5.468354430379747, 5.5696202531645564, 5.670886075949367, 5.772151898734177, 5.8734177215189876, 5.974683544303797, 6.075949367088607, 6.177215189873418, 6.2784810126582276, 6.379746835443038, 6.481012658227848, 6.582278481012658, 6.6835443037974684, 6.784810126582278, 6.886075949367089, 6.987341772151899, 7.0886075949367084, 7.189873417721519, 7.291139240506329, 7.3924050632911396, 7.493670886075949, 7.594936708860759, 7.69620253164557, 7.7974683544303796, 7.898734177215189, 8.0], "x": [0.2735450433703587, 0.265828142715711, 0.25832897048351017, 0.25104133608211177, 0.24395928940578926, 0.23707702980746556, 0.23038892018256185, 0.22388948964753916, 0.21757341342182862, 0.2114355179014576, 0.20547077682031564, 0.19967430476899026, 0.19404135047863347, 0.18856730159335697, 0.18324768069750846, 0.17807813789077637, 0.17305443915993343, 0.16817246802152072, 0.1634282191559046, 0.1588177976191772, 0.15433743486230264, 0.14998346598364193, 0.1457523295495789, 0.14164055833240843, 0.1376447833094015, 0.13376173002453753, 0.12998822031503962, 0.12632116390039724, 0.1227575574098142, 0.11929448293065793, 0.1159291042253156, 0.11265866492224462, 0.10948048723446789, 0.10639196814746002, 0.1033905779750483, 0.10047385927430036, 0.09763942323625413, 0.09488494855189306, 0.09220818041875364, 0.08960692654586297, 0.08707905595922347, 0.08462249719071104, 0.08223523801224165, 0.07991532395551115, 0.07766085531048425, 0.07546998665112656, 0.07334092556145927, 0.07127192740680376, 0.06926129662490604, 0.06730738677872308, 0.06540859824445369, 0.06356337684239724, 0.061770210613210065, 0.060027630703920726, 0.058334210049084706, 0.05668856194939037, 0.05508933884910683, 0.05353523076977014, 0.0520249649562932, 0.050557304682360686, 0.04913104824682452, 0.04774502773939482, 0.04639810776789408, 0.04508918527034285, 0.04381718834934965, 0.04258107541246791, 0.04137983411090457, 0.0402124805579499, 0.039078058766161994, 0.037975639776525884, 0.036904320908811794, 0.03586322451282011, 0.03485149778026195, 0.033868312179516406, 0.03291286266365623, 0.03198436705888536, 0.03108206548022068, 0.030205219125909795, 0.029353109022590432, 0.028525037283495175], "k": 0.2825854869746016}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 2.06), (0.06, 1.96), (0.12, 1.87), (0.17, 1.78), (0.23, 1.70), (0.29, 1.62), (0.35, 1.54), (0.41, 1.47), (0.46, 1.40), (0.52, 1.33), (0.58, 1.27), (0.64, 1.21), (0.70, 1.15), (0.75, 1.10), (0.81, 1.05), (0.87, 1.00), (0.93, 0.95), (0.99, 0.90), (1.04, 0.86), (1.10, 0.82), (1.16, 0.78), (1.22, 0.74), (1.28, 0.71), (1.33, 0.68), (1.39, 0.64), (1.45, 0.61), (1.51, 0.58), (1.57, 0.56), (1.62, 0.53), (1.68, 0.51), (1.74, 0.48), (1.80, 0.46), (1.86, 0.44), (1.91, 0.42), (1.97, 0.40), (2.03, 0.38), (2.09, 0.36), (2.14, 0.34), (2.20, 0.33), (2.26, 0.31), (2.32, 0.30), (2.38, 0.28), (2.43, 0.27), (2.49, 0.26), (2.55, 0.24), (2.61, 0.23), (2.67, 0.22), (2.72, 0.21), (2.78, 0.20), (2.84, 0.19), (2.90, 0.18), (2.96, 0.17), (3.01, 0.17), (3.07, 0.16), (3.13, 0.15), (3.19, 0.14), (3.25, 0.14), (3.30, 0.13), (3.36, 0.12), (3.42, 0.12), (3.48, 0.11), (3.54, 0.11), (3.59, 0.10), (3.65, 0.10), (3.71, 0.09), (3.77, 0.09), (3.83, 0.08), (3.88, 0.08), (3.94, 0.08), (4.00, 0.07)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.057971014492753624, 0.11594202898550725, 0.17391304347826086, 0.2318840579710145, 0.2898550724637681, 0.34782608695652173, 0.4057971014492754, 0.463768115942029, 0.5217391304347826, 0.5797101449275363, 0.6376811594202899, 0.6956521739130435, 0.7536231884057971, 0.8115942028985508, 0.8695652173913043, 0.927536231884058, 0.9855072463768116, 1.0434782608695652, 1.1014492753623188, 1.1594202898550725, 1.2173913043478262, 1.2753623188405798, 1.3333333333333333, 1.391304347826087, 1.4492753623188406, 1.5072463768115942, 1.565217391304348, 1.6231884057971016, 1.681159420289855, 1.7391304347826086, 1.7971014492753623, 1.855072463768116, 1.9130434782608696, 1.9710144927536233, 2.028985507246377, 2.0869565217391304, 2.1449275362318843, 2.2028985507246377, 2.260869565217391, 2.318840579710145, 2.3768115942028984, 2.4347826086956523, 2.4927536231884058, 2.5507246376811596, 2.608695652173913, 2.6666666666666665, 2.7246376811594204, 2.782608695652174, 2.8405797101449277, 2.898550724637681, 2.956521739130435, 3.0144927536231885, 3.072463768115942, 3.130434782608696, 3.1884057971014492, 3.246376811594203, 3.3043478260869565, 3.36231884057971, 3.420289855072464, 3.4782608695652173, 3.536231884057971, 3.5942028985507246, 3.6521739130434785, 3.710144927536232, 3.7681159420289854, 3.8260869565217392, 3.8840579710144927, 3.9420289855072466, 4.0], "x": [2.0587723186971014, 1.9614613294623204, 1.8687498585389586, 1.7804205212874724, 1.6962662150958683, 1.6160895815607539, 1.5397025840499994, 1.4669261959486797, 1.3975897368284615, 1.33153050287575, 1.2685936679628675, 1.2086316515737863, 1.151503824984589, 1.0970762325469925, 1.0452212440303608, 0.9958172617186336, 0.9487484335687859, 0.9039043878881243, 0.8611799771700748, 0.82047499719006, 0.7816939802405002, 0.7447459971390192, 0.7095444326641345, 0.6760067328145298, 0.6440542398713386, 0.6136120253109074, 0.5846087107316106, 0.5569762840372977, 0.5306499464423244, 0.5055679632389429, 0.4816715183402831, 0.45890457513096566, 0.43721374651873746, 0.41654816845473197, 0.39685938058950665, 0.3781012134149226, 0.36022967966803154, 0.34320287048801756, 0.3269808575903663, 0.31152560448082767, 0.2968008683021684, 0.28277211799444973, 0.2694064595955887, 0.2566725493595853, 0.24454052572332938, 0.23298194239323883, 0.2219696926891412, 0.2114779530227615, 0.2014821231076116, 0.19195876071681642, 0.18288553415831932, 0.17424116886724705, 0.16600539188964525, 0.1581588913293394, 0.15068326874777477, 0.1435609920765518, 0.1367753607978186, 0.1303104633883397, 0.12415113818252606, 0.11828294267031576, 0.11269211818494827, 0.10736555417512963, 0.10229075954647576, 0.09745583174109888, 0.09284943308785924, 0.08846076371455677, 0.08427953151425949, 0.08029593010410842, 0.07650061987953281, 0.07288470113441334], "k": 0.835246587293921}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 1.78), (0.11, 1.45), (0.22, 1.19), (0.33, 0.98), (0.44, 0.80), (0.55, 0.65), (0.66, 0.54), (0.77, 0.44), (0.88, 0.36), (0.99, 0.29), (1.10, 0.24), (1.21, 0.20), (1.32, 0.16), (1.43, 0.13), (1.54, 0.11), (1.65, 0.09), (1.76, 0.07), (1.87, 0.06), (1.98, 0.05), (2.09, 0.04), (2.20, 0.03), (2.31, 0.03), (2.42, 0.02), (2.53, 0.02), (2.64, 0.01), (2.75, 0.01), (2.86, 0.01), (2.97, 0.01), (3.08, 0.01), (3.19, 0.01), (3.30, 0.00), (3.41, 0.00), (3.52, 0.00), (3.63, 0.00), (3.74, 0.00), (3.85, 0.00), (3.96, 0.00), (4.07, 0.00), (4.18, 0.00), (4.29, 0.00), (4.40, 0.00), (4.51, 0.00), (4.62, 0.00), (4.73, 0.00), (4.84, 0.00), (4.95, 0.00), (5.06, 0.00), (5.17, 0.00), (5.28, 0.00), (5.39, 0.00), (5.50, 0.00), (5.61, 0.00), (5.72, 0.00), (5.83, 0.00), (5.94, 0.00), (6.06, 0.00), (6.17, 0.00), (6.28, 0.00), (6.39, 0.00), (6.50, 0.00), (6.61, 0.00), (6.72, 0.00), (6.83, 0.00), (6.94, 0.00), (7.05, 0.00), (7.16, 0.00), (7.27, 0.00), (7.38, 0.00), (7.49, 0.00), (7.60, 0.00), (7.71, 0.00), (7.82, 0.00), (7.93, 0.00), (8.04, 0.00), (8.15, 0.00), (8.26, 0.00), (8.37, 0.00), (8.48, 0.00), (8.59, 0.00), (8.70, 0.00), (8.81, 0.00), (8.92, 0.00), (9.03, 0.00), (9.14, 0.00), (9.25, 0.00), (9.36, 0.00), (9.47, 0.00), (9.58, 0.00), (9.69, 0.00), (9.80, 0.00), (9.91, 0.00), (10.02, 0.00), (10.13, 0.00), (10.24, 0.00), (10.35, 0.00), (10.46, 0.00), (10.57, 0.00), (10.68, 0.00), (10.79, 0.00), (10.90, 0.00), (11.01, 0.00), (11.12, 0.00), (11.23, 0.00), (11.34, 0.00), (11.45, 0.00), (11.56, 0.00), (11.67, 0.00), (11.78, 0.00), (11.89, 0.00), (12.00, 0.00)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.11009174311926606, 0.22018348623853212, 0.3302752293577982, 0.44036697247706424, 0.5504587155963303, 0.6605504587155964, 0.7706422018348624, 0.8807339449541285, 0.9908256880733946, 1.1009174311926606, 1.2110091743119267, 1.3211009174311927, 1.4311926605504588, 1.5412844036697249, 1.651376146788991, 1.761467889908257, 1.871559633027523, 1.981651376146789, 2.091743119266055, 2.2018348623853212, 2.3119266055045875, 2.4220183486238533, 2.532110091743119, 2.6422018348623855, 2.7522935779816518, 2.8623853211009176, 2.9724770642201834, 3.0825688073394497, 3.192660550458716, 3.302752293577982, 3.4128440366972477, 3.522935779816514, 3.6330275229357802, 3.743119266055046, 3.853211009174312, 3.963302752293578, 4.0733944954128445, 4.18348623853211, 4.293577981651376, 4.4036697247706424, 4.513761467889909, 4.623853211009175, 4.73394495412844, 4.844036697247707, 4.954128440366973, 5.064220183486238, 5.174311926605505, 5.284403669724771, 5.394495412844037, 5.5045871559633035, 5.614678899082569, 5.724770642201835, 5.8348623853211015, 5.944954128440367, 6.055045871559633, 6.165137614678899, 6.275229357798166, 6.385321100917432, 6.495412844036697, 6.605504587155964, 6.71559633027523, 6.825688073394495, 6.935779816513762, 7.045871559633028, 7.155963302752294, 7.2660550458715605, 7.376146788990826, 7.486238532110092, 7.596330275229358, 7.706422018348624, 7.81651376146789, 7.926605504587156, 8.036697247706423, 8.146788990825689, 8.256880733944955, 8.36697247706422, 8.477064220183486, 8.587155963302752, 8.697247706422019, 8.807339449541285, 8.917431192660551, 9.027522935779817, 9.137614678899084, 9.24770642201835, 9.357798165137615, 9.46788990825688, 9.577981651376147, 9.688073394495413, 9.79816513761468, 9.908256880733946, 10.018348623853212, 10.128440366972477, 10.238532110091743, 10.34862385321101, 10.458715596330276, 10.568807339449542, 10.678899082568808, 10.788990825688074, 10.89908256880734, 11.009174311926607, 11.119266055045872, 11.229357798165138, 11.339449541284404, 11.44954128440367, 11.559633027522937, 11.669724770642203, 11.77981651376147, 11.889908256880734, 12.0], "x": [1.7764729908151027, 1.4547511421162194, 1.191293586967074, 0.9755485570775942, 0.7988752816077369, 0.6541978013490488, 0.5357216090431893, 0.4387016341669283, 0.3592521210920095, 0.294191031610191, 0.24091259554245595, 0.19728296552204905, 0.16155472634188822, 0.13229692400828047, 0.10833775410164777, 0.08871762677279514, 0.07265073972891763, 0.059493584832291016, 0.048719209543950134, 0.03989608868357288, 0.0326708487864727, 0.02675411050275776, 0.021908902491153136, 0.017941168378136065, 0.014691996737297897, 0.012031254790377087, 0.009852377024884007, 0.008068097263822899, 0.006606953108371304, 0.005410424298492291, 0.004430588604985455, 0.0036282025588537875, 0.002971129947168768, 0.0024330542974907877, 0.001992424377271848, 0.0016315926016578087, 0.001336108284382226, 0.0010941367730132134, 0.000895986764408098, 0.0007337221233035717, 0.0006008436558409718, 0.0004920296363209308, 0.0004029222442535644, 0.00032995228063740427, 0.0002701973236983774, 0.0002212641798213802, 0.00018119289935947892, 0.00014837847881494587, 0.00012150687821848827, 9.950147530213585e-05, 8.1481509462443e-05, 6.672581616197029e-05, 5.4642330542338797e-05, 4.4746790031397014e-05, 3.664320116230503e-05, 3.0007017652792808e-05, 2.457273401784507e-05, 2.01227052927777e-05, 1.6478583342084822e-05, 1.3494528601030228e-05, 1.1050550581622751e-05, 9.049066803720658e-06, 7.410202734723215e-06, 6.068091636205917e-06, 4.969213987274597e-06, 4.069166046481819e-06, 3.3320222495226856e-06, 2.728661349852923e-06, 2.2344875297464905e-06, 1.8299668026830274e-06, 1.4985411613024501e-06, 1.226671823635749e-06, 1.003970889549628e-06, 8.220443075313248e-07, 6.730739525817871e-07, 5.514935107694957e-07, 4.518831070574832e-07, 3.698098589246845e-07, 3.0325445068373793e-07, 2.483782292277855e-07, 2.0352698107938306e-07, 1.6690148050371042e-07, 1.3691287464999667e-07, 1.1244914826549927e-07, 9.233359752866831e-08, 7.549388181058198e-08, 6.167935251246109e-08, 5.031864421808434e-08, 4.053552813103106e-08, 3.3315061342239176e-08, 2.7192035611354934e-08, 2.206886032005832e-08, 1.788081877917024e-08, 1.4615989697681668e-08, 1.1973337414042823e-08, 9.821836031448787e-09, 8.14514408630372e-09, 6.753005717662228e-09, 5.590900852372107e-09, 4.647427982548078e-09, 3.847113499912202e-09, 3.176122657309959e-09, 2.625867536564368e-09, 2.160772640694893e-09, 1.7769534917061502e-09, 1.4658795605547994e-09, 1.2044559516866392e-09, 9.913918144520315e-10, 8.19143074031454e-10, 6.742371875797447e-10], "k": 1.814805495446283}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 1.06), (0.10, 1.01), (0.20, 0.97), (0.31, 0.93), (0.41, 0.89), (0.51, 0.85), (0.61, 0.82), (0.71, 0.78), (0.81, 0.75), (0.92, 0.72), (1.02, 0.69), (1.12, 0.66), (1.22, 0.63), (1.32, 0.60), (1.42, 0.58), (1.53, 0.55), (1.63, 0.53), (1.73, 0.51), (1.83, 0.49), (1.93, 0.47), (2.03, 0.45), (2.14, 0.43), (2.24, 0.41), (2.34, 0.39), (2.44, 0.38), (2.54, 0.36), (2.64, 0.34), (2.75, 0.33), (2.85, 0.32), (2.95, 0.30), (3.05, 0.29), (3.15, 0.28), (3.25, 0.27), (3.36, 0.25), (3.46, 0.24), (3.56, 0.23), (3.66, 0.22), (3.76, 0.21), (3.86, 0.21), (3.97, 0.20), (4.07, 0.19), (4.17, 0.18), (4.27, 0.17), (4.37, 0.17), (4.47, 0.16), (4.58, 0.15), (4.68, 0.15), (4.78, 0.14), (4.88, 0.13), (4.98, 0.13), (5.08, 0.12), (5.19, 0.12), (5.29, 0.11), (5.39, 0.11), (5.49, 0.10), (5.59, 0.10), (5.69, 0.09), (5.80, 0.09), (5.90, 0.09), (6.00, 0.08)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.1016949152542373, 0.2033898305084746, 0.3050847457627119, 0.4067796610169492, 0.5084745762711864, 0.6101694915254238, 0.7118644067796611, 0.8135593220338984, 0.9152542372881356, 1.0169491525423728, 1.1186440677966103, 1.2203389830508475, 1.3220338983050848, 1.4237288135593222, 1.5254237288135595, 1.6271186440677967, 1.728813559322034, 1.8305084745762712, 1.9322033898305087, 2.0338983050847457, 2.135593220338983, 2.2372881355932206, 2.3389830508474576, 2.440677966101695, 2.5423728813559325, 2.6440677966101696, 2.745762711864407, 2.8474576271186445, 2.9491525423728815, 3.050847457627119, 3.152542372881356, 3.2542372881355934, 3.355932203389831, 3.457627118644068, 3.5593220338983054, 3.6610169491525424, 3.76271186440678, 3.8644067796610173, 3.9661016949152543, 4.067796610169491, 4.169491525423729, 4.271186440677966, 4.372881355932203, 4.474576271186441, 4.576271186440678, 4.677966101694915, 4.779661016949153, 4.88135593220339, 4.983050847457627, 5.084745762711865, 5.186440677966102, 5.288135593220339, 5.389830508474577, 5.491525423728814, 5.593220338983051, 5.694915254237289, 5.796610169491526, 5.898305084745763, 6.0], "x": [1.0556004635108867, 1.0111055641001923, 0.9684861626600221, 0.9276632125205699, 0.8885610053296639, 0.8511070090341106, 0.8152317418018107, 0.7808686399688254, 0.7479540068337823, 0.7164268087091191, 0.6862285204770994, 0.6573030893932074, 0.6295969091761777, 0.6030585918638481, 0.5776388932974115, 0.5532906673753822, 0.5299687509296656, 0.5076298833183973, 0.4862326284438117, 0.4657372948515966, 0.446105866397635, 0.42730193080288176, 0.409290609581828, 0.39203848378575246, 0.375513549804843, 0.35968515916658433, 0.3445239617595969, 0.330001828045513, 0.3160918200921398, 0.3027681410816855, 0.29000607222842745, 0.27778194079786916, 0.2660730726635066, 0.25485774754237156, 0.24411516311275627, 0.23382539316085332, 0.22396934994835366, 0.21452875197894725, 0.2054860873672654, 0.19682458236881487, 0.18852817138313355, 0.18058146381754872, 0.17296971901276936, 0.16567881994641848, 0.15869524316958855, 0.15200603227171194, 0.145598779973935, 0.13946160295442478, 0.13358311533162345, 0.12795241277655056, 0.12255905232317381, 0.1173930295033578, 0.11244476040865162, 0.10770506713575181, 0.10316515918234495, 0.0988166137441805, 0.0946513646366071, 0.09066168680900764, 0.08684017921188238, 0.08317975250849557], "k": 0.4234768224035562}}
|
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 1.43), (0.06, 1.38), (0.12, 1.33), (0.17, 1.28), (0.23, 1.23), (0.29, 1.19), (0.35, 1.14), (0.41, 1.10), (0.46, 1.06), (0.52, 1.02), (0.58, 0.99), (0.64, 0.95), (0.70, 0.92), (0.75, 0.88), (0.81, 0.85), (0.87, 0.82), (0.93, 0.79), (0.99, 0.76), (1.04, 0.73), (1.10, 0.71), (1.16, 0.68), (1.22, 0.66), (1.28, 0.63), (1.33, 0.61), (1.39, 0.59), (1.45, 0.56), (1.51, 0.54), (1.57, 0.52), (1.62, 0.51), (1.68, 0.49), (1.74, 0.47), (1.80, 0.45), (1.86, 0.44), (1.91, 0.42), (1.97, 0.40), (2.03, 0.39), (2.09, 0.38), (2.14, 0.36), (2.20, 0.35), (2.26, 0.34), (2.32, 0.32), (2.38, 0.31), (2.43, 0.30), (2.49, 0.29), (2.55, 0.28), (2.61, 0.27), (2.67, 0.26), (2.72, 0.25), (2.78, 0.24), (2.84, 0.23), (2.90, 0.22), (2.96, 0.22), (3.01, 0.21), (3.07, 0.20), (3.13, 0.19), (3.19, 0.19), (3.25, 0.18), (3.30, 0.17), (3.36, 0.17), (3.42, 0.16), (3.48, 0.15), (3.54, 0.15), (3.59, 0.14), (3.65, 0.14), (3.71, 0.13), (3.77, 0.13), (3.83, 0.12), (3.88, 0.12), (3.94, 0.11), (4.00, 0.11)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.057971014492753624, 0.11594202898550725, 0.17391304347826086, 0.2318840579710145, 0.2898550724637681, 0.34782608695652173, 0.4057971014492754, 0.463768115942029, 0.5217391304347826, 0.5797101449275363, 0.6376811594202899, 0.6956521739130435, 0.7536231884057971, 0.8115942028985508, 0.8695652173913043, 0.927536231884058, 0.9855072463768116, 1.0434782608695652, 1.1014492753623188, 1.1594202898550725, 1.2173913043478262, 1.2753623188405798, 1.3333333333333333, 1.391304347826087, 1.4492753623188406, 1.5072463768115942, 1.565217391304348, 1.6231884057971016, 1.681159420289855, 1.7391304347826086, 1.7971014492753623, 1.855072463768116, 1.9130434782608696, 1.9710144927536233, 2.028985507246377, 2.0869565217391304, 2.1449275362318843, 2.2028985507246377, 2.260869565217391, 2.318840579710145, 2.3768115942028984, 2.4347826086956523, 2.4927536231884058, 2.5507246376811596, 2.608695652173913, 2.6666666666666665, 2.7246376811594204, 2.782608695652174, 2.8405797101449277, 2.898550724637681, 2.956521739130435, 3.0144927536231885, 3.072463768115942, 3.130434782608696, 3.1884057971014492, 3.246376811594203, 3.3043478260869565, 3.36231884057971, 3.420289855072464, 3.4782608695652173, 3.536231884057971, 3.5942028985507246, 3.6521739130434785, 3.710144927536232, 3.7681159420289854, 3.8260869565217392, 3.8840579710144927, 3.9420289855072466, 4.0], "x": [1.428614472834799, 1.3765760534305396, 1.3264331538751246, 1.2781167416177963, 1.231560287895998, 1.1866996978045743, 1.1434731913796676, 1.1018212329584902, 1.0616864639734949, 1.0230136636232259, 0.9857495867982015, 0.9498428844079296, 0.9152440731689926, 0.8819055506373071, 0.8497814255376981, 0.8188274472714518, 0.7890009894698465, 0.7602609845072432, 0.7325678583164004, 0.7058834764480444, 0.6801710956559172, 0.6553953085899749, 0.6315220003466167, 0.6085182977436168, 0.586352529403313, 0.5649941689020954, 0.5444137958017671, 0.5245830726187903, 0.5054746954262185, 0.4870623619745853, 0.46932071507332496, 0.45222531950192124, 0.43575263939854253, 0.41987999415198285, 0.40458552224099015, 0.3898481636272802, 0.3756476259656092, 0.3619643535633601, 0.3487795049604556, 0.33607492633099934, 0.3238331224296545, 0.3120372358587445, 0.3006710244286982, 0.28971883663833914, 0.27916559070920044, 0.26899675544193924, 0.25919832856763114, 0.24975681610225373, 0.24065921757594866, 0.23189300762238096, 0.2234461152567776, 0.21530690705666003, 0.2074641757068514, 0.1999071231839925, 0.19262534271120801, 0.1856088061870973, 0.1788478523813908, 0.1723331729424584, 0.16605579601044743, 0.16000707696643676, 0.1541786873226016, 0.14856260258057646, 0.143151088090277, 0.13793669188585103, 0.13291223434318844, 0.12807079761263757, 0.12340571377708869, 0.11891055896915001, 0.11457914402723082, 0.11040550511464323], "k": 0.6400750557147368}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 1.25), (0.11, 1.13), (0.22, 1.03), (0.33, 0.93), (0.44, 0.84), (0.55, 0.76), (0.66, 0.69), (0.77, 0.62), (0.88, 0.56), (0.99, 0.51), (1.10, 0.46), (1.21, 0.42), (1.32, 0.38), (1.43, 0.34), (1.54, 0.31), (1.65, 0.28), (1.76, 0.25), (1.87, 0.23), (1.98, 0.21), (2.09, 0.19), (2.20, 0.17), (2.31, 0.15), (2.42, 0.14), (2.53, 0.13), (2.64, 0.11), (2.75, 0.10), (2.86, 0.09), (2.97, 0.09), (3.08, 0.08), (3.19, 0.07), (3.30, 0.06), (3.41, 0.06), (3.52, 0.05), (3.63, 0.05), (3.74, 0.04), (3.85, 0.04), (3.96, 0.03), (4.07, 0.03), (4.18, 0.03), (4.29, 0.03), (4.40, 0.02), (4.51, 0.02), (4.62, 0.02), (4.73, 0.02), (4.84, 0.02), (4.95, 0.01), (5.06, 0.01), (5.17, 0.01), (5.28, 0.01), (5.39, 0.01), (5.50, 0.01), (5.61, 0.01), (5.72, 0.01), (5.83, 0.01), (5.94, 0.01), (6.06, 0.01), (6.17, 0.00), (6.28, 0.00), (6.39, 0.00), (6.50, 0.00), (6.61, 0.00), (6.72, 0.00), (6.83, 0.00), (6.94, 0.00), (7.05, 0.00), (7.16, 0.00), (7.27, 0.00), (7.38, 0.00), (7.49, 0.00), (7.60, 0.00), (7.71, 0.00), (7.82, 0.00), (7.93, 0.00), (8.04, 0.00), (8.15, 0.00), (8.26, 0.00), (8.37, 0.00), (8.48, 0.00), (8.59, 0.00), (8.70, 0.00), (8.81, 0.00), (8.92, 0.00), (9.03, 0.00), (9.14, 0.00), (9.25, 0.00), (9.36, 0.00), (9.47, 0.00), (9.58, 0.00), (9.69, 0.00), (9.80, 0.00), (9.91, 0.00), (10.02, 0.00), (10.13, 0.00), (10.24, 0.00), (10.35, 0.00), (10.46, 0.00), (10.57, 0.00), (10.68, 0.00), (10.79, 0.00), (10.90, 0.00), (11.01, 0.00), (11.12, 0.00), (11.23, 0.00), (11.34, 0.00), (11.45, 0.00), (11.56, 0.00), (11.67, 0.00), (11.78, 0.00), (11.89, 0.00), (12.00, 0.00)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.11009174311926606, 0.22018348623853212, 0.3302752293577982, 0.44036697247706424, 0.5504587155963303, 0.6605504587155964, 0.7706422018348624, 0.8807339449541285, 0.9908256880733946, 1.1009174311926606, 1.2110091743119267, 1.3211009174311927, 1.4311926605504588, 1.5412844036697249, 1.651376146788991, 1.761467889908257, 1.871559633027523, 1.981651376146789, 2.091743119266055, 2.2018348623853212, 2.3119266055045875, 2.4220183486238533, 2.532110091743119, 2.6422018348623855, 2.7522935779816518, 2.8623853211009176, 2.9724770642201834, 3.0825688073394497, 3.192660550458716, 3.302752293577982, 3.4128440366972477, 3.522935779816514, 3.6330275229357802, 3.743119266055046, 3.853211009174312, 3.963302752293578, 4.0733944954128445, 4.18348623853211, 4.293577981651376, 4.4036697247706424, 4.513761467889909, 4.623853211009175, 4.73394495412844, 4.844036697247707, 4.954128440366973, 5.064220183486238, 5.174311926605505, 5.284403669724771, 5.394495412844037, 5.5045871559633035, 5.614678899082569, 5.724770642201835, 5.8348623853211015, 5.944954128440367, 6.055045871559633, 6.165137614678899, 6.275229357798166, 6.385321100917432, 6.495412844036697, 6.605504587155964, 6.71559633027523, 6.825688073394495, 6.935779816513762, 7.045871559633028, 7.155963302752294, 7.2660550458715605, 7.376146788990826, 7.486238532110092, 7.596330275229358, 7.706422018348624, 7.81651376146789, 7.926605504587156, 8.036697247706423, 8.146788990825689, 8.256880733944955, 8.36697247706422, 8.477064220183486, 8.587155963302752, 8.697247706422019, 8.807339449541285, 8.917431192660551, 9.027522935779817, 9.137614678899084, 9.24770642201835, 9.357798165137615, 9.46788990825688, 9.577981651376147, 9.688073394495413, 9.79816513761468, 9.908256880733946, 10.018348623853212, 10.128440366972477, 10.238532110091743, 10.34862385321101, 10.458715596330276, 10.568807339449542, 10.678899082568808, 10.788990825688074, 10.89908256880734, 11.009174311926607, 11.119266055045872, 11.229357798165138, 11.339449541284404, 11.44954128440367, 11.559633027522937, 11.669724770642203, 11.77981651376147, 11.889908256880734, 12.0], "x": [1.253035215886893, 1.134194143566922, 1.0266242252702282, 0.9292564846492246, 0.8411234391518524, 0.7613491053344297, 0.6891407930614438, 0.6237808975255211, 0.5646199039761763, 0.5110698978752258, 0.46259871299006033, 0.4187246369101406, 0.3790116988422446, 0.3430652477785622, 0.310528050175807, 0.28107676448464897, 0.25441871550543177, 0.2302889844857524, 0.20844777656429742, 0.18867804761862206, 0.17078333078830002, 0.15458579490590815, 0.13992447654329354, 0.12665367508589953, 0.11464151065580712, 0.1037686120037227, 0.09392692695893133, 0.08501865243353343, 0.07695526187782116, 0.06965662338310069, 0.0630502124242483, 0.05707037000178811, 0.05165767087250567, 0.04675832383527863, 0.042323643591552246, 0.038309559625884, 0.03467618237104074, 0.03138740320217049, 0.02841054043952137, 0.025716011539523964, 0.023277038625472687, 0.021069384274137848, 0.019071109411874076, 0.01726235651744812, 0.01562515001070036, 0.014143220673325154, 0.012801841003928336, 0.01158768148598727, 0.010488675787184107, 0.009493902866460032, 0.008593476544651809, 0.007778449124316812, 0.007040720871223073, 0.0063729608257995585, 0.005768532733219825, 0.005221430273984941, 0.004726216309040539, 0.004277969800257779, 0.003872236073343368, 0.0035049832649214807, 0.0031725615826845247, 0.0028716676854978057, 0.0025993112879904856, 0.002352785927429194, 0.002129641675866449, 0.0019276612773502684, 0.0017448370512870189, 0.0015793521470500401, 0.001429562216695726, 0.0012939785606161987, 0.0011712537144944045, 0.001060168838495468, 0.0009596193918259225, 0.0008686064697072585, 0.0007862255100386038, 0.0007116576061251323, 0.0006441621834397428, 0.0005830679701040644, 0.0005277682969600412, 0.00047771331833484416, 0.0004324056925903834, 0.0003913951425056879, 0.0003542739534729084, 0.00032067370321928483, 0.00029026011269901557, 0.00026273105973494365, 0.000237812988204147, 0.00021525809522494083, 0.0001948424771591225, 0.00017636304773361742, 0.00015963627275266366, 0.0001444959738048605, 0.00013079156167705052, 0.00011838697005907135, 0.00010715881128670205, 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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 1.23), (0.10, 1.20), (0.20, 1.17), (0.30, 1.14), (0.40, 1.11), (0.51, 1.08), (0.61, 1.05), (0.71, 1.02), (0.81, 1.00), (0.91, 0.97), (1.01, 0.95), (1.11, 0.92), (1.21, 0.90), (1.31, 0.87), (1.42, 0.85), (1.52, 0.83), (1.62, 0.81), (1.72, 0.79), (1.82, 0.77), (1.92, 0.75), (2.02, 0.73), (2.12, 0.71), (2.22, 0.69), (2.33, 0.67), (2.43, 0.66), (2.53, 0.64), (2.63, 0.62), (2.73, 0.61), (2.83, 0.59), (2.93, 0.58), (3.03, 0.56), (3.13, 0.55), (3.24, 0.53), (3.34, 0.52), (3.44, 0.51), (3.54, 0.49), (3.64, 0.48), (3.74, 0.47), (3.84, 0.46), (3.94, 0.44), (4.04, 0.43), (4.15, 0.42), (4.25, 0.41), (4.35, 0.40), (4.45, 0.39), (4.55, 0.38), (4.65, 0.37), (4.75, 0.36), (4.85, 0.35), (4.96, 0.34), (5.06, 0.33), (5.16, 0.32), (5.26, 0.32), (5.36, 0.31), (5.46, 0.30), (5.56, 0.29), (5.66, 0.29), (5.76, 0.28), (5.87, 0.27), (5.97, 0.26), (6.07, 0.26), (6.17, 0.25), (6.27, 0.24), (6.37, 0.24), (6.47, 0.23), (6.57, 0.23), (6.67, 0.22), (6.78, 0.21), (6.88, 0.21), (6.98, 0.20), (7.08, 0.20), (7.18, 0.19), (7.28, 0.19), (7.38, 0.18), (7.48, 0.18), (7.58, 0.17), (7.69, 0.17), (7.79, 0.16), (7.89, 0.16), (7.99, 0.16), (8.09, 0.15), (8.19, 0.15), (8.29, 0.14), (8.39, 0.14), (8.49, 0.14), (8.60, 0.13), (8.70, 0.13), (8.80, 0.13), (8.90, 0.12), (9.00, 0.12)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.10112359550561797, 0.20224719101123595, 0.3033707865168539, 0.4044943820224719, 0.5056179775280899, 0.6067415730337078, 0.7078651685393258, 0.8089887640449438, 0.9101123595505618, 1.0112359550561798, 1.1123595505617978, 1.2134831460674156, 1.3146067415730336, 1.4157303370786516, 1.5168539325842696, 1.6179775280898876, 1.7191011235955056, 1.8202247191011236, 1.9213483146067416, 2.0224719101123596, 2.1235955056179776, 2.2247191011235956, 2.3258426966292136, 2.426966292134831, 2.528089887640449, 2.629213483146067, 2.730337078651685, 2.831460674157303, 2.932584269662921, 3.033707865168539, 3.134831460674157, 3.235955056179775, 3.337078651685393, 3.438202247191011, 3.539325842696629, 3.640449438202247, 3.741573033707865, 3.842696629213483, 3.943820224719101, 4.044943820224719, 4.146067415730337, 4.247191011235955, 4.348314606741573, 4.449438202247191, 4.550561797752809, 4.651685393258427, 4.752808988764045, 4.853932584269662, 4.955056179775281, 5.056179775280898, 5.157303370786517, 5.258426966292134, 5.359550561797753, 5.46067415730337, 5.561797752808989, 5.662921348314606, 5.764044943820225, 5.865168539325842, 5.966292134831461, 6.067415730337078, 6.168539325842697, 6.269662921348314, 6.370786516853933, 6.47191011235955, 6.573033707865168, 6.674157303370786, 6.775280898876404, 6.876404494382022, 6.97752808988764, 7.078651685393258, 7.179775280898876, 7.280898876404494, 7.382022471910112, 7.48314606741573, 7.584269662921348, 7.685393258426966, 7.786516853932584, 7.887640449438202, 7.98876404494382, 8.089887640449438, 8.191011235955056, 8.292134831460674, 8.393258426966291, 8.49438202247191, 8.595505617977528, 8.696629213483146, 8.797752808988763, 8.898876404494382, 9.0], "x": [1.2276545465010902, 1.1960580711534292, 1.1652748013021796, 1.1352837999534238, 1.1060646803695353, 1.0775975754977998, 1.049863141503937, 1.022842517609871, 0.9965173311069789, 0.9708696829910421, 0.9458821265329047, 0.9215376717084652, 0.8978197795919179, 0.8747123397960893, 0.8521996389064561, 0.8302663636843339, 0.8088975813709484, 0.7880787521467966, 0.7677957376048729, 0.7480347587122697, 0.7287823803385348, 0.7100255075718039, 0.6917513819833344, 0.6739475822060104, 0.6566020038101614, 0.6397028532747221, 0.6232386414489944, 0.6071981734131873, 0.5915705434654315, 0.5763451266351345, 0.5615115700798531, 0.5470597891498252, 0.5329799579293492, 0.5192625034624259, 0.5058981014734224, 0.49287766494900037, 0.4801923392244735, 0.46783349578777145, 0.4557927316473013, 0.4440618614380858, 0.43263290994032866, 0.4214981091428179, 0.41064989224451254, 0.40008087880739235, 0.38978388177591233, 0.3797519009053936, 0.3699781173138948, 0.36045588661154, 0.3511787320128052, 0.3421403458289626, 0.33333458298465957, 0.32475545689494417, 0.3163971341462924, 0.3082539314491145, 0.3003203123298788, 0.29259088310957554, 0.28506038906205555, 0.27772370942024843, 0.27057585577980175, 0.26361196836140816, 0.256827312649457, 0.2502172757501608, 0.24377736300618574, 0.23750319589775462, 0.23139050875627645, 0.22543514589963204, 0.21963305766951402, 0.21398029879844555, 0.20847302602826853, 0.20310749529011554, 0.19788005928326496, 0.19278716439180663, 0.18782534655252892, 0.18299123203965764, 0.17828153420501033, 0.17369305121135092, 0.1692226639429569, 0.16486733254997085, 0.16062409515369483, 0.15649006676684732, 0.15246243682462207, 0.14853846735882686, 0.14471549093644784, 0.14099090739598782, 0.13736218416735171, 0.13382685413202144, 0.13038251384267166, 0.12702682196694043, 0.12375749688679225, 0.12057231508198486], "k": 0.2578456610153866}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 1.09), (0.10, 1.06), (0.20, 1.03), (0.30, 1.00), (0.41, 0.97), (0.51, 0.95), (0.61, 0.92), (0.71, 0.89), (0.81, 0.87), (0.91, 0.85), (1.01, 0.82), (1.11, 0.80), (1.22, 0.78), (1.32, 0.76), (1.42, 0.74), (1.52, 0.72), (1.62, 0.70), (1.72, 0.68), (1.82, 0.66), (1.92, 0.64), (2.03, 0.62), (2.13, 0.61), (2.23, 0.59), (2.33, 0.57), (2.43, 0.56), (2.53, 0.54), (2.63, 0.53), (2.73, 0.51), (2.84, 0.50), (2.94, 0.49), (3.04, 0.47), (3.14, 0.46), (3.24, 0.45), (3.34, 0.44), (3.44, 0.42), (3.54, 0.41), (3.65, 0.40), (3.75, 0.39), (3.85, 0.38), (3.95, 0.37), (4.05, 0.36), (4.15, 0.35), (4.25, 0.34), (4.35, 0.33), (4.46, 0.32), (4.56, 0.31), (4.66, 0.30), (4.76, 0.30), (4.86, 0.29), (4.96, 0.28), (5.06, 0.27), (5.16, 0.26), (5.27, 0.26), (5.37, 0.25), (5.47, 0.24), (5.57, 0.24), (5.67, 0.23), (5.77, 0.22), (5.87, 0.22), (5.97, 0.21), (6.08, 0.21), (6.18, 0.20), (6.28, 0.19), (6.38, 0.19), (6.48, 0.18), (6.58, 0.18), (6.68, 0.17), (6.78, 0.17), (6.89, 0.17), (6.99, 0.16), (7.09, 0.16), (7.19, 0.15), (7.29, 0.15), (7.39, 0.14), (7.49, 0.14), (7.59, 0.14), (7.70, 0.13), (7.80, 0.13), (7.90, 0.13), (8.00, 0.12)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.10126582278481013, 0.20253164556962025, 0.3037974683544304, 0.4050632911392405, 0.5063291139240507, 0.6075949367088608, 0.7088607594936709, 0.810126582278481, 0.9113924050632911, 1.0126582278481013, 1.1139240506329113, 1.2151898734177216, 1.3164556962025316, 1.4177215189873418, 1.5189873417721518, 1.620253164556962, 1.7215189873417722, 1.8227848101265822, 1.9240506329113924, 2.0253164556962027, 2.1265822784810124, 2.2278481012658227, 2.329113924050633, 2.430379746835443, 2.5316455696202533, 2.632911392405063, 2.7341772151898733, 2.8354430379746836, 2.9367088607594938, 3.0379746835443036, 3.1392405063291138, 3.240506329113924, 3.3417721518987342, 3.4430379746835444, 3.5443037974683542, 3.6455696202531644, 3.7468354430379747, 3.848101265822785, 3.9493670886075947, 4.050632911392405, 4.151898734177215, 4.253164556962025, 4.3544303797468356, 4.455696202531645, 4.556962025316456, 4.658227848101266, 4.7594936708860756, 4.860759493670886, 4.962025316455696, 5.063291139240507, 5.1645569620253164, 5.265822784810126, 5.367088607594937, 5.468354430379747, 5.5696202531645564, 5.670886075949367, 5.772151898734177, 5.8734177215189876, 5.974683544303797, 6.075949367088607, 6.177215189873418, 6.2784810126582276, 6.379746835443038, 6.481012658227848, 6.582278481012658, 6.6835443037974684, 6.784810126582278, 6.886075949367089, 6.987341772151899, 7.0886075949367084, 7.189873417721519, 7.291139240506329, 7.3924050632911396, 7.493670886075949, 7.594936708860759, 7.69620253164557, 7.7974683544303796, 7.898734177215189, 8.0], "x": [1.0859872902056682, 1.0563166879285741, 1.0274567163832544, 0.9993852325519966, 0.9720806942584014, 0.9455221460588885, 0.9196892195072267, 0.8945620830085799, 0.8701214534100511, 0.8463485721795647, 0.8232251852099719, 0.8007335542983309, 0.7788564365540349, 0.7575770503125127, 0.7368790595706771, 0.7167465652995425, 0.6971640938639307, 0.6781166318486962, 0.6595895749851819, 0.6415687104647548, 0.6240402025041177, 0.6069905932292267, 0.5904068011325417, 0.5742761003204111, 0.5585861116294736, 0.5433247948607126, 0.5284804372518559, 0.5140416475375459, 0.4999973450326642, 0.4863367510213936, 0.4730493830805598, 0.46012504353864886, 0.44755381550146023, 0.43532605261899887, 0.42343236973233067, 0.4118636362429567, 0.40061097160364295, 0.3896657421488934, 0.3790195487239247, 0.3686642235822455, 0.35859182391097155, 0.34879461568474557, 0.33926507903413455, 0.3299959016538319, 0.3209799723789314, 0.31221037176677907, 0.30368036803488274, 0.29538341509169247, 0.2873131460003988, 0.27946336776621244, 0.27182805554991707, 0.26440134985509856, 0.2571775516041775, 0.2501511177510195, 0.2433166555442821, 0.23666891977457608, 0.23020280890670508, 0.22391336098614306, 0.217795749332013, 0.21184527875839762, 0.20605738278831762, 0.20042761990141983, 0.19495166992288004, 0.18962532968029702, 0.18444451150545388, 0.1794052397439291, 0.17450364774869723, 0.1697359749543326, 0.1650985616037107, 0.1605878481722629, 0.15620037309058057, 0.15193276959124274, 0.1477817632421588, 0.14374416842349336, 0.13981688567149114, 0.13599690110538717, 0.13228128338160192, 0.12866718154441878, 0.12515182253482843, 0.12173250761388829], "k": 0.27355232848405336}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 1.14), (0.10, 1.11), (0.20, 1.08), (0.30, 1.05), (0.41, 1.02), (0.51, 1.00), (0.61, 0.97), (0.71, 0.95), (0.81, 0.92), (0.91, 0.90), (1.01, 0.88), (1.11, 0.85), (1.22, 0.83), (1.32, 0.81), (1.42, 0.79), (1.52, 0.77), (1.62, 0.75), (1.72, 0.73), (1.82, 0.71), (1.92, 0.69), (2.03, 0.68), (2.13, 0.66), (2.23, 0.64), (2.33, 0.62), (2.43, 0.61), (2.53, 0.59), (2.63, 0.58), (2.73, 0.56), (2.84, 0.55), (2.94, 0.53), (3.04, 0.52), (3.14, 0.51), (3.24, 0.49), (3.34, 0.48), (3.44, 0.47), (3.54, 0.46), (3.65, 0.45), (3.75, 0.43), (3.85, 0.42), (3.95, 0.41), (4.05, 0.40), (4.15, 0.39), (4.25, 0.38), (4.35, 0.37), (4.46, 0.36), (4.56, 0.35), (4.66, 0.34), (4.76, 0.33), (4.86, 0.33), (4.96, 0.32), (5.06, 0.31), (5.16, 0.30), (5.27, 0.29), (5.37, 0.29), (5.47, 0.28), (5.57, 0.27), (5.67, 0.26), (5.77, 0.26), (5.87, 0.25), (5.97, 0.24), (6.08, 0.24), (6.18, 0.23), (6.28, 0.23), (6.38, 0.22), (6.48, 0.21), (6.58, 0.21), (6.68, 0.20), (6.78, 0.20), (6.89, 0.19), (6.99, 0.19), (7.09, 0.18), (7.19, 0.18), (7.29, 0.17), (7.39, 0.17), (7.49, 0.17), (7.59, 0.16), (7.70, 0.16), (7.80, 0.15), (7.90, 0.15), (8.00, 0.15)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.10126582278481013, 0.20253164556962025, 0.3037974683544304, 0.4050632911392405, 0.5063291139240507, 0.6075949367088608, 0.7088607594936709, 0.810126582278481, 0.9113924050632911, 1.0126582278481013, 1.1139240506329113, 1.2151898734177216, 1.3164556962025316, 1.4177215189873418, 1.5189873417721518, 1.620253164556962, 1.7215189873417722, 1.8227848101265822, 1.9240506329113924, 2.0253164556962027, 2.1265822784810124, 2.2278481012658227, 2.329113924050633, 2.430379746835443, 2.5316455696202533, 2.632911392405063, 2.7341772151898733, 2.8354430379746836, 2.9367088607594938, 3.0379746835443036, 3.1392405063291138, 3.240506329113924, 3.3417721518987342, 3.4430379746835444, 3.5443037974683542, 3.6455696202531644, 3.7468354430379747, 3.848101265822785, 3.9493670886075947, 4.050632911392405, 4.151898734177215, 4.253164556962025, 4.3544303797468356, 4.455696202531645, 4.556962025316456, 4.658227848101266, 4.7594936708860756, 4.860759493670886, 4.962025316455696, 5.063291139240507, 5.1645569620253164, 5.265822784810126, 5.367088607594937, 5.468354430379747, 5.5696202531645564, 5.670886075949367, 5.772151898734177, 5.8734177215189876, 5.974683544303797, 6.075949367088607, 6.177215189873418, 6.2784810126582276, 6.379746835443038, 6.481012658227848, 6.582278481012658, 6.6835443037974684, 6.784810126582278, 6.886075949367089, 6.987341772151899, 7.0886075949367084, 7.189873417721519, 7.291139240506329, 7.3924050632911396, 7.493670886075949, 7.594936708860759, 7.69620253164557, 7.7974683544303796, 7.898734177215189, 8.0], "x": [1.1362744851933722, 1.1070756483462973, 1.078627135247223, 1.0509096537132743, 1.0239044235302281, 0.9975931413495998, 0.9719579842260733, 0.9469815754217433, 0.9226469854853159, 0.898937721395094, 0.8758377070034606, 0.8533312831673092, 0.8314032073949751, 0.8100386335237928, 0.7892230814473951, 0.768942437960705, 0.7491829417159086, 0.7299311829238718, 0.71117412925548, 0.6928990788035834, 0.67509365028429, 0.6577457705416732, 0.6408436765955458, 0.6243759143152047, 0.6083313242887708, 0.5926990318643339, 0.5774684429472614, 0.5626292346177454, 0.5481713491280259, 0.5340849885077662, 0.5203606049240184, 0.5069888965925284, 0.49396080152998906, 0.48126748920317697, 0.4689003587150463, 0.4568510286389662, 0.44511133123518176, 0.43367330709865076, 0.4225292017293544, 0.4116714640405956, 0.4010927354522177, 0.3907858478424349, 0.3807438195632684, 0.37095984316864716, 0.36142728445063055, 0.3521396830737497, 0.3430907456397317, 0.33427434115852944, 0.3256844922308105, 0.31731537638668184, 0.30916132151321, 0.30121680153715735, 0.2934764322126858, 0.28593496679712255, 0.2785872940810702, 0.2714284344456665, 0.2644535365617374, 0.2576578729085104, 0.25103683727862935, 0.2445859422900112, 0.23830081601020855, 0.2321771989385239, 0.22621094037126366, 0.22039799656172943, 0.21473442787208744, 0.20921639609509457, 0.20384016134485863, 0.19860207915929134, 0.19349859941316125, 0.18852626343140363, 0.18368170174078802, 0.17896163184413705, 0.17436285393684725, 0.16988225049038075, 0.16551678478742254, 0.1612634983120857, 0.15711950882996112, 0.15308200818098813, 0.14914825899836762, 0.14531559499359256], "k": 0.25707527855699025}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 0.82), (0.10, 0.80), (0.20, 0.78), (0.31, 0.76), (0.41, 0.74), (0.51, 0.72), (0.61, 0.70), (0.71, 0.68), (0.81, 0.67), (0.92, 0.65), (1.02, 0.63), (1.12, 0.62), (1.22, 0.60), (1.32, 0.59), (1.42, 0.57), (1.53, 0.56), (1.63, 0.54), (1.73, 0.53), (1.83, 0.51), (1.93, 0.50), (2.03, 0.49), (2.14, 0.47), (2.24, 0.46), (2.34, 0.45), (2.44, 0.44), (2.54, 0.43), (2.64, 0.42), (2.75, 0.41), (2.85, 0.40), (2.95, 0.39), (3.05, 0.38), (3.15, 0.37), (3.25, 0.36), (3.36, 0.35), (3.46, 0.34), (3.56, 0.33), (3.66, 0.32), (3.76, 0.31), (3.86, 0.30), (3.97, 0.30), (4.07, 0.29), (4.17, 0.28), (4.27, 0.27), (4.37, 0.27), (4.47, 0.26), (4.58, 0.25), (4.68, 0.25), (4.78, 0.24), (4.88, 0.23), (4.98, 0.23), (5.08, 0.22), (5.19, 0.22), (5.29, 0.21), (5.39, 0.21), (5.49, 0.20), (5.59, 0.20), (5.69, 0.19), (5.80, 0.19), (5.90, 0.18), (6.00, 0.18)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.1016949152542373, 0.2033898305084746, 0.3050847457627119, 0.4067796610169492, 0.5084745762711864, 0.6101694915254238, 0.7118644067796611, 0.8135593220338984, 0.9152542372881356, 1.0169491525423728, 1.1186440677966103, 1.2203389830508475, 1.3220338983050848, 1.4237288135593222, 1.5254237288135595, 1.6271186440677967, 1.728813559322034, 1.8305084745762712, 1.9322033898305087, 2.0338983050847457, 2.135593220338983, 2.2372881355932206, 2.3389830508474576, 2.440677966101695, 2.5423728813559325, 2.6440677966101696, 2.745762711864407, 2.8474576271186445, 2.9491525423728815, 3.050847457627119, 3.152542372881356, 3.2542372881355934, 3.355932203389831, 3.457627118644068, 3.5593220338983054, 3.6610169491525424, 3.76271186440678, 3.8644067796610173, 3.9661016949152543, 4.067796610169491, 4.169491525423729, 4.271186440677966, 4.372881355932203, 4.474576271186441, 4.576271186440678, 4.677966101694915, 4.779661016949153, 4.88135593220339, 4.983050847457627, 5.084745762711865, 5.186440677966102, 5.288135593220339, 5.389830508474577, 5.491525423728814, 5.593220338983051, 5.694915254237289, 5.796610169491526, 5.898305084745763, 6.0], "x": [0.8225581192790713, 0.8013223057706441, 0.7806347439356341, 0.7604812560374069, 0.7408480628215864, 0.7217217318119629, 0.7030891818577656, 0.6849376677595304, 0.6672547675819042, 0.6500283834383948, 0.633246727040402, 0.6168983091138123, 0.6009719499417486, 0.5854567650063465, 0.5703421485186455, 0.5556177556353544, 0.5412735064764255, 0.5272995702665996, 0.5136863782747748, 0.5004246302820997, 0.487505262617651, 0.47491943828802713, 0.4626585418510371, 0.4507141798965634, 0.43907818178460545, 0.42774258799715775, 0.416699642734251, 0.4059417913046433, 0.3954616733776261, 0.385252118180347, 0.37530614145626606, 0.3656169380523494, 0.3561778784408285, 0.3469825055046084, 0.33802452756720125, 0.3292978164202739, 0.32079640269850457, 0.3125144694137367, 0.3044463487482736, 0.29658651839287464, 0.2889296015980031, 0.2814703601298227, 0.2742036913799764, 0.2671246260046572, 0.2602283221595549, 0.25351005813226946, 0.24696523746860535, 0.2405893830722208, 0.23437813422861462, 0.2283272407328991, 0.22243256174788123, 0.2166900643223422, 0.2110958197996358, 0.20564600103756422, 0.2003368789601559, 0.1951648211561061, 0.1901262892114499, 0.18521783628913985, 0.18043610423683665, 0.1757778210966406], "k": 0.2571997209890723}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 1.69), (0.10, 1.57), (0.20, 1.45), (0.31, 1.34), (0.41, 1.25), (0.51, 1.15), (0.61, 1.07), (0.71, 0.99), (0.81, 0.92), (0.92, 0.85), (1.02, 0.79), (1.12, 0.73), (1.22, 0.68), (1.32, 0.63), (1.42, 0.58), (1.53, 0.54), (1.63, 0.50), (1.73, 0.46), (1.83, 0.43), (1.93, 0.40), (2.03, 0.37), (2.14, 0.34), (2.24, 0.32), (2.34, 0.29), (2.44, 0.27), (2.54, 0.25), (2.64, 0.23), (2.75, 0.22), (2.85, 0.20), (2.95, 0.19), (3.05, 0.17), (3.15, 0.16), (3.25, 0.15), (3.36, 0.14), (3.46, 0.13), (3.56, 0.12), (3.66, 0.11), (3.76, 0.10), (3.86, 0.09), (3.97, 0.09), (4.07, 0.08), (4.17, 0.07), (4.27, 0.07), (4.37, 0.06), (4.47, 0.06), (4.58, 0.05), (4.68, 0.05), (4.78, 0.05), (4.88, 0.04), (4.98, 0.04), (5.08, 0.04), (5.19, 0.03), (5.29, 0.03), (5.39, 0.03), (5.49, 0.03), (5.59, 0.03), (5.69, 0.02), (5.80, 0.02), (5.90, 0.02), (6.00, 0.02)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.1016949152542373, 0.2033898305084746, 0.3050847457627119, 0.4067796610169492, 0.5084745762711864, 0.6101694915254238, 0.7118644067796611, 0.8135593220338984, 0.9152542372881356, 1.0169491525423728, 1.1186440677966103, 1.2203389830508475, 1.3220338983050848, 1.4237288135593222, 1.5254237288135595, 1.6271186440677967, 1.728813559322034, 1.8305084745762712, 1.9322033898305087, 2.0338983050847457, 2.135593220338983, 2.2372881355932206, 2.3389830508474576, 2.440677966101695, 2.5423728813559325, 2.6440677966101696, 2.745762711864407, 2.8474576271186445, 2.9491525423728815, 3.050847457627119, 3.152542372881356, 3.2542372881355934, 3.355932203389831, 3.457627118644068, 3.5593220338983054, 3.6610169491525424, 3.76271186440678, 3.8644067796610173, 3.9661016949152543, 4.067796610169491, 4.169491525423729, 4.271186440677966, 4.372881355932203, 4.474576271186441, 4.576271186440678, 4.677966101694915, 4.779661016949153, 4.88135593220339, 4.983050847457627, 5.084745762711865, 5.186440677966102, 5.288135593220339, 5.389830508474577, 5.491525423728814, 5.593220338983051, 5.694915254237289, 5.796610169491526, 5.898305084745763, 6.0], "x": [1.6902910641267694, 1.5662232206804345, 1.451261945072547, 1.3447388702088106, 1.2460345709558016, 1.1545753078295349, 1.0698291199599732, 0.991303341420128, 0.9185413729434418, 0.8511201557741309, 0.7886476769327833, 0.7307606988324266, 0.6771226593935274, 0.6274216405554099, 0.5813686827166505, 0.5386960322297099, 0.4991555757405833, 0.4625174022206136, 0.4285684812428362, 0.39711142153734114, 0.3679633198908906, 0.34095469854660543, 0.3159285176368505, 0.29273926370137626, 0.27125210944607364, 0.2513421189333969, 0.2328935292523983, 0.21579906992217718, 0.19995935107811824, 0.1852822709327492, 0.1716824946702086, 0.15908094517456323, 0.1474043539976522, 0.13658482795575766, 0.12655945852049802, 0.11726995456952359, 0.1086623017668857, 0.10068645386188736, 0.09329603982315558, 0.08644808577724858, 0.08010277087309839, 0.07422320527045181, 0.06877519905329753, 0.06372707861291219, 0.059049491435690285, 0.05471524105412127, 0.050699125806382625, 0.046977794235432656, 0.04352960958822902, 0.04033452299991144, 0.037373957002416094, 0.03463069716646859, 0.0320887935927098, 0.029733466372435523, 0.027551021341990993, 0.025528768437718802, 0.023654949068765592, 0.02191866893586342, 0.020309831968995253, 0.018819084179701105], "k": 0.7496307659303704}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 0.81), (0.10, 0.79), (0.20, 0.78), (0.30, 0.76), (0.41, 0.75), (0.51, 0.74), (0.61, 0.72), (0.71, 0.71), (0.81, 0.70), (0.91, 0.69), (1.01, 0.67), (1.11, 0.66), (1.22, 0.65), (1.32, 0.64), (1.42, 0.63), (1.52, 0.61), (1.62, 0.60), (1.72, 0.59), (1.82, 0.58), (1.92, 0.57), (2.03, 0.56), (2.13, 0.55), (2.23, 0.54), (2.33, 0.53), (2.43, 0.52), (2.53, 0.51), (2.63, 0.50), (2.73, 0.49), (2.84, 0.49), (2.94, 0.48), (3.04, 0.47), (3.14, 0.46), (3.24, 0.45), (3.34, 0.44), (3.44, 0.43), (3.54, 0.43), (3.65, 0.42), (3.75, 0.41), (3.85, 0.40), (3.95, 0.40), (4.05, 0.39), (4.15, 0.38), (4.25, 0.38), (4.35, 0.37), (4.46, 0.36), (4.56, 0.36), (4.66, 0.35), (4.76, 0.34), (4.86, 0.34), (4.96, 0.33), (5.06, 0.33), (5.16, 0.32), (5.27, 0.31), (5.37, 0.31), (5.47, 0.30), (5.57, 0.30), (5.67, 0.29), (5.77, 0.29), (5.87, 0.28), (5.97, 0.28), (6.08, 0.27), (6.18, 0.27), (6.28, 0.26), (6.38, 0.26), (6.48, 0.25), (6.58, 0.25), (6.68, 0.24), (6.78, 0.24), (6.89, 0.23), (6.99, 0.23), (7.09, 0.23), (7.19, 0.22), (7.29, 0.22), (7.39, 0.21), (7.49, 0.21), (7.59, 0.21), (7.70, 0.20), (7.80, 0.20), (7.90, 0.20), (8.00, 0.19)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.10126582278481013, 0.20253164556962025, 0.3037974683544304, 0.4050632911392405, 0.5063291139240507, 0.6075949367088608, 0.7088607594936709, 0.810126582278481, 0.9113924050632911, 1.0126582278481013, 1.1139240506329113, 1.2151898734177216, 1.3164556962025316, 1.4177215189873418, 1.5189873417721518, 1.620253164556962, 1.7215189873417722, 1.8227848101265822, 1.9240506329113924, 2.0253164556962027, 2.1265822784810124, 2.2278481012658227, 2.329113924050633, 2.430379746835443, 2.5316455696202533, 2.632911392405063, 2.7341772151898733, 2.8354430379746836, 2.9367088607594938, 3.0379746835443036, 3.1392405063291138, 3.240506329113924, 3.3417721518987342, 3.4430379746835444, 3.5443037974683542, 3.6455696202531644, 3.7468354430379747, 3.848101265822785, 3.9493670886075947, 4.050632911392405, 4.151898734177215, 4.253164556962025, 4.3544303797468356, 4.455696202531645, 4.556962025316456, 4.658227848101266, 4.7594936708860756, 4.860759493670886, 4.962025316455696, 5.063291139240507, 5.1645569620253164, 5.265822784810126, 5.367088607594937, 5.468354430379747, 5.5696202531645564, 5.670886075949367, 5.772151898734177, 5.8734177215189876, 5.974683544303797, 6.075949367088607, 6.177215189873418, 6.2784810126582276, 6.379746835443038, 6.481012658227848, 6.582278481012658, 6.6835443037974684, 6.784810126582278, 6.886075949367089, 6.987341772151899, 7.0886075949367084, 7.189873417721519, 7.291139240506329, 7.3924050632911396, 7.493670886075949, 7.594936708860759, 7.69620253164557, 7.7974683544303796, 7.898734177215189, 8.0], "x": [0.806816311184648, 0.7922842739204072, 0.7780140526301981, 0.7640008169032021, 0.7502399814875652, 0.7367269988603666, 0.7234574035726091, 0.7104268127799908, 0.6976309208192678, 0.6850655070139698, 0.6727264157108993, 0.6606095705130289, 0.6487109686395797, 0.6370266787041708, 0.6255528404803656, 0.6142856589634652, 0.6032214121463597, 0.5923564473349473, 0.5816871789564596, 0.5712100870381474, 0.5609217116965495, 0.5508186520765339, 0.5408975695290219, 0.5311551833583481, 0.5215882691497561, 0.5121936588152471, 0.5029682540784998, 0.4939090105957933, 0.485012938413986, 0.4762771026182499, 0.46769861553735764, 0.45927464169939836, 0.45100239691377475, 0.44287914613882584, 0.4349022068248584, 0.4270689446147898, 0.41937677160481684, 0.41182314638717044, 0.4044055736975637, 0.39712160319940143, 0.38996882840184205, 0.3829448859374214, 0.37604745550932833, 0.3692742587352222, 0.3626230578436384, 0.356091655222377, 0.3496778929509087, 0.34337965273435833, 0.33719485370856955, 0.3311214523254015, 0.3251574424068864, 0.3193008543419387, 0.3135497532653889, 0.307902238970139, 0.3023564452419226, 0.29691053921264254, 0.2915627208444941, 0.28631122390774894, 0.281154313713197, 0.2760902866227199, 0.27111746991678887, 0.2662342213368351, 0.2614389286511931, 0.25673000825935155, 0.25210590260205823, 0.24756508384977616, 0.2431060519338056, 0.23872733393634787, 0.2344274836484419, 0.23020508113996152, 0.2260587311993554, 0.2219870633615128, 0.21798873246527417, 0.2140624176032558, 0.21020682169823127, 0.20642067108968667, 0.20270271508753174, 0.1990517251759985, 0.19546649510849665, 0.19194584045800706], "k": 0.17948534750203982}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 1.68), (0.11, 1.57), (0.22, 1.47), (0.33, 1.37), (0.44, 1.28), (0.55, 1.20), (0.66, 1.12), (0.77, 1.04), (0.88, 0.98), (0.99, 0.91), (1.10, 0.85), (1.21, 0.80), (1.32, 0.74), (1.43, 0.69), (1.54, 0.65), (1.65, 0.61), (1.76, 0.57), (1.87, 0.53), (1.98, 0.49), (2.09, 0.46), (2.20, 0.43), (2.31, 0.40), (2.42, 0.38), (2.53, 0.35), (2.64, 0.33), (2.75, 0.31), (2.86, 0.29), (2.97, 0.27), (3.08, 0.25), (3.19, 0.23), (3.30, 0.22), (3.41, 0.20), (3.52, 0.19), (3.63, 0.18), (3.74, 0.17), (3.85, 0.16), (3.96, 0.15), (4.07, 0.14), (4.18, 0.13), (4.29, 0.12), (4.40, 0.11), (4.51, 0.10), (4.62, 0.10), (4.73, 0.09), (4.84, 0.08), (4.95, 0.08), (5.06, 0.07), (5.17, 0.07), (5.28, 0.06), (5.39, 0.06), (5.50, 0.06), (5.61, 0.05), (5.72, 0.05), (5.83, 0.05), (5.94, 0.04), (6.06, 0.04), (6.17, 0.04), (6.28, 0.04), (6.39, 0.03), (6.50, 0.03), (6.61, 0.03), (6.72, 0.03), (6.83, 0.02), (6.94, 0.02), (7.05, 0.02), (7.16, 0.02), (7.27, 0.02), (7.38, 0.02), (7.49, 0.02), (7.60, 0.02), (7.71, 0.01), (7.82, 0.01), (7.93, 0.01), (8.04, 0.01), (8.15, 0.01), (8.26, 0.01), (8.37, 0.01), (8.48, 0.01), (8.59, 0.01), (8.70, 0.01), (8.81, 0.01), (8.92, 0.01), (9.03, 0.01), (9.14, 0.01), (9.25, 0.01), (9.36, 0.01), (9.47, 0.00), (9.58, 0.00), (9.69, 0.00), (9.80, 0.00), (9.91, 0.00), (10.02, 0.00), (10.13, 0.00), (10.24, 0.00), (10.35, 0.00), (10.46, 0.00), (10.57, 0.00), (10.68, 0.00), (10.79, 0.00), (10.90, 0.00), (11.01, 0.00), (11.12, 0.00), (11.23, 0.00), (11.34, 0.00), (11.45, 0.00), (11.56, 0.00), (11.67, 0.00), (11.78, 0.00), (11.89, 0.00), (12.00, 0.00)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.11009174311926606, 0.22018348623853212, 0.3302752293577982, 0.44036697247706424, 0.5504587155963303, 0.6605504587155964, 0.7706422018348624, 0.8807339449541285, 0.9908256880733946, 1.1009174311926606, 1.2110091743119267, 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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 1.82), (0.06, 1.77), (0.12, 1.73), (0.17, 1.68), (0.23, 1.64), (0.29, 1.60), (0.35, 1.56), (0.41, 1.52), (0.46, 1.48), (0.52, 1.44), (0.58, 1.40), (0.64, 1.37), (0.70, 1.33), (0.75, 1.30), (0.81, 1.26), (0.87, 1.23), (0.93, 1.20), (0.99, 1.17), (1.04, 1.14), (1.10, 1.11), (1.16, 1.08), (1.22, 1.05), (1.28, 1.02), (1.33, 1.00), (1.39, 0.97), (1.45, 0.95), (1.51, 0.92), (1.57, 0.90), (1.62, 0.87), (1.68, 0.85), (1.74, 0.83), (1.80, 0.81), (1.86, 0.79), (1.91, 0.77), (1.97, 0.75), (2.03, 0.73), (2.09, 0.71), (2.14, 0.69), (2.20, 0.67), (2.26, 0.66), (2.32, 0.64), (2.38, 0.62), (2.43, 0.61), (2.49, 0.59), (2.55, 0.58), (2.61, 0.56), (2.67, 0.55), (2.72, 0.53), (2.78, 0.52), (2.84, 0.50), (2.90, 0.49), (2.96, 0.48), (3.01, 0.47), (3.07, 0.45), (3.13, 0.44), (3.19, 0.43), (3.25, 0.42), (3.30, 0.41), (3.36, 0.40), (3.42, 0.39), (3.48, 0.38), (3.54, 0.37), (3.59, 0.36), (3.65, 0.35), (3.71, 0.34), (3.77, 0.33), (3.83, 0.32), (3.88, 0.32), (3.94, 0.31), (4.00, 0.30)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.057971014492753624, 0.11594202898550725, 0.17391304347826086, 0.2318840579710145, 0.2898550724637681, 0.34782608695652173, 0.4057971014492754, 0.463768115942029, 0.5217391304347826, 0.5797101449275363, 0.6376811594202899, 0.6956521739130435, 0.7536231884057971, 0.8115942028985508, 0.8695652173913043, 0.927536231884058, 0.9855072463768116, 1.0434782608695652, 1.1014492753623188, 1.1594202898550725, 1.2173913043478262, 1.2753623188405798, 1.3333333333333333, 1.391304347826087, 1.4492753623188406, 1.5072463768115942, 1.565217391304348, 1.6231884057971016, 1.681159420289855, 1.7391304347826086, 1.7971014492753623, 1.855072463768116, 1.9130434782608696, 1.9710144927536233, 2.028985507246377, 2.0869565217391304, 2.1449275362318843, 2.2028985507246377, 2.260869565217391, 2.318840579710145, 2.3768115942028984, 2.4347826086956523, 2.4927536231884058, 2.5507246376811596, 2.608695652173913, 2.6666666666666665, 2.7246376811594204, 2.782608695652174, 2.8405797101449277, 2.898550724637681, 2.956521739130435, 3.0144927536231885, 3.072463768115942, 3.130434782608696, 3.1884057971014492, 3.246376811594203, 3.3043478260869565, 3.36231884057971, 3.420289855072464, 3.4782608695652173, 3.536231884057971, 3.5942028985507246, 3.6521739130434785, 3.710144927536232, 3.7681159420289854, 3.8260869565217392, 3.8840579710144927, 3.9420289855072466, 4.0], "x": [1.8208575785320105, 1.773810960617707, 1.7279798991541542, 1.683332997710964, 1.6398396600999439, 1.597470079271028, 1.5561952367152032, 1.515986838305262, 1.4768173296799527, 1.4386598649269982, 1.4014882829190107, 1.3652771209790846, 1.3300015865498536, 1.295637511516457, 1.2621613388945343, 1.2295501063609628, 1.1977814421174506, 1.166833596486805, 1.1366853758976496, 1.107316122397464, 1.0787057028831042, 1.0508345042606981, 1.0236834310331726, 0.9972338770517524, 0.9714677168821136, 0.9463672938080034, 0.9219154056084746, 0.8980952967361654, 0.8748906431136725, 0.852285542170274, 0.8302645040388784, 0.8088124370552198, 0.7879146432650432, 0.7675568027563235, 0.7477249626397374, 0.7284055279320821, 0.7095852545763293, 0.6912512484369929, 0.6733909459014099, 0.6559921097663015, 0.6390428226478982, 0.6225314708235885, 0.6064467347230938, 0.5907775906294939, 0.5755132987430902, 0.5606433982456446, 0.546157699586791, 0.5320462766081264, 0.5182994607041456, 0.5049078306635585, 0.49186220864901575, 0.4791536546364145, 0.4667734595828821, 0.45471313937018104, 0.4429644291391459, 0.43151927769354614, 0.4203698419457289, 0.4095084810287063, 0.39892775176222006, 0.3886204035237528, 0.37857937306484796, 0.3687977789810039, 0.35926891802904265, 0.3499862603062322, 0.34094344457415543, 0.3321342736463336, 0.32355271072725833, 0.31519287515634153, 0.3070490378226721, 0.2991156173325599], "k": 0.4515581752675736}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 1.31), (0.10, 1.28), (0.20, 1.25), (0.31, 1.21), (0.41, 1.18), (0.51, 1.15), (0.61, 1.12), (0.71, 1.09), (0.81, 1.06), (0.92, 1.03), (1.02, 1.01), (1.12, 0.98), (1.22, 0.96), (1.32, 0.93), (1.42, 0.91), (1.53, 0.88), (1.63, 0.86), (1.73, 0.84), (1.83, 0.82), (1.93, 0.79), (2.03, 0.77), (2.14, 0.75), (2.24, 0.73), (2.34, 0.71), (2.44, 0.70), (2.54, 0.68), (2.64, 0.66), (2.75, 0.64), (2.85, 0.63), (2.95, 0.61), (3.05, 0.59), (3.15, 0.58), (3.25, 0.56), (3.36, 0.55), (3.46, 0.53), (3.56, 0.52), (3.66, 0.51), (3.76, 0.49), (3.86, 0.48), (3.97, 0.47), (4.07, 0.46), (4.17, 0.44), (4.27, 0.43), (4.37, 0.42), (4.47, 0.41), (4.58, 0.40), (4.68, 0.39), (4.78, 0.38), (4.88, 0.37), (4.98, 0.36), (5.08, 0.35), (5.19, 0.34), (5.29, 0.33), (5.39, 0.32), (5.49, 0.31), (5.59, 0.31), (5.69, 0.30), (5.80, 0.29), (5.90, 0.28), (6.00, 0.28)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.1016949152542373, 0.2033898305084746, 0.3050847457627119, 0.4067796610169492, 0.5084745762711864, 0.6101694915254238, 0.7118644067796611, 0.8135593220338984, 0.9152542372881356, 1.0169491525423728, 1.1186440677966103, 1.2203389830508475, 1.3220338983050848, 1.4237288135593222, 1.5254237288135595, 1.6271186440677967, 1.728813559322034, 1.8305084745762712, 1.9322033898305087, 2.0338983050847457, 2.135593220338983, 2.2372881355932206, 2.3389830508474576, 2.440677966101695, 2.5423728813559325, 2.6440677966101696, 2.745762711864407, 2.8474576271186445, 2.9491525423728815, 3.050847457627119, 3.152542372881356, 3.2542372881355934, 3.355932203389831, 3.457627118644068, 3.5593220338983054, 3.6610169491525424, 3.76271186440678, 3.8644067796610173, 3.9661016949152543, 4.067796610169491, 4.169491525423729, 4.271186440677966, 4.372881355932203, 4.474576271186441, 4.576271186440678, 4.677966101694915, 4.779661016949153, 4.88135593220339, 4.983050847457627, 5.084745762711865, 5.186440677966102, 5.288135593220339, 5.389830508474577, 5.491525423728814, 5.593220338983051, 5.694915254237289, 5.796610169491526, 5.898305084745763, 6.0], "x": [1.3129193246381585, 1.2786395927409067, 1.245254882308119, 1.2127418248026693, 1.1810776638078777, 1.1502402334908355, 1.1202079616856673, 1.090959819825516, 1.0624753341923776, 1.0347345649146802, 1.0077180831975854, 0.9814069816517275, 0.9557828592203519, 0.9308277921198511, 0.906524306716635, 0.8828553801725565, 0.859804418807461, 0.8373552927954897, 0.8154923021360505, 0.7942001540507111, 0.7734639388489778, 0.753269135903563, 0.7336016075849763, 0.7144475900390531, 0.6957936752196799, 0.6776268063559903, 0.6599342667124444, 0.6427036711091195, 0.6259229594179975, 0.6095803845378305, 0.5936645068894899, 0.5781641863009026, 0.5630685721138414, 0.5483671001777545, 0.5340494798323973, 0.5201056871580266, 0.5065259579532743, 0.49330078481757295, 0.4804209123564314, 0.4678773253058314, 0.455661245794, 0.4437641273661938, 0.43217763809781, 0.42089366556690144, 0.40990431188058746, 0.39920188666284473, 0.38877889978833446, 0.3786280523898887, 0.36874223882734314, 0.35911453936371796, 0.3497382153132457, 0.34060670296237955, 0.33171360991081983, 0.3230527112848616, 0.31461794508541724, 0.3064034076926952, 0.29840334821151704, 0.2906121665854069, 0.28302440921795996, 0.27563476512587815], "k": 0.2601552902104656}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 0.70), (0.10, 0.66), (0.20, 0.63), (0.31, 0.60), (0.41, 0.57), (0.51, 0.54), (0.61, 0.51), (0.71, 0.48), (0.81, 0.46), (0.92, 0.44), (1.02, 0.41), (1.12, 0.39), (1.22, 0.37), (1.32, 0.35), (1.42, 0.34), (1.53, 0.32), (1.63, 0.30), (1.73, 0.29), (1.83, 0.27), (1.93, 0.26), (2.03, 0.25), (2.14, 0.23), (2.24, 0.22), (2.34, 0.21), (2.44, 0.20), (2.54, 0.19), (2.64, 0.18), (2.75, 0.17), (2.85, 0.16), (2.95, 0.15), (3.05, 0.15), (3.15, 0.14), (3.25, 0.13), (3.36, 0.13), (3.46, 0.12), (3.56, 0.11), (3.66, 0.11), (3.76, 0.10), (3.86, 0.10), (3.97, 0.09), (4.07, 0.09), (4.17, 0.08), (4.27, 0.08), (4.37, 0.07), (4.47, 0.07), (4.58, 0.07), (4.68, 0.06), (4.78, 0.06), (4.88, 0.06), (4.98, 0.05), (5.08, 0.05), (5.19, 0.05), (5.29, 0.05), (5.39, 0.04), (5.49, 0.04), (5.59, 0.04), (5.69, 0.04), (5.80, 0.04), (5.90, 0.03), (6.00, 0.03)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.1016949152542373, 0.2033898305084746, 0.3050847457627119, 0.4067796610169492, 0.5084745762711864, 0.6101694915254238, 0.7118644067796611, 0.8135593220338984, 0.9152542372881356, 1.0169491525423728, 1.1186440677966103, 1.2203389830508475, 1.3220338983050848, 1.4237288135593222, 1.5254237288135595, 1.6271186440677967, 1.728813559322034, 1.8305084745762712, 1.9322033898305087, 2.0338983050847457, 2.135593220338983, 2.2372881355932206, 2.3389830508474576, 2.440677966101695, 2.5423728813559325, 2.6440677966101696, 2.745762711864407, 2.8474576271186445, 2.9491525423728815, 3.050847457627119, 3.152542372881356, 3.2542372881355934, 3.355932203389831, 3.457627118644068, 3.5593220338983054, 3.6610169491525424, 3.76271186440678, 3.8644067796610173, 3.9661016949152543, 4.067796610169491, 4.169491525423729, 4.271186440677966, 4.372881355932203, 4.474576271186441, 4.576271186440678, 4.677966101694915, 4.779661016949153, 4.88135593220339, 4.983050847457627, 5.084745762711865, 5.186440677966102, 5.288135593220339, 5.389830508474577, 5.491525423728814, 5.593220338983051, 5.694915254237289, 5.796610169491526, 5.898305084745763, 6.0], "x": [0.6957576291917122, 0.6606257685456742, 0.6272678548221459, 0.5955943181954986, 0.5655201247900564, 0.5369645101434708, 0.5098507715386889, 0.48410613128434693, 0.4596615001045858, 0.43645118573357655, 0.41441281990670786, 0.39348728310665826, 0.37361837432603356, 0.3547527299690149, 0.33683969536224284, 0.3198311694366487, 0.3036814796966057, 0.2883472586724282, 0.27378733063387595, 0.25996260136334215, 0.2468359434490946, 0.2343721012153012, 0.22253760992698052, 0.21130069979789304, 0.20063118953130507, 0.19050043215076837, 0.18088122238296042, 0.17174772887937706, 0.16307542583418336, 0.15484102519481432, 0.14702241660877705, 0.1395986039376316, 0.13254965261783397, 0.12585663383094142, 0.11950157515731882, 0.11346741094215261, 0.10773793679187937, 0.10229776988021058, 0.09713230243527071, 0.09222766122656173, 0.08757067743655181, 0.08314884627064603, 0.07895029180798141, 0.07496374110877423, 0.07117848994747121, 0.06758437189768039, 0.06417173686984716, 0.06093142185403448, 0.0578547239190326, 0.05493338206587287, 0.05215955246499312, 0.04952578510497562, 0.0470250082505176, 0.0446505074546322, 0.042395905150740355, 0.04025514760155614, 0.0382224869278025, 0.03629246348631287, 0.03445989495147494, 0.03271986173812739], "k": 0.5095031220308249}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 0.44), (0.06, 0.42), (0.12, 0.40), (0.17, 0.38), (0.23, 0.36), (0.29, 0.35), (0.35, 0.33), (0.41, 0.31), (0.46, 0.30), (0.52, 0.28), (0.58, 0.27), (0.64, 0.26), (0.70, 0.24), (0.75, 0.23), (0.81, 0.22), (0.87, 0.21), (0.93, 0.20), (0.99, 0.19), (1.04, 0.18), (1.10, 0.17), (1.16, 0.16), (1.22, 0.16), (1.28, 0.15), (1.33, 0.14), (1.39, 0.13), (1.45, 0.13), (1.51, 0.12), (1.57, 0.12), (1.62, 0.11), (1.68, 0.10), (1.74, 0.10), (1.80, 0.09), (1.86, 0.09), (1.91, 0.09), (1.97, 0.08), (2.03, 0.08), (2.09, 0.07), (2.14, 0.07), (2.20, 0.07), (2.26, 0.06), (2.32, 0.06), (2.38, 0.06), (2.43, 0.05), (2.49, 0.05), (2.55, 0.05), (2.61, 0.05), (2.67, 0.04), (2.72, 0.04), (2.78, 0.04), (2.84, 0.04), (2.90, 0.04), (2.96, 0.04), (3.01, 0.03), (3.07, 0.03), (3.13, 0.03), (3.19, 0.03), (3.25, 0.03), (3.30, 0.03), (3.36, 0.02), (3.42, 0.02), (3.48, 0.02), (3.54, 0.02), (3.59, 0.02), (3.65, 0.02), (3.71, 0.02), (3.77, 0.02), (3.83, 0.02), (3.88, 0.02), (3.94, 0.02), (4.00, 0.01)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.057971014492753624, 0.11594202898550725, 0.17391304347826086, 0.2318840579710145, 0.2898550724637681, 0.34782608695652173, 0.4057971014492754, 0.463768115942029, 0.5217391304347826, 0.5797101449275363, 0.6376811594202899, 0.6956521739130435, 0.7536231884057971, 0.8115942028985508, 0.8695652173913043, 0.927536231884058, 0.9855072463768116, 1.0434782608695652, 1.1014492753623188, 1.1594202898550725, 1.2173913043478262, 1.2753623188405798, 1.3333333333333333, 1.391304347826087, 1.4492753623188406, 1.5072463768115942, 1.565217391304348, 1.6231884057971016, 1.681159420289855, 1.7391304347826086, 1.7971014492753623, 1.855072463768116, 1.9130434782608696, 1.9710144927536233, 2.028985507246377, 2.0869565217391304, 2.1449275362318843, 2.2028985507246377, 2.260869565217391, 2.318840579710145, 2.3768115942028984, 2.4347826086956523, 2.4927536231884058, 2.5507246376811596, 2.608695652173913, 2.6666666666666665, 2.7246376811594204, 2.782608695652174, 2.8405797101449277, 2.898550724637681, 2.956521739130435, 3.0144927536231885, 3.072463768115942, 3.130434782608696, 3.1884057971014492, 3.246376811594203, 3.3043478260869565, 3.36231884057971, 3.420289855072464, 3.4782608695652173, 3.536231884057971, 3.5942028985507246, 3.6521739130434785, 3.710144927536232, 3.7681159420289854, 3.8260869565217392, 3.8840579710144927, 3.9420289855072466, 4.0], "x": [0.44280948632828093, 0.4213232261089459, 0.40087952332681553, 0.38142779399448135, 0.3629199149075382, 0.3453100888252552, 0.3285547336492307, 0.3126123698323622, 0.2974435831676988, 0.28301086583626983, 0.2692784746099874, 0.256212370196634, 0.2437802638109038, 0.23195141285428242, 0.22069652472136078, 0.2099877511857869, 0.19979859545937684, 0.19010384449467138, 0.18087950869755123, 0.17210276131012278, 0.16375188497765117, 0.1558062157957291, 0.14824609301296657, 0.14105280395596898, 0.13420854855167624, 0.12769639529329477, 0.12150023051314705, 0.1156047192601423, 0.10999527535969908, 0.10465801618396492, 0.09957973487766501, 0.09474786487934266, 0.09015044973770006, 0.08577611360979993, 0.08161403158616211, 0.07765390482091933, 0.07388593363601362, 0.0703007942922685, 0.0668896148433407, 0.06364395354113946, 0.06055578009138076, 0.057617454650606595, 0.054821703835491904, 0.0521616095798392, 0.049630591136880106, 0.04722238447884981, 0.04493102949239548, 0.04275085719990313, 0.04067647352999885, 0.03870274364334069, 0.036824783946292766, 0.03503794875941783, 0.03333781533521596, 0.03172017633286202, 0.030181029780317403, 0.028716567032772998, 0.027323163318486283, 0.025997371093947386, 0.024735910490066987, 0.02353565893270616, 0.02239364642150151, 0.021307047791359453, 0.02027317377220794, 0.01928946556635965, 0.0183534893166202, 0.017462929760541916, 0.016615583324748346, 0.015809353061376392, 0.015042243552996023, 0.01431235528169045], "k": 0.8580040693202049}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 0.52), (0.10, 0.48), (0.20, 0.44), (0.30, 0.40), (0.40, 0.37), (0.51, 0.34), (0.61, 0.31), (0.71, 0.29), (0.81, 0.26), (0.91, 0.24), (1.01, 0.22), (1.11, 0.21), (1.21, 0.19), (1.31, 0.17), (1.42, 0.16), (1.52, 0.15), (1.62, 0.13), (1.72, 0.12), (1.82, 0.11), (1.92, 0.10), (2.02, 0.10), (2.12, 0.09), (2.22, 0.08), (2.33, 0.07), (2.43, 0.07), (2.53, 0.06), (2.63, 0.06), (2.73, 0.05), (2.83, 0.05), (2.93, 0.05), (3.03, 0.04), (3.13, 0.04), (3.24, 0.04), (3.34, 0.03), (3.44, 0.03), (3.54, 0.03), (3.64, 0.03), (3.74, 0.02), (3.84, 0.02), (3.94, 0.02), (4.04, 0.02), (4.15, 0.02), (4.25, 0.02), (4.35, 0.01), (4.45, 0.01), (4.55, 0.01), (4.65, 0.01), (4.75, 0.01), (4.85, 0.01), (4.96, 0.01), (5.06, 0.01), (5.16, 0.01), (5.26, 0.01), (5.36, 0.01), (5.46, 0.01), (5.56, 0.01), (5.66, 0.00), (5.76, 0.00), (5.87, 0.00), (5.97, 0.00), (6.07, 0.00), (6.17, 0.00), (6.27, 0.00), (6.37, 0.00), (6.47, 0.00), (6.57, 0.00), (6.67, 0.00), (6.78, 0.00), (6.88, 0.00), (6.98, 0.00), (7.08, 0.00), (7.18, 0.00), (7.28, 0.00), (7.38, 0.00), (7.48, 0.00), (7.58, 0.00), (7.69, 0.00), (7.79, 0.00), (7.89, 0.00), (7.99, 0.00), (8.09, 0.00), (8.19, 0.00), (8.29, 0.00), (8.39, 0.00), (8.49, 0.00), (8.60, 0.00), (8.70, 0.00), (8.80, 0.00), (8.90, 0.00), (9.00, 0.00)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.10112359550561797, 0.20224719101123595, 0.3033707865168539, 0.4044943820224719, 0.5056179775280899, 0.6067415730337078, 0.7078651685393258, 0.8089887640449438, 0.9101123595505618, 1.0112359550561798, 1.1123595505617978, 1.2134831460674156, 1.3146067415730336, 1.4157303370786516, 1.5168539325842696, 1.6179775280898876, 1.7191011235955056, 1.8202247191011236, 1.9213483146067416, 2.0224719101123596, 2.1235955056179776, 2.2247191011235956, 2.3258426966292136, 2.426966292134831, 2.528089887640449, 2.629213483146067, 2.730337078651685, 2.831460674157303, 2.932584269662921, 3.033707865168539, 3.134831460674157, 3.235955056179775, 3.337078651685393, 3.438202247191011, 3.539325842696629, 3.640449438202247, 3.741573033707865, 3.842696629213483, 3.943820224719101, 4.044943820224719, 4.146067415730337, 4.247191011235955, 4.348314606741573, 4.449438202247191, 4.550561797752809, 4.651685393258427, 4.752808988764045, 4.853932584269662, 4.955056179775281, 5.056179775280898, 5.157303370786517, 5.258426966292134, 5.359550561797753, 5.46067415730337, 5.561797752808989, 5.662921348314606, 5.764044943820225, 5.865168539325842, 5.966292134831461, 6.067415730337078, 6.168539325842697, 6.269662921348314, 6.370786516853933, 6.47191011235955, 6.573033707865168, 6.674157303370786, 6.775280898876404, 6.876404494382022, 6.97752808988764, 7.078651685393258, 7.179775280898876, 7.280898876404494, 7.382022471910112, 7.48314606741573, 7.584269662921348, 7.685393258426966, 7.786516853932584, 7.887640449438202, 7.98876404494382, 8.089887640449438, 8.191011235955056, 8.292134831460674, 8.393258426966291, 8.49438202247191, 8.595505617977528, 8.696629213483146, 8.797752808988763, 8.898876404494382, 9.0], "x": [0.5167271864628541, 0.47511519666642754, 0.436854190884703, 0.4016743464616558, 0.3693275045829755, 0.3395855814951739, 0.3122388180280476, 0.2870942281472891, 0.2639745537238974, 0.24271669844232602, 0.22317073765412962, 0.20519881210356355, 0.18867416540952714, 0.1734802504075319, 0.15950988956579723, 0.14666456433482608, 0.13485367329118514, 0.12399391450082183, 0.11400869132236165, 0.10482757741842891, 0.09638581828036957, 0.0886238735713564, 0.08148699749016669, 0.07492485089766167, 0.06889115562746627, 0.06334335262392216, 0.058242315437481734, 0.05355206321350954, 0.04923951805222954, 0.04527426072158897, 0.04162832667780342, 0.038275998578595684, 0.03519363428195857, 0.032359491675435864, 0.029753583384721102, 0.027357527972215495, 0.025154427420101707, 0.02312874108735907, 0.021266184451132195, 0.019553622151355525, 0.017978973017241422, 0.016531128144772003, 0.015199879000597563, 0.01397583347167717, 0.012850360221356218, 0.011815521363770938, 0.010864018184184922, 0.00998913991163909, 0.009184714876412899, 0.008445070021092972, 0.007764988856218173, 0.0071396749068885585, 0.006564717545010689, 0.006036061312404415, 0.005549977823827373, 0.005103038381846418, 0.004692090927172028, 0.004314237082429798, 0.00396681192467527, 0.0036473649715418007, 0.0033536428668615513, 0.0030835741883850423, 0.0028352541198178906, 0.0026069313985633735, 0.002396995568306259, 0.002203965654036379, 0.002026480409199356, 0.0018632879984482468, 0.0017132372665218775, 0.0015752698142403629, 0.0014484132071617042, 0.0013317723937193763, 0.001224524504355385, 0.0011259136419815574, 0.0010352437347838504, 0.0009518754033548475, 0.0008752209612467213, 0.000804739273921035, 0.0007399335708756446, 0.0006803467711537897, 0.0006255583573896033, 0.0005751821732879068, 0.0005288626273156368, 0.0004862730165134572, 0.000447113443616295, 0.0004111073949617389, 0.00037800082015170125, 0.00034756048593487915, 0.00031957145229834813, 0.00029383626937778875], "k": 0.8302493518912311}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 0.88), (0.11, 0.72), (0.22, 0.58), (0.33, 0.47), (0.44, 0.38), (0.55, 0.31), (0.66, 0.25), (0.77, 0.20), (0.88, 0.17), (0.99, 0.13), (1.10, 0.11), (1.21, 0.09), (1.32, 0.07), (1.43, 0.06), (1.54, 0.05), (1.65, 0.04), (1.76, 0.03), (1.87, 0.03), (1.98, 0.02), (2.09, 0.02), (2.20, 0.01), (2.31, 0.01), (2.42, 0.01), (2.53, 0.01), (2.64, 0.01), (2.75, 0.00), (2.86, 0.00), (2.97, 0.00), (3.08, 0.00), (3.19, 0.00), (3.30, 0.00), (3.41, 0.00), (3.52, 0.00), (3.63, 0.00), (3.74, 0.00), (3.85, 0.00), (3.96, 0.00), (4.07, 0.00), (4.18, 0.00), (4.29, 0.00), (4.40, 0.00), (4.51, 0.00), (4.62, 0.00), (4.73, 0.00), (4.84, 0.00), (4.95, 0.00), (5.06, 0.00), (5.17, 0.00), (5.28, 0.00), (5.39, 0.00), (5.50, 0.00), (5.61, 0.00), (5.72, 0.00), (5.83, 0.00), (5.94, 0.00), (6.06, 0.00), (6.17, 0.00), (6.28, 0.00), (6.39, 0.00), (6.50, 0.00), (6.61, 0.00), (6.72, 0.00), (6.83, 0.00), (6.94, 0.00), (7.05, 0.00), (7.16, 0.00), (7.27, 0.00), (7.38, 0.00), (7.49, 0.00), (7.60, 0.00), (7.71, 0.00), (7.82, 0.00), (7.93, 0.00), (8.04, 0.00), (8.15, 0.00), (8.26, 0.00), (8.37, 0.00), (8.48, 0.00), (8.59, 0.00), (8.70, 0.00), (8.81, 0.00), (8.92, 0.00), (9.03, 0.00), (9.14, 0.00), (9.25, 0.00), (9.36, 0.00), (9.47, 0.00), (9.58, 0.00), (9.69, 0.00), (9.80, 0.00), (9.91, 0.00), (10.02, 0.00), (10.13, 0.00), (10.24, 0.00), (10.35, 0.00), (10.46, 0.00), (10.57, 0.00), (10.68, 0.00), (10.79, 0.00), (10.90, 0.00), (11.01, 0.00), (11.12, 0.00), (11.23, 0.00), (11.34, 0.00), (11.45, 0.00), (11.56, 0.00), (11.67, -0.00), (11.78, -0.00), (11.89, -0.00), (12.00, -0.00)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.11009174311926606, 0.22018348623853212, 0.3302752293577982, 0.44036697247706424, 0.5504587155963303, 0.6605504587155964, 0.7706422018348624, 0.8807339449541285, 0.9908256880733946, 1.1009174311926606, 1.2110091743119267, 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2.5569686379477613e-05, 2.0747531563733107e-05, 1.6834558077179923e-05, 1.3660258274643347e-05, 1.1084158855422293e-05, 8.993990737031604e-06, 7.297089242915493e-06, 5.920095768583779e-06, 4.803299162266555e-06, 3.897620175596398e-06, 3.162718861438746e-06, 2.5664953996404508e-06, 2.0824003537192547e-06, 1.6895954829296062e-06, 1.3705393775352764e-06, 1.1124977523849503e-06, 9.030128764656607e-07, 7.332578340595591e-07, 5.952558536054379e-07, 4.832247304263967e-07, 3.9212239018384816e-07, 3.1786438913425594e-07, 2.5834402328372444e-07, 2.0975997796343123e-07, 1.7042553635681716e-07, 1.3856806602753617e-07, 1.1260477178349536e-07, 9.158353600772464e-08, 7.43847697504196e-08, 6.017300203399786e-08, 4.867085251472564e-08, 3.844368196018497e-08, 3.153461094235152e-08, 2.5615080854362827e-08, 2.066141739063425e-08, 1.657837789598792e-08, 1.3355956846081635e-08, 1.0847014865056249e-08, 8.799896865257436e-09, 7.209045360573135e-09, 5.93027379080919e-09, 4.865627704259407e-09, 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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 1.37), (0.10, 1.31), (0.20, 1.26), (0.30, 1.21), (0.40, 1.16), (0.51, 1.12), (0.61, 1.07), (0.71, 1.03), (0.81, 0.99), (0.91, 0.95), (1.01, 0.91), (1.11, 0.88), (1.21, 0.84), (1.31, 0.81), (1.42, 0.78), (1.52, 0.75), (1.62, 0.72), (1.72, 0.69), (1.82, 0.66), (1.92, 0.63), (2.02, 0.61), (2.12, 0.59), (2.22, 0.56), (2.33, 0.54), (2.43, 0.52), (2.53, 0.50), (2.63, 0.48), (2.73, 0.46), (2.83, 0.44), (2.93, 0.42), (3.03, 0.41), (3.13, 0.39), (3.24, 0.38), (3.34, 0.36), (3.44, 0.35), (3.54, 0.33), (3.64, 0.32), (3.74, 0.31), (3.84, 0.29), (3.94, 0.28), (4.04, 0.27), (4.15, 0.26), (4.25, 0.25), (4.35, 0.24), (4.45, 0.23), (4.55, 0.22), (4.65, 0.21), (4.75, 0.20), (4.85, 0.20), (4.96, 0.19), (5.06, 0.18), (5.16, 0.17), (5.26, 0.17), (5.36, 0.16), (5.46, 0.15), (5.56, 0.15), (5.66, 0.14), (5.76, 0.14), (5.87, 0.13), (5.97, 0.13), (6.07, 0.12), (6.17, 0.12), (6.27, 0.11), (6.37, 0.11), (6.47, 0.10), (6.57, 0.10), (6.67, 0.10), (6.78, 0.09), (6.88, 0.09), (6.98, 0.08), (7.08, 0.08), (7.18, 0.08), (7.28, 0.07), (7.38, 0.07), (7.48, 0.07), (7.58, 0.07), (7.69, 0.06), (7.79, 0.06), (7.89, 0.06), (7.99, 0.06), (8.09, 0.05), (8.19, 0.05), (8.29, 0.05), (8.39, 0.05), (8.49, 0.05), (8.60, 0.04), (8.70, 0.04), (8.80, 0.04), (8.90, 0.04), (9.00, 0.04)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.10112359550561797, 0.20224719101123595, 0.3033707865168539, 0.4044943820224719, 0.5056179775280899, 0.6067415730337078, 0.7078651685393258, 0.8089887640449438, 0.9101123595505618, 1.0112359550561798, 1.1123595505617978, 1.2134831460674156, 1.3146067415730336, 1.4157303370786516, 1.5168539325842696, 1.6179775280898876, 1.7191011235955056, 1.8202247191011236, 1.9213483146067416, 2.0224719101123596, 2.1235955056179776, 2.2247191011235956, 2.3258426966292136, 2.426966292134831, 2.528089887640449, 2.629213483146067, 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7.98876404494382, 8.089887640449438, 8.191011235955056, 8.292134831460674, 8.393258426966291, 8.49438202247191, 8.595505617977528, 8.696629213483146, 8.797752808988763, 8.898876404494382, 9.0], "x": [1.3677518449014898, 1.313614131345902, 1.2616192498524896, 1.2116823950461049, 1.163722118619613, 1.1176601885894095, 1.0734214583555104, 1.0309337411110402, 0.990127762312657, 0.9509369910917839, 0.9132974669489043, 0.8771477291267988, 0.8424288482835356, 0.8090842109323895, 0.7770594044508867, 0.7463021867246874, 0.7167623871586551, 0.6883918194524543, 0.6611442025561763, 0.6349750888951176, 0.6098417893070798, 0.5857033050887354, 0.5625202650263091, 0.5402548487610259, 0.5188707238477643, 0.49833300780924167, 0.47860820239684976, 0.45966414284473356, 0.4414699182018419, 0.42399584742467616, 0.4072134322480918, 0.39109529204058385, 0.3756151321789489, 0.36074770168742226, 0.34646874646520254, 0.3327549737385173, 0.31958401457792635, 0.3069343824516533, 0.2947854420789314, 0.28311737617318117, 0.2719111501545494, 0.2611484835548016, 0.2508118205527708, 0.2408842977314492, 0.23134972040427806, 0.22219253706938366, 0.21339781109290715, 0.20495119316360855, 0.19683890500709328, 0.18904771498899214, 0.1815649122402575, 0.17437828953254753, 0.16747612463183317, 0.16084715933690527, 0.1544805780425438, 0.14836599540929826, 0.14249343834870587, 0.13685332641325054, 0.1314364582135371, 0.12623399803547503, 0.12123746021256869, 0.11643869262908131, 0.11182986726996011, 0.10740346695681628, 0.10315227068190724, 0.09906934286528038, 0.09514802356917318, 0.09138191684750688, 0.08776487793931345, 0.08429100638467629, 0.08095463596652776, 0.07775032542706088, 0.0746728476195654, 0.07171718208141953, 0.06887850694692761, 0.0661521901670174, 0.0635337840807657, 0.06101901907552029, 0.05860379278721064, 0.056284164638554304, 0.05405634978168093, 0.051916715326228075, 0.049861771164899926, 0.047888165005017615, 0.045992676963920474, 0.04417221532618869, 0.042423810628741794, 0.04074461063983618, 0.039131875810562954, 0.037582975279271874], "k": 0.39937472037973365}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 0.77), (0.10, 0.76), (0.20, 0.74), (0.31, 0.73), (0.41, 0.71), (0.51, 0.70), (0.61, 0.68), (0.71, 0.67), (0.81, 0.66), (0.92, 0.64), (1.02, 0.63), (1.12, 0.62), (1.22, 0.61), (1.32, 0.60), (1.42, 0.58), (1.53, 0.57), (1.63, 0.56), (1.73, 0.55), (1.83, 0.54), (1.93, 0.53), (2.03, 0.52), (2.14, 0.51), (2.24, 0.50), (2.34, 0.49), (2.44, 0.48), (2.54, 0.47), (2.64, 0.46), (2.75, 0.45), (2.85, 0.44), (2.95, 0.43), (3.05, 0.43), (3.15, 0.42), (3.25, 0.41), (3.36, 0.40), (3.46, 0.39), (3.56, 0.39), (3.66, 0.38), (3.76, 0.37), (3.86, 0.36), (3.97, 0.36), (4.07, 0.35), (4.17, 0.34), (4.27, 0.34), (4.37, 0.33), (4.47, 0.32), (4.58, 0.32), (4.68, 0.31), (4.78, 0.30), (4.88, 0.30), (4.98, 0.29), (5.08, 0.29), (5.19, 0.28), (5.29, 0.27), (5.39, 0.27), (5.49, 0.26), (5.59, 0.26), (5.69, 0.25), (5.80, 0.25), (5.90, 0.24), (6.00, 0.24)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.1016949152542373, 0.2033898305084746, 0.3050847457627119, 0.4067796610169492, 0.5084745762711864, 0.6101694915254238, 0.7118644067796611, 0.8135593220338984, 0.9152542372881356, 1.0169491525423728, 1.1186440677966103, 1.2203389830508475, 1.3220338983050848, 1.4237288135593222, 1.5254237288135595, 1.6271186440677967, 1.728813559322034, 1.8305084745762712, 1.9322033898305087, 2.0338983050847457, 2.135593220338983, 2.2372881355932206, 2.3389830508474576, 2.440677966101695, 2.5423728813559325, 2.6440677966101696, 2.745762711864407, 2.8474576271186445, 2.9491525423728815, 3.050847457627119, 3.152542372881356, 3.2542372881355934, 3.355932203389831, 3.457627118644068, 3.5593220338983054, 3.6610169491525424, 3.76271186440678, 3.8644067796610173, 3.9661016949152543, 4.067796610169491, 4.169491525423729, 4.271186440677966, 4.372881355932203, 4.474576271186441, 4.576271186440678, 4.677966101694915, 4.779661016949153, 4.88135593220339, 4.983050847457627, 5.084745762711865, 5.186440677966102, 5.288135593220339, 5.389830508474577, 5.491525423728814, 5.593220338983051, 5.694915254237289, 5.796610169491526, 5.898305084745763, 6.0], "x": [0.770780663813059, 0.755645344843834, 0.7408072902469645, 0.726260562170329, 0.7119994782323413, 0.698018427381178, 0.684311911032215, 0.6708745366129226, 0.6577010262677825, 0.6447861962447864, 0.6321249661721567, 0.6197123561297209, 0.6075434838099003, 0.5956135627279779, 0.5839178956697383, 0.5724518834076683, 0.5612110198340882, 0.5501908890352648, 0.5393871622196799, 0.5287955887368969, 0.5184120016715095, 0.5082323143046428, 0.4982525166386792, 0.4884686738740043, 0.4788769418215378, 0.46947355304956073, 0.46025481288869696, 0.451217100122923, 0.44235685744421854, 0.4336705986823533, 0.42515490543541445, 0.41680642677009383, 0.40862188149110396, 0.4005980506318048, 0.39273177817835503, 0.38501997034683316, 0.3774595943131688, 0.37004767638879554, 0.36278130100877015, 0.3556576105601905, 0.34867380346380816, 0.34182713268550835, 0.3351149049888021, 0.32853448078951597, 0.3220832721507874, 0.31575874147419786, 0.30955840120270267, 0.303479813651248, 0.29752058807739507, 0.2916783803814132, 0.2859508921798597, 0.28033586985869885, 0.27483110417301765, 0.2694344308429555, 0.26414372734565744, 0.2589569129820346, 0.25387194830083676, 0.2488868344491258, 0.2439996118132709, 0.23920835617873912], "k": 0.19501148836177576}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 2.96), (0.11, 2.45), (0.22, 2.02), (0.33, 1.67), (0.44, 1.38), (0.55, 1.14), (0.66, 0.94), (0.77, 0.78), (0.88, 0.65), (0.99, 0.53), (1.10, 0.44), (1.21, 0.36), (1.32, 0.30), (1.43, 0.25), (1.54, 0.21), (1.65, 0.17), (1.76, 0.14), (1.87, 0.12), (1.98, 0.10), (2.09, 0.08), (2.20, 0.07), (2.31, 0.05), (2.42, 0.04), (2.53, 0.04), (2.64, 0.03), (2.75, 0.03), (2.86, 0.02), (2.97, 0.02), (3.08, 0.01), (3.19, 0.01), (3.30, 0.01), (3.41, 0.01), (3.52, 0.01), (3.63, 0.01), (3.74, 0.00), (3.85, 0.00), (3.96, 0.00), (4.07, 0.00), (4.18, 0.00), (4.29, 0.00), (4.40, 0.00), (4.51, 0.00), (4.62, 0.00), (4.73, 0.00), (4.84, 0.00), (4.95, 0.00), (5.06, 0.00), (5.17, 0.00), (5.28, 0.00), (5.39, 0.00), (5.50, 0.00), (5.61, 0.00), (5.72, 0.00), (5.83, 0.00), (5.94, 0.00), (6.06, 0.00), (6.17, 0.00), (6.28, 0.00), (6.39, 0.00), (6.50, 0.00), (6.61, 0.00), (6.72, 0.00), (6.83, 0.00), (6.94, 0.00), (7.05, 0.00), (7.16, 0.00), (7.27, 0.00), (7.38, 0.00), (7.49, 0.00), (7.60, 0.00), (7.71, 0.00), (7.82, 0.00), (7.93, 0.00), (8.04, 0.00), (8.15, 0.00), (8.26, 0.00), (8.37, 0.00), (8.48, 0.00), (8.59, 0.00), (8.70, 0.00), (8.81, 0.00), (8.92, 0.00), (9.03, 0.00), (9.14, 0.00), (9.25, 0.00), (9.36, 0.00), (9.47, 0.00), (9.58, 0.00), (9.69, 0.00), (9.80, 0.00), (9.91, 0.00), (10.02, 0.00), (10.13, 0.00), (10.24, 0.00), (10.35, 0.00), (10.46, 0.00), (10.57, 0.00), (10.68, 0.00), (10.79, 0.00), (10.90, 0.00), (11.01, 0.00), (11.12, 0.00), (11.23, 0.00), (11.34, 0.00), (11.45, 0.00), (11.56, 0.00), (11.67, 0.00), (11.78, 0.00), (11.89, 0.00), (12.00, 0.00)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.11009174311926606, 0.22018348623853212, 0.3302752293577982, 0.44036697247706424, 0.5504587155963303, 0.6605504587155964, 0.7706422018348624, 0.8807339449541285, 0.9908256880733946, 1.1009174311926606, 1.2110091743119267, 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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 0.89), (0.06, 0.87), (0.12, 0.86), (0.17, 0.85), (0.23, 0.83), (0.29, 0.82), (0.35, 0.81), (0.41, 0.79), (0.46, 0.78), (0.52, 0.77), (0.58, 0.76), (0.64, 0.75), (0.70, 0.73), (0.75, 0.72), (0.81, 0.71), (0.87, 0.70), (0.93, 0.69), (0.99, 0.68), (1.04, 0.67), (1.10, 0.66), (1.16, 0.65), (1.22, 0.64), (1.28, 0.63), (1.33, 0.62), (1.39, 0.61), (1.45, 0.60), (1.51, 0.59), (1.57, 0.58), (1.62, 0.57), (1.68, 0.56), (1.74, 0.55), (1.80, 0.54), (1.86, 0.54), (1.91, 0.53), (1.97, 0.52), (2.03, 0.51), (2.09, 0.50), (2.14, 0.50), (2.20, 0.49), (2.26, 0.48), (2.32, 0.47), (2.38, 0.47), (2.43, 0.46), (2.49, 0.45), (2.55, 0.44), (2.61, 0.44), (2.67, 0.43), (2.72, 0.42), (2.78, 0.42), (2.84, 0.41), (2.90, 0.40), (2.96, 0.40), (3.01, 0.39), (3.07, 0.39), (3.13, 0.38), (3.19, 0.37), (3.25, 0.37), (3.30, 0.36), (3.36, 0.36), (3.42, 0.35), (3.48, 0.35), (3.54, 0.34), (3.59, 0.33), (3.65, 0.33), (3.71, 0.32), (3.77, 0.32), (3.83, 0.31), (3.88, 0.31), (3.94, 0.30), (4.00, 0.30)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.057971014492753624, 0.11594202898550725, 0.17391304347826086, 0.2318840579710145, 0.2898550724637681, 0.34782608695652173, 0.4057971014492754, 0.463768115942029, 0.5217391304347826, 0.5797101449275363, 0.6376811594202899, 0.6956521739130435, 0.7536231884057971, 0.8115942028985508, 0.8695652173913043, 0.927536231884058, 0.9855072463768116, 1.0434782608695652, 1.1014492753623188, 1.1594202898550725, 1.2173913043478262, 1.2753623188405798, 1.3333333333333333, 1.391304347826087, 1.4492753623188406, 1.5072463768115942, 1.565217391304348, 1.6231884057971016, 1.681159420289855, 1.7391304347826086, 1.7971014492753623, 1.855072463768116, 1.9130434782608696, 1.9710144927536233, 2.028985507246377, 2.0869565217391304, 2.1449275362318843, 2.2028985507246377, 2.260869565217391, 2.318840579710145, 2.3768115942028984, 2.4347826086956523, 2.4927536231884058, 2.5507246376811596, 2.608695652173913, 2.6666666666666665, 2.7246376811594204, 2.782608695652174, 2.8405797101449277, 2.898550724637681, 2.956521739130435, 3.0144927536231885, 3.072463768115942, 3.130434782608696, 3.1884057971014492, 3.246376811594203, 3.3043478260869565, 3.36231884057971, 3.420289855072464, 3.4782608695652173, 3.536231884057971, 3.5942028985507246, 3.6521739130434785, 3.710144927536232, 3.7681159420289854, 3.8260869565217392, 3.8840579710144927, 3.9420289855072466, 4.0], "x": [0.8871141528568303, 0.8732677410231211, 0.8596375293517757, 0.8462200142758268, 0.8330119243627157, 0.8200099908257144, 0.8072109942359306, 0.794611767026268, 0.7822091916653916, 0.7700001978635368, 0.7579817703524829, 0.7461509304778488, 0.7345047506580619, 0.723040348125474, 0.7117548862248979, 0.7006455713680331, 0.6897096538615656, 0.6789444237574592, 0.6683472172676056, 0.6579154134222006, 0.6476464330053965, 0.6375377377401669, 0.6275868290416405, 0.6177912429100823, 0.6081485544590353, 0.5986563764223066, 0.5893123574293209, 0.5801141811083298, 0.5710595652429482, 0.5621462699639433, 0.5533720938002361, 0.5447348666956567, 0.5362324533963948, 0.5278627524338955, 0.5196236906302003, 0.5115132280755446, 0.5035293568800582, 0.495670099812002, 0.4879335110474015, 0.48031767759957567, 0.4728207147479729, 0.46544076706376525, 0.45817600799479286, 0.4510246397759446, 0.4439848927414677, 0.4370550246280196, 0.4302333202450862, 0.4235180911059233, 0.41690767567326825, 0.41040043806228055, 0.40399476773488574, 0.39768907914453655, 0.3914818116823231, 0.3853714294777348, 0.37935642037571027, 0.3734352956236661, 0.3676065895976547, 0.36186886028348303, 0.35622068808340895, 0.3506606751417706, 0.34518744530383527, 0.33979964375384347, 0.3344959366617989, 0.3292750108390037, 0.32413557362012985, 0.3190763537274976, 0.3140960991748657, 0.30919357743940956, 0.3043675753695135, 0.2996168989334389], "k": 0.27136726561749613}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 1.11), (0.06, 1.05), (0.12, 1.00), (0.17, 0.95), (0.23, 0.90), (0.29, 0.85), (0.35, 0.81), (0.41, 0.77), (0.46, 0.73), (0.52, 0.69), (0.58, 0.65), (0.64, 0.62), (0.70, 0.59), (0.75, 0.56), (0.81, 0.53), (0.87, 0.50), (0.93, 0.48), (0.99, 0.45), (1.04, 0.43), (1.10, 0.41), (1.16, 0.39), (1.22, 0.37), (1.28, 0.35), (1.33, 0.33), (1.39, 0.31), (1.45, 0.30), (1.51, 0.28), (1.57, 0.27), (1.62, 0.25), (1.68, 0.24), (1.74, 0.23), (1.80, 0.22), (1.86, 0.20), (1.91, 0.19), (1.97, 0.18), (2.03, 0.17), (2.09, 0.17), (2.14, 0.16), (2.20, 0.15), (2.26, 0.14), (2.32, 0.13), (2.38, 0.13), (2.43, 0.12), (2.49, 0.11), (2.55, 0.11), (2.61, 0.10), (2.67, 0.10), (2.72, 0.09), (2.78, 0.09), (2.84, 0.08), (2.90, 0.08), (2.96, 0.07), (3.01, 0.07), (3.07, 0.07), (3.13, 0.06), (3.19, 0.06), (3.25, 0.06), (3.30, 0.05), (3.36, 0.05), (3.42, 0.05), (3.48, 0.05), (3.54, 0.04), (3.59, 0.04), (3.65, 0.04), (3.71, 0.04), (3.77, 0.04), (3.83, 0.03), (3.88, 0.03), (3.94, 0.03), (4.00, 0.03)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.057971014492753624, 0.11594202898550725, 0.17391304347826086, 0.2318840579710145, 0.2898550724637681, 0.34782608695652173, 0.4057971014492754, 0.463768115942029, 0.5217391304347826, 0.5797101449275363, 0.6376811594202899, 0.6956521739130435, 0.7536231884057971, 0.8115942028985508, 0.8695652173913043, 0.927536231884058, 0.9855072463768116, 1.0434782608695652, 1.1014492753623188, 1.1594202898550725, 1.2173913043478262, 1.2753623188405798, 1.3333333333333333, 1.391304347826087, 1.4492753623188406, 1.5072463768115942, 1.565217391304348, 1.6231884057971016, 1.681159420289855, 1.7391304347826086, 1.7971014492753623, 1.855072463768116, 1.9130434782608696, 1.9710144927536233, 2.028985507246377, 2.0869565217391304, 2.1449275362318843, 2.2028985507246377, 2.260869565217391, 2.318840579710145, 2.3768115942028984, 2.4347826086956523, 2.4927536231884058, 2.5507246376811596, 2.608695652173913, 2.6666666666666665, 2.7246376811594204, 2.782608695652174, 2.8405797101449277, 2.898550724637681, 2.956521739130435, 3.0144927536231885, 3.072463768115942, 3.130434782608696, 3.1884057971014492, 3.246376811594203, 3.3043478260869565, 3.36231884057971, 3.420289855072464, 3.4782608695652173, 3.536231884057971, 3.5942028985507246, 3.6521739130434785, 3.710144927536232, 3.7681159420289854, 3.8260869565217392, 3.8840579710144927, 3.9420289855072466, 4.0], "x": [1.1079183142158309, 1.0509122684326915, 0.9968393493657743, 0.9455486500727811, 0.8968970342111581, 0.8507486960761572, 0.8069748173145498, 0.7654533023912984, 0.7260682332706769, 0.6887096005690156, 0.6532732057505444, 0.619660137487217, 0.5877765684022611, 0.5575335148354013, 0.528846566744106, 0.5016356575755798, 0.4758248399371562, 0.45134207713649666, 0.42811903973663984, 0.4060908947892236, 0.38519616119901146, 0.3653765350269765, 0.34657669610672964, 0.3287441712085935, 0.3118291933046033, 0.29578454623091377, 0.28056544993356036, 0.26612942539739753, 0.2524361830767428, 0.2394475035359192, 0.2271271347033012, 0.21544068975436756, 0.20435555074824666, 0.19384077897163127, 0.1838670249755825, 0.1744064544129925, 0.1654326632170055, 0.1569206021171975, 0.14884651583335812, 0.14118786805500333, 0.13392328201265422, 0.1270324844168007, 0.12049624070563793, 0.11429630783081096, 0.10841538344460011, 0.10283705136225452, 0.09754574284765136, 0.09252669060396167, 0.08776588437682716, 0.08325003778630864, 0.07896654685371292, 0.07490345508985323, 0.07104942345303357, 0.06739369414850688, 0.06392606329366542, 0.060636854034950574, 0.05751688753426708, 0.05455745505617776, 0.05175029579328663, 0.04908757223208311, 0.04656185474567354, 0.0441660944043304, 0.041893602959757095, 0.039738037794340604, 0.037693383952755795, 0.0357539344825912, 0.03391427578095592, 0.03216927395625024, 0.030514058512321692, 0.02894400905669092], "k": 0.91121871835725}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 1.92), (0.06, 1.82), (0.12, 1.73), (0.17, 1.64), (0.23, 1.55), (0.29, 1.47), (0.35, 1.40), (0.41, 1.32), (0.46, 1.26), (0.52, 1.19), (0.58, 1.13), (0.64, 1.07), (0.70, 1.02), (0.75, 0.96), (0.81, 0.91), (0.87, 0.87), (0.93, 0.82), (0.99, 0.78), (1.04, 0.74), (1.10, 0.70), (1.16, 0.66), (1.22, 0.63), (1.28, 0.60), (1.33, 0.57), (1.39, 0.54), (1.45, 0.51), (1.51, 0.48), (1.57, 0.46), (1.62, 0.43), (1.68, 0.41), (1.74, 0.39), (1.80, 0.37), (1.86, 0.35), (1.91, 0.33), (1.97, 0.32), (2.03, 0.30), (2.09, 0.28), (2.14, 0.27), (2.20, 0.26), (2.26, 0.24), (2.32, 0.23), (2.38, 0.22), (2.43, 0.21), (2.49, 0.20), (2.55, 0.19), (2.61, 0.18), (2.67, 0.17), (2.72, 0.16), (2.78, 0.15), (2.84, 0.14), (2.90, 0.14), (2.96, 0.13), (3.01, 0.12), (3.07, 0.12), (3.13, 0.11), (3.19, 0.10), (3.25, 0.10), (3.30, 0.09), (3.36, 0.09), (3.42, 0.08), (3.48, 0.08), (3.54, 0.08), (3.59, 0.07), (3.65, 0.07), (3.71, 0.06), (3.77, 0.06), (3.83, 0.06), (3.88, 0.06), (3.94, 0.05), (4.00, 0.05)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.057971014492753624, 0.11594202898550725, 0.17391304347826086, 0.2318840579710145, 0.2898550724637681, 0.34782608695652173, 0.4057971014492754, 0.463768115942029, 0.5217391304347826, 0.5797101449275363, 0.6376811594202899, 0.6956521739130435, 0.7536231884057971, 0.8115942028985508, 0.8695652173913043, 0.927536231884058, 0.9855072463768116, 1.0434782608695652, 1.1014492753623188, 1.1594202898550725, 1.2173913043478262, 1.2753623188405798, 1.3333333333333333, 1.391304347826087, 1.4492753623188406, 1.5072463768115942, 1.565217391304348, 1.6231884057971016, 1.681159420289855, 1.7391304347826086, 1.7971014492753623, 1.855072463768116, 1.9130434782608696, 1.9710144927536233, 2.028985507246377, 2.0869565217391304, 2.1449275362318843, 2.2028985507246377, 2.260869565217391, 2.318840579710145, 2.3768115942028984, 2.4347826086956523, 2.4927536231884058, 2.5507246376811596, 2.608695652173913, 2.6666666666666665, 2.7246376811594204, 2.782608695652174, 2.8405797101449277, 2.898550724637681, 2.956521739130435, 3.0144927536231885, 3.072463768115942, 3.130434782608696, 3.1884057971014492, 3.246376811594203, 3.3043478260869565, 3.36231884057971, 3.420289855072464, 3.4782608695652173, 3.536231884057971, 3.5942028985507246, 3.6521739130434785, 3.710144927536232, 3.7681159420289854, 3.8260869565217392, 3.8840579710144927, 3.9420289855072466, 4.0], "x": [1.9182577935678182, 1.8192340596504568, 1.7253220649413081, 1.636257956534807, 1.5517914992653, 1.4716853185826033, 1.3957143583916942, 1.3236652308488646, 1.2553353619450525, 1.1905327742342098, 1.1290754295827523, 1.0707906109430552, 1.0155145550799445, 0.9630919447875982, 0.9133754803333596, 0.8662254653532505, 0.8215094211748853, 0.7791017069294237, 0.7388831335852427, 0.7007406956421757, 0.6645672442720415, 0.6302611424155445, 0.5977259780005285, 0.566870329182233, 0.5376075045026668, 0.5098552786591574, 0.48353567059160824, 0.45857472567762464, 0.43490230774329286, 0.4124519002959751, 0.3911604222429871, 0.3709680467981968, 0.35181803669832373, 0.3336565829106512, 0.3164326537938618, 0.3000978514771436, 0.2846062818846221, 0.26991441361997015, 0.2559809640458978, 0.24276678517112665, 0.23023474346299533, 0.2183496277625518, 0.2070780430041147, 0.19638831555428, 0.18625041168598785, 0.17663584344248667, 0.16751759526720802, 0.15887004806160285, 0.1506689010813452, 0.14289111192650528, 0.13551482596094047, 0.12851931582239867, 0.12188492689389789, 0.1155930157751806, 0.10962590320899061, 0.10396682483580409, 0.09859987979670391, 0.09350998708255943, 0.08868284204105244, 0.0841048816778956, 0.07976324434983874, 0.0756457291189464, 0.07174076595627445, 0.06803738415154717, 0.0645251773649329, 0.06119427638962658, 0.05803532264652911, 0.05503943963521653, 0.05219820882424201, 0.04950364721590834], "k": 0.9142815738653819}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 1.51), (0.10, 1.39), (0.20, 1.28), (0.30, 1.18), (0.40, 1.09), (0.51, 1.00), (0.61, 0.93), (0.71, 0.85), (0.81, 0.79), (0.91, 0.73), (1.01, 0.67), (1.11, 0.62), (1.21, 0.57), (1.31, 0.53), (1.42, 0.48), (1.52, 0.45), (1.62, 0.41), (1.72, 0.38), (1.82, 0.35), (1.92, 0.32), (2.02, 0.30), (2.12, 0.27), (2.22, 0.25), (2.33, 0.23), (2.43, 0.22), (2.53, 0.20), (2.63, 0.18), (2.73, 0.17), (2.83, 0.16), (2.93, 0.14), (3.03, 0.13), (3.13, 0.12), (3.24, 0.11), (3.34, 0.10), (3.44, 0.10), (3.54, 0.09), (3.64, 0.08), (3.74, 0.08), (3.84, 0.07), (3.94, 0.06), (4.04, 0.06), (4.15, 0.05), (4.25, 0.05), (4.35, 0.05), (4.45, 0.04), (4.55, 0.04), (4.65, 0.04), (4.75, 0.03), (4.85, 0.03), (4.96, 0.03), (5.06, 0.03), (5.16, 0.02), (5.26, 0.02), (5.36, 0.02), (5.46, 0.02), (5.56, 0.02), (5.66, 0.02), (5.76, 0.01), (5.87, 0.01), (5.97, 0.01), (6.07, 0.01), (6.17, 0.01), (6.27, 0.01), (6.37, 0.01), (6.47, 0.01), (6.57, 0.01), (6.67, 0.01), (6.78, 0.01), (6.88, 0.01), (6.98, 0.01), (7.08, 0.01), (7.18, 0.00), (7.28, 0.00), (7.38, 0.00), (7.48, 0.00), (7.58, 0.00), (7.69, 0.00), (7.79, 0.00), (7.89, 0.00), (7.99, 0.00), (8.09, 0.00), (8.19, 0.00), (8.29, 0.00), (8.39, 0.00), (8.49, 0.00), (8.60, 0.00), (8.70, 0.00), (8.80, 0.00), (8.90, 0.00), (9.00, 0.00)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.10112359550561797, 0.20224719101123595, 0.3033707865168539, 0.4044943820224719, 0.5056179775280899, 0.6067415730337078, 0.7078651685393258, 0.8089887640449438, 0.9101123595505618, 1.0112359550561798, 1.1123595505617978, 1.2134831460674156, 1.3146067415730336, 1.4157303370786516, 1.5168539325842696, 1.6179775280898876, 1.7191011235955056, 1.8202247191011236, 1.9213483146067416, 2.0224719101123596, 2.1235955056179776, 2.2247191011235956, 2.3258426966292136, 2.426966292134831, 2.528089887640449, 2.629213483146067, 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7.98876404494382, 8.089887640449438, 8.191011235955056, 8.292134831460674, 8.393258426966291, 8.49438202247191, 8.595505617977528, 8.696629213483146, 8.797752808988763, 8.898876404494382, 9.0], "x": [1.505916141509641, 1.3887722983990032, 1.2807409237695995, 1.1811132181089152, 1.0892354229878622, 1.004504831069049, 0.9263652739461468, 0.8543041500508506, 0.7878485897193533, 0.7265625492226092, 0.6700438952305937, 0.6179217867735336, 0.5698542068948932, 0.5255257339904227, 0.4846455462100177, 0.4469453942606272, 0.41217790785043346, 0.38011495300836273, 0.35054614659635586, 0.32327747174141225, 0.2981300033624514, 0.2749387337646943, 0.2535514890682656, 0.23382794226830592, 0.21563867149982946, 0.19886432959618158, 0.1833948477174333, 0.16912872364864234, 0.1559723491259319, 0.1438393967224919, 0.13265025703192665, 0.12233150947481686, 0.11281544933074814, 0.10403963447933705, 0.0959464820260405, 0.08848288810921913, 0.08159988500479506, 0.07525230657689239, 0.06939849761448529, 0.06400005247431784, 0.059021544963214816, 0.05443031166925496, 0.05019622594725663, 0.046291506625990325, 0.04269053147125213, 0.03936967272995627, 0.03630714073208367, 0.03348284075193274, 0.030878240523270612, 0.028476249769032413, 0.02626110771498317, 0.0242182797041642, 0.022334361823974747, 0.02059699170993607, 0.018994770311081433, 0.01751718413902003, 0.016154537990684774, 0.014897891095858054, 0.013738997364830665, 0.012670253196533223, 0.011684645551775525, 0.010775707385413757, 0.009937474823035499, 0.009164447462098834, 0.008451553391340563, 0.007794114614183235, 0.007187817413597359, 0.006628683597271471, 0.006113044168271891, 0.00563751597726994, 0.0051989786333675, 0.004794554752051866, 0.004421590681344, 0.0040776390609709254, 0.0037604431988447844, 0.0034679216630822307, 0.003198155151681254, 0.0029493735507673965, 0.002719944491170915, 0.0025083627372845104, 0.0023132395896568597, 0.0021332947023556406, 0.001967347551157403, 0.0018143092285313731, 0.001673175386265962, 0.0015430200728486362, 0.001422989812478918, 0.0013122964718708591, 0.0012102138171496612, 0.001116072393021665], "k": 0.8008156025830042}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 1.71), (0.10, 1.58), (0.20, 1.47), (0.30, 1.36), (0.40, 1.26), (0.51, 1.17), (0.61, 1.08), (0.71, 1.00), (0.81, 0.93), (0.91, 0.86), (1.01, 0.80), (1.11, 0.74), (1.21, 0.68), (1.31, 0.63), (1.42, 0.59), (1.52, 0.54), (1.62, 0.50), (1.72, 0.47), (1.82, 0.43), (1.92, 0.40), (2.02, 0.37), (2.12, 0.35), (2.22, 0.32), (2.33, 0.30), (2.43, 0.27), (2.53, 0.25), (2.63, 0.24), (2.73, 0.22), (2.83, 0.20), (2.93, 0.19), (3.03, 0.17), (3.13, 0.16), (3.24, 0.15), (3.34, 0.14), (3.44, 0.13), (3.54, 0.12), (3.64, 0.11), (3.74, 0.10), (3.84, 0.09), (3.94, 0.09), (4.04, 0.08), (4.15, 0.08), (4.25, 0.07), (4.35, 0.06), (4.45, 0.06), (4.55, 0.06), (4.65, 0.05), (4.75, 0.05), (4.85, 0.04), (4.96, 0.04), (5.06, 0.04), (5.16, 0.04), (5.26, 0.03), (5.36, 0.03), (5.46, 0.03), (5.56, 0.03), (5.66, 0.02), (5.76, 0.02), (5.87, 0.02), (5.97, 0.02), (6.07, 0.02), (6.17, 0.02), (6.27, 0.02), (6.37, 0.01), (6.47, 0.01), (6.57, 0.01), (6.67, 0.01), (6.78, 0.01), (6.88, 0.01), (6.98, 0.01), (7.08, 0.01), (7.18, 0.01), (7.28, 0.01), (7.38, 0.01), (7.48, 0.01), (7.58, 0.01), (7.69, 0.01), (7.79, 0.00), (7.89, 0.00), (7.99, 0.00), (8.09, 0.00), (8.19, 0.00), (8.29, 0.00), (8.39, 0.00), (8.49, 0.00), (8.60, 0.00), (8.70, 0.00), (8.80, 0.00), (8.90, 0.00), (9.00, 0.00)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.10112359550561797, 0.20224719101123595, 0.3033707865168539, 0.4044943820224719, 0.5056179775280899, 0.6067415730337078, 0.7078651685393258, 0.8089887640449438, 0.9101123595505618, 1.0112359550561798, 1.1123595505617978, 1.2134831460674156, 1.3146067415730336, 1.4157303370786516, 1.5168539325842696, 1.6179775280898876, 1.7191011235955056, 1.8202247191011236, 1.9213483146067416, 2.0224719101123596, 2.1235955056179776, 2.2247191011235956, 2.3258426966292136, 2.426966292134831, 2.528089887640449, 2.629213483146067, 2.730337078651685, 2.831460674157303, 2.932584269662921, 3.033707865168539, 3.134831460674157, 3.235955056179775, 3.337078651685393, 3.438202247191011, 3.539325842696629, 3.640449438202247, 3.741573033707865, 3.842696629213483, 3.943820224719101, 4.044943820224719, 4.146067415730337, 4.247191011235955, 4.348314606741573, 4.449438202247191, 4.550561797752809, 4.651685393258427, 4.752808988764045, 4.853932584269662, 4.955056179775281, 5.056179775280898, 5.157303370786517, 5.258426966292134, 5.359550561797753, 5.46067415730337, 5.561797752808989, 5.662921348314606, 5.764044943820225, 5.865168539325842, 5.966292134831461, 6.067415730337078, 6.168539325842697, 6.269662921348314, 6.370786516853933, 6.47191011235955, 6.573033707865168, 6.674157303370786, 6.775280898876404, 6.876404494382022, 6.97752808988764, 7.078651685393258, 7.179775280898876, 7.280898876404494, 7.382022471910112, 7.48314606741573, 7.584269662921348, 7.685393258426966, 7.786516853932584, 7.887640449438202, 7.98876404494382, 8.089887640449438, 8.191011235955056, 8.292134831460674, 8.393258426966291, 8.49438202247191, 8.595505617977528, 8.696629213483146, 8.797752808988763, 8.898876404494382, 9.0], "x": [1.705835882735367, 1.5808667244301808, 1.4650527316151714, 1.3577232568155297, 1.258256667022793, 1.166077090067176, 1.0806505086041696, 1.0014822740520433, 0.9281138826214854, 0.8601204454293078, 0.7971081942420536, 0.7387122095825782, 0.6845943200953398, 0.6344410688577041, 0.5879620248366556, 0.5448880330085282, 0.5049696412511359, 0.467975664524475, 0.43369185868577265, 0.40191967750333507, 0.37247512032934615, 0.3451876662782589, 0.3198992849650212, 0.2964635232726752, 0.2747446618042837, 0.2546169201013431, 0.23596373402842272, 0.21867707497488648, 0.20265683498171258, 0.18781023306002553, 0.17405129200693728, 0.16130032712812736, 0.14948349631938151, 0.13853236376130018, 0.12838350923645686, 0.11897815794241097, 0.11026183968449028, 0.10218407741445064, 0.09469809461116428, 0.08776053506147011, 0.08133121678349252, 0.07537291038443253, 0.06985110585864786, 0.06473382796471576, 0.05999144056263822, 0.055596479917705804, 0.0515234931250651, 0.04774889207580323, 0.044250817590887434, 0.041009011575162076, 0.038004699908611814, 0.03522048322173767, 0.032640237841549714, 0.030249020575866623, 0.02803298383880193, 0.025979293586319688, 0.024076055749039954, 0.0223122490675732, 0.020677658227241248, 0.01916281717838685, 0.017758953318968172, 0.01645793591687106, 0.015252231038882262, 0.014134855827726446, 0.013099339082388525, 0.012139684268493567, 0.011250333421962272, 0.010426136328170452, 0.009662319854515695, 0.008954460210309559, 0.008298458354850002, 0.007690515008662719, 0.007127109415952555, 0.006604978907238022, 0.006121099467834538, 0.0056726690060814626, 0.005257090499304186, 0.004871957083160951, 0.004515038537735608, 0.004184267723014103, 0.003877729127498104, 0.0035936475343455233, 0.0033303776639635792, 0.0030863950966853316, 0.0028602867053718673, 0.002650742656591147, 0.002456549742957589, 0.0022765833329345562, 0.0021098011185306464, 0.001955237081171569], "k": 0.7523665738393914}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 0.51), (0.06, 0.48), (0.12, 0.45), (0.17, 0.43), (0.23, 0.40), (0.29, 0.38), (0.35, 0.36), (0.41, 0.34), (0.46, 0.32), (0.52, 0.30), (0.58, 0.28), (0.64, 0.27), (0.70, 0.25), (0.75, 0.24), (0.81, 0.22), (0.87, 0.21), (0.93, 0.20), (0.99, 0.19), (1.04, 0.18), (1.10, 0.17), (1.16, 0.16), (1.22, 0.15), (1.28, 0.14), (1.33, 0.13), (1.39, 0.12), (1.45, 0.12), (1.51, 0.11), (1.57, 0.10), (1.62, 0.10), (1.68, 0.09), (1.74, 0.09), (1.80, 0.08), (1.86, 0.08), (1.91, 0.07), (1.97, 0.07), (2.03, 0.06), (2.09, 0.06), (2.14, 0.06), (2.20, 0.05), (2.26, 0.05), (2.32, 0.05), (2.38, 0.04), (2.43, 0.04), (2.49, 0.04), (2.55, 0.04), (2.61, 0.04), (2.67, 0.03), (2.72, 0.03), (2.78, 0.03), (2.84, 0.03), (2.90, 0.03), (2.96, 0.02), (3.01, 0.02), (3.07, 0.02), (3.13, 0.02), (3.19, 0.02), (3.25, 0.02), (3.30, 0.02), (3.36, 0.02), (3.42, 0.02), (3.48, 0.01), (3.54, 0.01), (3.59, 0.01), (3.65, 0.01), (3.71, 0.01), (3.77, 0.01), (3.83, 0.01), (3.88, 0.01), (3.94, 0.01), (4.00, 0.01)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.057971014492753624, 0.11594202898550725, 0.17391304347826086, 0.2318840579710145, 0.2898550724637681, 0.34782608695652173, 0.4057971014492754, 0.463768115942029, 0.5217391304347826, 0.5797101449275363, 0.6376811594202899, 0.6956521739130435, 0.7536231884057971, 0.8115942028985508, 0.8695652173913043, 0.927536231884058, 0.9855072463768116, 1.0434782608695652, 1.1014492753623188, 1.1594202898550725, 1.2173913043478262, 1.2753623188405798, 1.3333333333333333, 1.391304347826087, 1.4492753623188406, 1.5072463768115942, 1.565217391304348, 1.6231884057971016, 1.681159420289855, 1.7391304347826086, 1.7971014492753623, 1.855072463768116, 1.9130434782608696, 1.9710144927536233, 2.028985507246377, 2.0869565217391304, 2.1449275362318843, 2.2028985507246377, 2.260869565217391, 2.318840579710145, 2.3768115942028984, 2.4347826086956523, 2.4927536231884058, 2.5507246376811596, 2.608695652173913, 2.6666666666666665, 2.7246376811594204, 2.782608695652174, 2.8405797101449277, 2.898550724637681, 2.956521739130435, 3.0144927536231885, 3.072463768115942, 3.130434782608696, 3.1884057971014492, 3.246376811594203, 3.3043478260869565, 3.36231884057971, 3.420289855072464, 3.4782608695652173, 3.536231884057971, 3.5942028985507246, 3.6521739130434785, 3.710144927536232, 3.7681159420289854, 3.8260869565217392, 3.8840579710144927, 3.9420289855072466, 4.0], "x": [0.5101131579405276, 0.4806961605429261, 0.45297555622531194, 0.42685352432865126, 0.4022378933636999, 0.37904178092745755, 0.35718330694275396, 0.33658539982756497, 0.31717536407829977, 0.2988846075053872, 0.2816486340559259, 0.26540663247563806, 0.2501012620352498, 0.23567851594981082, 0.22208749572274103, 0.20928023783876343, 0.1972115437407447, 0.1858388233173625, 0.17512194360422484, 0.16502307558644486, 0.15550658061864261, 0.14653888350152464, 0.13808833138152166, 0.13012510474524433, 0.12262109843621564, 0.1155498305013528, 0.10888634527720727, 0.10260712790536265, 0.09669001801089003, 0.09111413396352717, 0.08585979766083701, 0.08090846647682627, 0.07624266522984094, 0.07184592904007472, 0.06770274436586415, 0.06379848625857606, 0.06011937759712598, 0.05665243552595078, 0.053385422559372446, 0.050306811118417304, 0.04740573619577278, 0.0446719584633751, 0.04209583223255297, 0.03966826493871344, 0.037380689161837594, 0.03522503338443125, 0.03319368861524437, 0.031279486472923786, 0.02947567262680488, 0.027775879838932628, 0.02617411021525473, 0.02466471106311345, 0.023242354540658778, 0.02190202192097103, 0.02063898466480473, 0.019448785022235723, 0.018327222170136683, 0.017270335826657972, 0.016274397171952396, 0.015335892471822418, 0.014451508661304107, 0.013618124038185728, 0.012832798987475727, 0.01209276197463663, 0.01139540090313763, 0.010738255262769673, 0.010119005927695159, 0.00953546698309649, 0.008985579064364408, 0.008467401831117483], "k": 1.0246022118850013}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 1.55), (0.10, 1.43), (0.20, 1.31), (0.31, 1.21), (0.41, 1.11), (0.51, 1.02), (0.61, 0.94), (0.71, 0.87), (0.81, 0.80), (0.92, 0.73), (1.02, 0.68), (1.12, 0.62), (1.22, 0.57), (1.32, 0.53), (1.42, 0.48), (1.53, 0.45), (1.63, 0.41), (1.73, 0.38), (1.83, 0.35), (1.93, 0.32), (2.03, 0.29), (2.14, 0.27), (2.24, 0.25), (2.34, 0.23), (2.44, 0.21), (2.54, 0.19), (2.64, 0.18), (2.75, 0.16), (2.85, 0.15), (2.95, 0.14), (3.05, 0.13), (3.15, 0.12), (3.25, 0.11), (3.36, 0.10), (3.46, 0.09), (3.56, 0.08), (3.66, 0.08), (3.76, 0.07), (3.86, 0.07), (3.97, 0.06), (4.07, 0.06), (4.17, 0.05), (4.27, 0.05), (4.37, 0.04), (4.47, 0.04), (4.58, 0.04), (4.68, 0.03), (4.78, 0.03), (4.88, 0.03), (4.98, 0.03), (5.08, 0.02), (5.19, 0.02), (5.29, 0.02), (5.39, 0.02), (5.49, 0.02), (5.59, 0.02), (5.69, 0.01), (5.80, 0.01), (5.90, 0.01), (6.00, 0.01)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.1016949152542373, 0.2033898305084746, 0.3050847457627119, 0.4067796610169492, 0.5084745762711864, 0.6101694915254238, 0.7118644067796611, 0.8135593220338984, 0.9152542372881356, 1.0169491525423728, 1.1186440677966103, 1.2203389830508475, 1.3220338983050848, 1.4237288135593222, 1.5254237288135595, 1.6271186440677967, 1.728813559322034, 1.8305084745762712, 1.9322033898305087, 2.0338983050847457, 2.135593220338983, 2.2372881355932206, 2.3389830508474576, 2.440677966101695, 2.5423728813559325, 2.6440677966101696, 2.745762711864407, 2.8474576271186445, 2.9491525423728815, 3.050847457627119, 3.152542372881356, 3.2542372881355934, 3.355932203389831, 3.457627118644068, 3.5593220338983054, 3.6610169491525424, 3.76271186440678, 3.8644067796610173, 3.9661016949152543, 4.067796610169491, 4.169491525423729, 4.271186440677966, 4.372881355932203, 4.474576271186441, 4.576271186440678, 4.677966101694915, 4.779661016949153, 4.88135593220339, 4.983050847457627, 5.084745762711865, 5.186440677966102, 5.288135593220339, 5.389830508474577, 5.491525423728814, 5.593220338983051, 5.694915254237289, 5.796610169491526, 5.898305084745763, 6.0], "x": [1.5502426537538616, 1.4265873000519784, 1.3127952902910034, 1.2080799216073235, 1.1117171647247943, 1.023040900541564, 0.9414378388486481, 0.8663438831742312, 0.7972398050335366, 0.7336478269071098, 0.6751282743992448, 0.6212765612690955, 0.5717203163274474, 0.5261169239271782, 0.4841510993448182, 0.4455326969898142, 0.4099946984595801, 0.3772913928516916, 0.3471966745134644, 0.31950246687169376, 0.29401729201117316, 0.27056494574801243, 0.24898327954879496, 0.2291230799887248, 0.21084703409585384, 0.1940287786214297, 0.1785520362642965, 0.1643097982456269, 0.15120359543618572, 0.1391428117722982, 0.12804405787654954, 0.1178305993626261, 0.10843181849632252, 0.09978273298840068, 0.09182354247168895, 0.08449922294526897, 0.07775913105907639, 0.07155666088770266, 0.06584893296341066, 0.06059648034576623, 0.05576299125971784, 0.05131504589917237, 0.04722189240239029, 0.043455229329085895, 0.03998901476227097, 0.03679928360435519, 0.03386398233991962, 0.031162815661764764, 0.028677108155370525, 0.026389673414386666, 0.02428469675819129, 0.022347623821765868, 0.020565061629180773, 0.018924686068538563, 0.017415154954486086, 0.01602603215965625, 0.014747712829572778, 0.013571358948017155, 0.012488837248484914, 0.011492662819731563], "k": 0.8174096710443716}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 1.80), (0.11, 1.52), (0.22, 1.28), (0.33, 1.08), (0.44, 0.91), (0.55, 0.77), (0.66, 0.64), (0.77, 0.54), (0.88, 0.46), (0.99, 0.39), (1.10, 0.32), (1.21, 0.27), (1.32, 0.23), (1.43, 0.19), (1.54, 0.16), (1.65, 0.14), (1.76, 0.12), (1.87, 0.10), (1.98, 0.08), (2.09, 0.07), (2.20, 0.06), (2.31, 0.05), (2.42, 0.04), (2.53, 0.03), (2.64, 0.03), (2.75, 0.02), (2.86, 0.02), (2.97, 0.02), (3.08, 0.01), (3.19, 0.01), (3.30, 0.01), (3.41, 0.01), (3.52, 0.01), (3.63, 0.01), (3.74, 0.01), (3.85, 0.00), (3.96, 0.00), (4.07, 0.00), (4.18, 0.00), (4.29, 0.00), (4.40, 0.00), (4.51, 0.00), (4.62, 0.00), (4.73, 0.00), (4.84, 0.00), (4.95, 0.00), (5.06, 0.00), (5.17, 0.00), (5.28, 0.00), (5.39, 0.00), (5.50, 0.00), (5.61, 0.00), (5.72, 0.00), (5.83, 0.00), (5.94, 0.00), (6.06, 0.00), (6.17, 0.00), (6.28, 0.00), (6.39, 0.00), (6.50, 0.00), (6.61, 0.00), (6.72, 0.00), (6.83, 0.00), (6.94, 0.00), (7.05, 0.00), (7.16, 0.00), (7.27, 0.00), (7.38, 0.00), (7.49, 0.00), (7.60, 0.00), (7.71, 0.00), (7.82, 0.00), (7.93, 0.00), (8.04, 0.00), (8.15, 0.00), (8.26, 0.00), (8.37, 0.00), (8.48, 0.00), (8.59, 0.00), (8.70, 0.00), (8.81, 0.00), (8.92, 0.00), (9.03, 0.00), (9.14, 0.00), (9.25, 0.00), (9.36, 0.00), (9.47, 0.00), (9.58, 0.00), (9.69, 0.00), (9.80, 0.00), (9.91, 0.00), (10.02, 0.00), (10.13, 0.00), (10.24, 0.00), (10.35, 0.00), (10.46, 0.00), (10.57, 0.00), (10.68, 0.00), (10.79, 0.00), (10.90, 0.00), (11.01, 0.00), (11.12, 0.00), (11.23, 0.00), (11.34, 0.00), (11.45, 0.00), (11.56, 0.00), (11.67, 0.00), (11.78, 0.00), (11.89, 0.00), (12.00, 0.00)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.11009174311926606, 0.22018348623853212, 0.3302752293577982, 0.44036697247706424, 0.5504587155963303, 0.6605504587155964, 0.7706422018348624, 0.8807339449541285, 0.9908256880733946, 1.1009174311926606, 1.2110091743119267, 1.3211009174311927, 1.4311926605504588, 1.5412844036697249, 1.651376146788991, 1.761467889908257, 1.871559633027523, 1.981651376146789, 2.091743119266055, 2.2018348623853212, 2.3119266055045875, 2.4220183486238533, 2.532110091743119, 2.6422018348623855, 2.7522935779816518, 2.8623853211009176, 2.9724770642201834, 3.0825688073394497, 3.192660550458716, 3.302752293577982, 3.4128440366972477, 3.522935779816514, 3.6330275229357802, 3.743119266055046, 3.853211009174312, 3.963302752293578, 4.0733944954128445, 4.18348623853211, 4.293577981651376, 4.4036697247706424, 4.513761467889909, 4.623853211009175, 4.73394495412844, 4.844036697247707, 4.954128440366973, 5.064220183486238, 5.174311926605505, 5.284403669724771, 5.394495412844037, 5.5045871559633035, 5.614678899082569, 5.724770642201835, 5.8348623853211015, 5.944954128440367, 6.055045871559633, 6.165137614678899, 6.275229357798166, 6.385321100917432, 6.495412844036697, 6.605504587155964, 6.71559633027523, 6.825688073394495, 6.935779816513762, 7.045871559633028, 7.155963302752294, 7.2660550458715605, 7.376146788990826, 7.486238532110092, 7.596330275229358, 7.706422018348624, 7.81651376146789, 7.926605504587156, 8.036697247706423, 8.146788990825689, 8.256880733944955, 8.36697247706422, 8.477064220183486, 8.587155963302752, 8.697247706422019, 8.807339449541285, 8.917431192660551, 9.027522935779817, 9.137614678899084, 9.24770642201835, 9.357798165137615, 9.46788990825688, 9.577981651376147, 9.688073394495413, 9.79816513761468, 9.908256880733946, 10.018348623853212, 10.128440366972477, 10.238532110091743, 10.34862385321101, 10.458715596330276, 10.568807339449542, 10.678899082568808, 10.788990825688074, 10.89908256880734, 11.009174311926607, 11.119266055045872, 11.229357798165138, 11.339449541284404, 11.44954128440367, 11.559633027522937, 11.669724770642203, 11.77981651376147, 11.889908256880734, 12.0], "x": [1.8047091451340003, 1.5202830019331146, 1.2806829855987496, 1.078844538686181, 0.908816247634005, 0.7655847991720137, 0.6449269256531762, 0.5432850112134869, 0.45766208397933217, 0.38553352170029587, 0.324772581608881, 0.27358769561001545, 0.2304696632148874, 0.19414712872053957, 0.16354910647529944, 0.13777340091380838, 0.11606000466128365, 0.09776868676739593, 0.08236013059105364, 0.06937999408472666, 0.05844555301347256, 0.049234404566536695, 0.04147495276602229, 0.034938408546473274, 0.029432038022183228, 0.024793484481935257, 0.020885976762457632, 0.017594300674205917, 0.01482140008118359, 0.012485514740636704, 0.010517770038023528, 0.008860146368721174, 0.007463767808810385, 0.006287461531887291, 0.005296543731311428, 0.004461796743209551, 0.003758607721135944, 0.0031662429109933373, 0.0026672365086605823, 0.0022468740255880536, 0.0018927611731513409, 0.0015944572999698964, 0.0013431668823015636, 0.0011314804525128135, 0.000953156472386733, 0.0008029367882088118, 0.0006763920209651573, 0.0005697904927444876, 0.00047999017569804863, 0.00040434262540387487, 0.0003406171567804177, 0.00028693507717597437, 0.00024171341681921207, 0.00020361879113018166, 0.000171527986141839, 0.00014449475568321327, 0.00012172200483905805, 0.00010253802001019355, 8.637761822525639e-05, 7.27649184013625e-05, 6.129746016378569e-05, 5.163760489245892e-05, 4.3499351885757123e-05, 3.6643810645685285e-05, 3.086867972086848e-05, 2.6003743047752882e-05, 2.1905603304577643e-05, 1.8453229904860585e-05, 1.554538900070886e-05, 1.3095323541484668e-05, 1.1031449389840575e-05, 9.292632882581747e-06, 7.828031879877204e-06, 6.594209346447182e-06, 5.554990790914884e-06, 4.679446705025163e-06, 3.9419002883418715e-06, 3.320485431078993e-06, 2.797211709722934e-06, 2.3563502003938968e-06, 1.9851010666173105e-06, 1.6723352947396495e-06, 1.408519521576861e-06, 1.1859799898315988e-06, 9.987109054669146e-07, 8.412117318751974e-07, 7.085378602291136e-07, 5.971232717927787e-07, 5.032898938166319e-07, 4.241707176930596e-07, 3.572821214455964e-07, 3.0115401675892355e-07, 2.537368241150463e-07, 2.13862900544171e-07, 1.8035666155797959e-07, 1.5215292791045737e-07, 1.2842518410357666e-07, 1.0849455074714026e-07, 9.153451807825227e-08, 7.697175886332392e-08, 6.471312496653398e-08, 5.435776312855544e-08, 4.484520295169811e-08, 3.801747113342117e-08, 3.202812533942676e-08, 2.6867476780079623e-08, 2.2443442862312346e-08, 1.873316175438835e-08, 1.573634032355214e-08, 1.327003166276334e-08], "k": 1.5578185075513415}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 0.55), (0.10, 0.52), (0.20, 0.50), (0.30, 0.47), (0.40, 0.45), (0.51, 0.43), (0.61, 0.40), (0.71, 0.38), (0.81, 0.37), (0.91, 0.35), (1.01, 0.33), (1.11, 0.31), (1.21, 0.30), (1.31, 0.28), (1.42, 0.27), (1.52, 0.26), (1.62, 0.24), (1.72, 0.23), (1.82, 0.22), (1.92, 0.21), (2.02, 0.20), (2.12, 0.19), (2.22, 0.18), (2.33, 0.17), (2.43, 0.16), (2.53, 0.15), (2.63, 0.15), (2.73, 0.14), (2.83, 0.13), (2.93, 0.13), (3.03, 0.12), (3.13, 0.11), (3.24, 0.11), (3.34, 0.10), (3.44, 0.10), (3.54, 0.09), (3.64, 0.09), (3.74, 0.08), (3.84, 0.08), (3.94, 0.08), (4.04, 0.07), (4.15, 0.07), (4.25, 0.06), (4.35, 0.06), (4.45, 0.06), (4.55, 0.06), (4.65, 0.05), (4.75, 0.05), (4.85, 0.05), (4.96, 0.05), (5.06, 0.04), (5.16, 0.04), (5.26, 0.04), (5.36, 0.04), (5.46, 0.03), (5.56, 0.03), (5.66, 0.03), (5.76, 0.03), (5.87, 0.03), (5.97, 0.03), (6.07, 0.03), (6.17, 0.02), (6.27, 0.02), (6.37, 0.02), (6.47, 0.02), (6.57, 0.02), (6.67, 0.02), (6.78, 0.02), (6.88, 0.02), (6.98, 0.02), (7.08, 0.02), (7.18, 0.01), (7.28, 0.01), (7.38, 0.01), (7.48, 0.01), (7.58, 0.01), (7.69, 0.01), (7.79, 0.01), (7.89, 0.01), (7.99, 0.01), (8.09, 0.01), (8.19, 0.01), (8.29, 0.01), (8.39, 0.01), (8.49, 0.01), (8.60, 0.01), (8.70, 0.01), (8.80, 0.01), (8.90, 0.01), (9.00, 0.01)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.10112359550561797, 0.20224719101123595, 0.3033707865168539, 0.4044943820224719, 0.5056179775280899, 0.6067415730337078, 0.7078651685393258, 0.8089887640449438, 0.9101123595505618, 1.0112359550561798, 1.1123595505617978, 1.2134831460674156, 1.3146067415730336, 1.4157303370786516, 1.5168539325842696, 1.6179775280898876, 1.7191011235955056, 1.8202247191011236, 1.9213483146067416, 2.0224719101123596, 2.1235955056179776, 2.2247191011235956, 2.3258426966292136, 2.426966292134831, 2.528089887640449, 2.629213483146067, 2.730337078651685, 2.831460674157303, 2.932584269662921, 3.033707865168539, 3.134831460674157, 3.235955056179775, 3.337078651685393, 3.438202247191011, 3.539325842696629, 3.640449438202247, 3.741573033707865, 3.842696629213483, 3.943820224719101, 4.044943820224719, 4.146067415730337, 4.247191011235955, 4.348314606741573, 4.449438202247191, 4.550561797752809, 4.651685393258427, 4.752808988764045, 4.853932584269662, 4.955056179775281, 5.056179775280898, 5.157303370786517, 5.258426966292134, 5.359550561797753, 5.46067415730337, 5.561797752808989, 5.662921348314606, 5.764044943820225, 5.865168539325842, 5.966292134831461, 6.067415730337078, 6.168539325842697, 6.269662921348314, 6.370786516853933, 6.47191011235955, 6.573033707865168, 6.674157303370786, 6.775280898876404, 6.876404494382022, 6.97752808988764, 7.078651685393258, 7.179775280898876, 7.280898876404494, 7.382022471910112, 7.48314606741573, 7.584269662921348, 7.685393258426966, 7.786516853932584, 7.887640449438202, 7.98876404494382, 8.089887640449438, 8.191011235955056, 8.292134831460674, 8.393258426966291, 8.49438202247191, 8.595505617977528, 8.696629213483146, 8.797752808988763, 8.898876404494382, 9.0], "x": [0.5500771308228076, 0.5226834143212088, 0.4966538855447745, 0.4719206111324753, 0.44841905489202444, 0.4260878715284795, 0.404868763935658, 0.38470634852179997, 0.36554805562703174, 0.3473438736191599, 0.33004621996182815, 0.3136099685090619, 0.2979922580543774, 0.2831523039483094, 0.26905137421110326, 0.2556526681646516, 0.2429212151916934, 0.2308237866375301, 0.21932880712293254, 0.20840627557880292, 0.19802768652012598, 0.1881659492235457, 0.1787953189487162, 0.16989134110642035, 0.1614307837293953, 0.15339155972960977, 0.14575268871749594, 0.1384942329811213, 0.13159724666576733, 0.1250437290586503, 0.118816574857605, 0.11289953222262324, 0.10727715710144903, 0.10193477524011238, 0.09685844292370475, 0.0920349108136262, 0.08745158953480714, 0.0830965153253576, 0.07895832257553018, 0.07502621299417209, 0.071289921069603, 0.06773969518697794, 0.06436627118487977, 0.061160842715483534, 0.058115043164428636, 0.055220924709195804, 0.05247093293195378, 0.049857889418137215, 0.04737497540825653, 0.04501571065760643, 0.04277393616182484, 0.04064380162291799, 0.03861974811036258, 0.03669649147459217, 0.03486901244813224, 0.03313254230452163, 0.03148254766017363, 0.02991472213437092, 0.028424974589784314, 0.027009415802228577, 0.02566435093029129, 0.024386270073637206, 0.02317183870231615, 0.022017886810141874, 0.020921402377202136, 0.019879522596489566, 0.01888952667800722, 0.01794883260676288, 0.01705498532872135, 0.016205651158735238, 0.01539861252374023, 0.014631764363577325, 0.01390310532588125, 0.013210733369013027, 0.012552841231772277, 0.011927712293194925, 0.011333714872233145, 0.010769298258868345, 0.010232989155480376, 0.009723388098210934, 0.009239165058538933, 0.008779056287674645, 0.00834186095990772, 0.00792643800871093, 0.007531703132168845, 0.007156625873768663, 0.006800227336596246, 0.0064615774385782445, 0.006139792253515277, 0.005834031791546133], "k": 0.5051500274254137}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 0.34), (0.10, 0.32), (0.20, 0.31), (0.30, 0.30), (0.41, 0.29), (0.51, 0.28), (0.61, 0.27), (0.71, 0.26), (0.81, 0.25), (0.91, 0.24), (1.01, 0.23), (1.11, 0.22), (1.22, 0.21), (1.32, 0.20), (1.42, 0.19), (1.52, 0.19), (1.62, 0.18), (1.72, 0.17), (1.82, 0.17), (1.92, 0.16), (2.03, 0.15), (2.13, 0.15), (2.23, 0.14), (2.33, 0.14), (2.43, 0.13), (2.53, 0.13), (2.63, 0.12), (2.73, 0.12), (2.84, 0.11), (2.94, 0.11), (3.04, 0.10), (3.14, 0.10), (3.24, 0.10), (3.34, 0.09), (3.44, 0.09), (3.54, 0.09), (3.65, 0.08), (3.75, 0.08), (3.85, 0.08), (3.95, 0.07), (4.05, 0.07), (4.15, 0.07), (4.25, 0.06), (4.35, 0.06), (4.46, 0.06), (4.56, 0.06), (4.66, 0.06), (4.76, 0.05), (4.86, 0.05), (4.96, 0.05), (5.06, 0.05), (5.16, 0.05), (5.27, 0.04), (5.37, 0.04), (5.47, 0.04), (5.57, 0.04), (5.67, 0.04), (5.77, 0.04), (5.87, 0.03), (5.97, 0.03), (6.08, 0.03), (6.18, 0.03), (6.28, 0.03), (6.38, 0.03), (6.48, 0.03), (6.58, 0.03), (6.68, 0.03), (6.78, 0.02), (6.89, 0.02), (6.99, 0.02), (7.09, 0.02), (7.19, 0.02), (7.29, 0.02), (7.39, 0.02), (7.49, 0.02), (7.59, 0.02), (7.70, 0.02), (7.80, 0.02), (7.90, 0.02), (8.00, 0.02)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.10126582278481013, 0.20253164556962025, 0.3037974683544304, 0.4050632911392405, 0.5063291139240507, 0.6075949367088608, 0.7088607594936709, 0.810126582278481, 0.9113924050632911, 1.0126582278481013, 1.1139240506329113, 1.2151898734177216, 1.3164556962025316, 1.4177215189873418, 1.5189873417721518, 1.620253164556962, 1.7215189873417722, 1.8227848101265822, 1.9240506329113924, 2.0253164556962027, 2.1265822784810124, 2.2278481012658227, 2.329113924050633, 2.430379746835443, 2.5316455696202533, 2.632911392405063, 2.7341772151898733, 2.8354430379746836, 2.9367088607594938, 3.0379746835443036, 3.1392405063291138, 3.240506329113924, 3.3417721518987342, 3.4430379746835444, 3.5443037974683542, 3.6455696202531644, 3.7468354430379747, 3.848101265822785, 3.9493670886075947, 4.050632911392405, 4.151898734177215, 4.253164556962025, 4.3544303797468356, 4.455696202531645, 4.556962025316456, 4.658227848101266, 4.7594936708860756, 4.860759493670886, 4.962025316455696, 5.063291139240507, 5.1645569620253164, 5.265822784810126, 5.367088607594937, 5.468354430379747, 5.5696202531645564, 5.670886075949367, 5.772151898734177, 5.8734177215189876, 5.974683544303797, 6.075949367088607, 6.177215189873418, 6.2784810126582276, 6.379746835443038, 6.481012658227848, 6.582278481012658, 6.6835443037974684, 6.784810126582278, 6.886075949367089, 6.987341772151899, 7.0886075949367084, 7.189873417721519, 7.291139240506329, 7.3924050632911396, 7.493670886075949, 7.594936708860759, 7.69620253164557, 7.7974683544303796, 7.898734177215189, 8.0], "x": [0.33638582778929316, 0.32346770507206113, 0.3110456649452602, 0.2991006607865327, 0.28761437301829423, 0.27656919098812666, 0.265948176510371, 0.2557350380432986, 0.24591411011600842, 0.2364703233438499, 0.22738920589875916, 0.21865684414136852, 0.210259840459309, 0.2021852958648336, 0.19442082250074202, 0.18695452703475646, 0.17977496335736337, 0.1728711150455696, 0.16623239140015514, 0.1598486130041424, 0.15370998895726784, 0.1478071051934042, 0.1421309080669137, 0.13667269283418462, 0.13142408756339047, 0.1263770434209147, 0.12152381962668792, 0.1168569749624481, 0.11236935115445407, 0.10805406222377255, 0.10390448883815745, 0.09991426804911809, 0.09607728233372764, 0.09238765080893498, 0.08883971067201314, 0.08542802040800203, 0.08214734967756229, 0.07899266689197847, 0.07595913226567148, 0.07304209350960206, 0.07023707726006582, 0.06753978093728437, 0.06494606783790331, 0.062451960721861675, 0.060053634475486034, 0.05774741036732185, 0.055529751535258826, 0.053397257081204755, 0.05134665610471288, 0.04937480364227757, 0.0474786758471624, 0.045655364380950664, 0.043902072283325135, 0.042216110797493836, 0.04059489502701943, 0.03903593973647211, 0.037536852508200866, 0.03609533386775375, 0.03470917326438504, 0.03337624556195557, 0.03209450646340944, 0.030861989168732902, 0.029676803478531372, 0.028537132157780372, 0.027441228109194103, 0.026387409673697095, 0.02537406032726234, 0.024399626135688336, 0.02346261323835093, 0.02256158474260862, 0.02169515790845181, 0.02086200395113156, 0.02006084535375313, 0.019290453930385594, 0.01854964762737306, 0.017837290017323492, 0.017152288701632896, 0.016493593499523153, 0.015860194410609534, 0.015251119359891943], "k": 0.3867006688991021}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 1.01), (0.10, 0.99), (0.20, 0.98), (0.30, 0.97), (0.41, 0.95), (0.51, 0.94), (0.61, 0.93), (0.71, 0.92), (0.81, 0.90), (0.91, 0.89), (1.01, 0.88), (1.11, 0.87), (1.22, 0.86), (1.32, 0.85), (1.42, 0.83), (1.52, 0.82), (1.62, 0.81), (1.72, 0.80), (1.82, 0.79), (1.92, 0.78), (2.03, 0.77), (2.13, 0.76), (2.23, 0.75), (2.33, 0.74), (2.43, 0.73), (2.53, 0.72), (2.63, 0.71), (2.73, 0.70), (2.84, 0.69), (2.94, 0.68), (3.04, 0.67), (3.14, 0.66), (3.24, 0.66), (3.34, 0.65), (3.44, 0.64), (3.54, 0.63), (3.65, 0.62), (3.75, 0.61), (3.85, 0.60), (3.95, 0.60), (4.05, 0.59), (4.15, 0.58), (4.25, 0.57), (4.35, 0.57), (4.46, 0.56), (4.56, 0.55), (4.66, 0.54), (4.76, 0.54), (4.86, 0.53), (4.96, 0.52), (5.06, 0.51), (5.16, 0.51), (5.27, 0.50), (5.37, 0.49), (5.47, 0.49), (5.57, 0.48), (5.67, 0.47), (5.77, 0.47), (5.87, 0.46), (5.97, 0.46), (6.08, 0.45), (6.18, 0.44), (6.28, 0.44), (6.38, 0.43), (6.48, 0.43), (6.58, 0.42), (6.68, 0.42), (6.78, 0.41), (6.89, 0.40), (6.99, 0.40), (7.09, 0.39), (7.19, 0.39), (7.29, 0.38), (7.39, 0.38), (7.49, 0.37), (7.59, 0.37), (7.70, 0.36), (7.80, 0.36), (7.90, 0.35), (8.00, 0.35)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.10126582278481013, 0.20253164556962025, 0.3037974683544304, 0.4050632911392405, 0.5063291139240507, 0.6075949367088608, 0.7088607594936709, 0.810126582278481, 0.9113924050632911, 1.0126582278481013, 1.1139240506329113, 1.2151898734177216, 1.3164556962025316, 1.4177215189873418, 1.5189873417721518, 1.620253164556962, 1.7215189873417722, 1.8227848101265822, 1.9240506329113924, 2.0253164556962027, 2.1265822784810124, 2.2278481012658227, 2.329113924050633, 2.430379746835443, 2.5316455696202533, 2.632911392405063, 2.7341772151898733, 2.8354430379746836, 2.9367088607594938, 3.0379746835443036, 3.1392405063291138, 3.240506329113924, 3.3417721518987342, 3.4430379746835444, 3.5443037974683542, 3.6455696202531644, 3.7468354430379747, 3.848101265822785, 3.9493670886075947, 4.050632911392405, 4.151898734177215, 4.253164556962025, 4.3544303797468356, 4.455696202531645, 4.556962025316456, 4.658227848101266, 4.7594936708860756, 4.860759493670886, 4.962025316455696, 5.063291139240507, 5.1645569620253164, 5.265822784810126, 5.367088607594937, 5.468354430379747, 5.5696202531645564, 5.670886075949367, 5.772151898734177, 5.8734177215189876, 5.974683544303797, 6.075949367088607, 6.177215189873418, 6.2784810126582276, 6.379746835443038, 6.481012658227848, 6.582278481012658, 6.6835443037974684, 6.784810126582278, 6.886075949367089, 6.987341772151899, 7.0886075949367084, 7.189873417721519, 7.291139240506329, 7.3924050632911396, 7.493670886075949, 7.594936708860759, 7.69620253164557, 7.7974683544303796, 7.898734177215189, 8.0], "x": [1.0068126825200447, 0.9933913571594852, 0.9801490143325191, 0.9670831671214688, 0.9541914853522324, 0.9414716566130695, 0.9289213881811332, 0.9165384198927543, 0.9043205208818607, 0.8922654917580322, 0.8803711592364541, 0.8686353871118984, 0.8570560593673769, 0.8456310897016461, 0.8343584204005169, 0.8232360210293976, 0.8122618888926306, 0.8014340468835064, 0.7907505452334851, 0.7802094570973737, 0.7698088834384652, 0.7595469518719531, 0.7494218155282751, 0.7394316526334611, 0.7295746660894785, 0.7198490829864206, 0.7102531511316834, 0.7007851414139145, 0.691443348371922, 0.6822260885695242, 0.6731317001334467, 0.6641585422912225, 0.6553049949090902, 0.6465694632474933, 0.6379503782210092, 0.629446188258525, 0.6210553629669369, 0.6127763929173415, 0.6046077886031503, 0.5965480770064763, 0.5885958061409616, 0.5807495433815202, 0.5730078748264877, 0.5653694050452136, 0.5578327591020217, 0.5503965803262182, 0.543059529434192, 0.5358202849610159, 0.528677543003719, 0.521630017145078, 0.5146764383267478, 0.5078155541921885, 0.5010461290188838, 0.49436694347551285, 0.4877767944615923, 0.48127449538664596, 0.4748588752406635, 0.4685287785030241, 0.4622830649802355, 0.4561206096703251, 0.45004030261885236, 0.44404104915809306, 0.4381217687578729, 0.432281395250443, 0.42651887660825916, 0.42083317503928064, 0.41522326711626883, 0.4096881425276483, 0.4042268043459583, 0.3988382688590779, 0.39352156538190225, 0.38827573607185856, 0.3830998357482601, 0.3779929317154978, 0.37295410401576407, 0.3679824457660425, 0.36307706153618147, 0.358237067850492, 0.3534615930856062, 0.34874977733775175], "k": 0.13252377699183612}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 1.34), (0.10, 1.28), (0.20, 1.23), (0.30, 1.18), (0.40, 1.13), (0.51, 1.08), (0.61, 1.04), (0.71, 0.99), (0.81, 0.95), (0.91, 0.91), (1.01, 0.87), (1.11, 0.84), (1.21, 0.80), (1.31, 0.77), (1.42, 0.74), (1.52, 0.71), (1.62, 0.68), (1.72, 0.65), (1.82, 0.62), (1.92, 0.60), (2.02, 0.57), (2.12, 0.55), (2.22, 0.53), (2.33, 0.50), (2.43, 0.48), (2.53, 0.46), (2.63, 0.44), (2.73, 0.43), (2.83, 0.41), (2.93, 0.39), (3.03, 0.37), (3.13, 0.36), (3.24, 0.34), (3.34, 0.33), (3.44, 0.32), (3.54, 0.30), (3.64, 0.29), (3.74, 0.28), (3.84, 0.27), (3.94, 0.26), (4.04, 0.25), (4.15, 0.24), (4.25, 0.23), (4.35, 0.22), (4.45, 0.21), (4.55, 0.20), (4.65, 0.19), (4.75, 0.18), (4.85, 0.17), (4.96, 0.17), (5.06, 0.16), (5.16, 0.15), (5.26, 0.15), (5.36, 0.14), (5.46, 0.14), (5.56, 0.13), (5.66, 0.12), (5.76, 0.12), (5.87, 0.11), (5.97, 0.11), (6.07, 0.11), (6.17, 0.10), (6.27, 0.10), (6.37, 0.09), (6.47, 0.09), (6.57, 0.09), (6.67, 0.08), (6.78, 0.08), (6.88, 0.07), (6.98, 0.07), (7.08, 0.07), (7.18, 0.07), (7.28, 0.06), (7.38, 0.06), (7.48, 0.06), (7.58, 0.06), (7.69, 0.05), (7.79, 0.05), (7.89, 0.05), (7.99, 0.05), (8.09, 0.05), (8.19, 0.04), (8.29, 0.04), (8.39, 0.04), (8.49, 0.04), (8.60, 0.04), (8.70, 0.03), (8.80, 0.03), (8.90, 0.03), (9.00, 0.03)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.10112359550561797, 0.20224719101123595, 0.3033707865168539, 0.4044943820224719, 0.5056179775280899, 0.6067415730337078, 0.7078651685393258, 0.8089887640449438, 0.9101123595505618, 1.0112359550561798, 1.1123595505617978, 1.2134831460674156, 1.3146067415730336, 1.4157303370786516, 1.5168539325842696, 1.6179775280898876, 1.7191011235955056, 1.8202247191011236, 1.9213483146067416, 2.0224719101123596, 2.1235955056179776, 2.2247191011235956, 2.3258426966292136, 2.426966292134831, 2.528089887640449, 2.629213483146067, 2.730337078651685, 2.831460674157303, 2.932584269662921, 3.033707865168539, 3.134831460674157, 3.235955056179775, 3.337078651685393, 3.438202247191011, 3.539325842696629, 3.640449438202247, 3.741573033707865, 3.842696629213483, 3.943820224719101, 4.044943820224719, 4.146067415730337, 4.247191011235955, 4.348314606741573, 4.449438202247191, 4.550561797752809, 4.651685393258427, 4.752808988764045, 4.853932584269662, 4.955056179775281, 5.056179775280898, 5.157303370786517, 5.258426966292134, 5.359550561797753, 5.46067415730337, 5.561797752808989, 5.662921348314606, 5.764044943820225, 5.865168539325842, 5.966292134831461, 6.067415730337078, 6.168539325842697, 6.269662921348314, 6.370786516853933, 6.47191011235955, 6.573033707865168, 6.674157303370786, 6.775280898876404, 6.876404494382022, 6.97752808988764, 7.078651685393258, 7.179775280898876, 7.280898876404494, 7.382022471910112, 7.48314606741573, 7.584269662921348, 7.685393258426966, 7.786516853932584, 7.887640449438202, 7.98876404494382, 8.089887640449438, 8.191011235955056, 8.292134831460674, 8.393258426966291, 8.49438202247191, 8.595505617977528, 8.696629213483146, 8.797752808988763, 8.898876404494382, 9.0], "x": [1.3359493701383514, 1.2805319191665119, 1.2274132565604485, 1.1764980338234463, 1.1276948669791642, 1.0809161411924346, 1.0360778697791264, 0.9930995425699735, 0.9519040586862159, 0.9124174765968623, 0.8745688505141028, 0.8382902146029649, 0.8035164918297133, 0.7701852508413196, 0.7382366410192157, 0.7076133144333457, 0.6782602968051712, 0.6501248924682107, 0.6231565937700188, 0.5973069859626741, 0.5725296648058594, 0.5487801549424208, 0.5260158190512828, 0.5041957780020333, 0.48328086145445, 0.4632335284755574, 0.4440178016519934, 0.4255991740685194, 0.40794458254924404, 0.39102233913087525, 0.3748020589287007, 0.3592546236581414, 0.34435212312408214, 0.3300678027967518, 0.31637602102458273, 0.303252198748206, 0.2906727747318244, 0.27861516721432816, 0.2670577300257841, 0.25597971469286707, 0.2453612349817342, 0.23518322720859655, 0.22542741930552956, 0.21607629980397122, 0.20711308260796146, 0.19852167412743388, 0.19028665172186526, 0.18239323358465248, 0.17482724741402422, 0.16757511054685448, 0.16062380565098675, 0.15396085327216655, 0.14757429076779868, 0.14145265387675776, 0.1355849541579241, 0.12996065609692337, 0.12456966316981222, 0.11940229875893899, 0.11444928541887178, 0.10970173100168153, 0.10515111360412134, 0.10078926425483418, 0.09660835135672291, 0.09260086975142552, 0.088759626073264, 0.08507772322231605, 0.08154855133909904, 0.07816577558975514, 0.07492332459345329, 0.07181537718013269, 0.06883635374874646, 0.06598090566604455, 0.06324390499796284, 0.06062043949968294, 0.058105800421479156, 0.055695473103238316, 0.053385129304657566, 0.05117062196721, 0.049047976451132465, 0.04701338213269783, 0.04506318611699618, 0.04319388746862899, 0.04140213081362037, 0.03968469948838938, 0.038038510027132745, 0.03646060703584217, 0.03494815816614444, 0.033498448282432716, 0.032108874883039935, 0.030776943436902543], "k": 0.4189590657636255}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 2.19), (0.11, 1.92), (0.22, 1.69), (0.33, 1.48), (0.44, 1.30), (0.55, 1.14), (0.66, 1.00), (0.77, 0.88), (0.88, 0.77), (0.99, 0.68), (1.10, 0.59), (1.21, 0.52), (1.32, 0.46), (1.43, 0.40), (1.54, 0.35), (1.65, 0.31), (1.76, 0.27), (1.87, 0.24), (1.98, 0.21), (2.09, 0.18), (2.20, 0.16), (2.31, 0.14), (2.42, 0.12), (2.53, 0.11), (2.64, 0.10), (2.75, 0.08), (2.86, 0.07), (2.97, 0.06), (3.08, 0.06), (3.19, 0.05), (3.30, 0.04), (3.41, 0.04), (3.52, 0.03), (3.63, 0.03), (3.74, 0.03), (3.85, 0.02), (3.96, 0.02), (4.07, 0.02), (4.18, 0.02), (4.29, 0.01), (4.40, 0.01), (4.51, 0.01), (4.62, 0.01), (4.73, 0.01), (4.84, 0.01), (4.95, 0.01), (5.06, 0.01), (5.17, 0.00), (5.28, 0.00), (5.39, 0.00), (5.50, 0.00), (5.61, 0.00), (5.72, 0.00), (5.83, 0.00), (5.94, 0.00), (6.06, 0.00), (6.17, 0.00), (6.28, 0.00), (6.39, 0.00), (6.50, 0.00), (6.61, 0.00), (6.72, 0.00), (6.83, 0.00), (6.94, 0.00), (7.05, 0.00), (7.16, 0.00), (7.27, 0.00), (7.38, 0.00), (7.49, 0.00), (7.60, 0.00), (7.71, 0.00), (7.82, 0.00), (7.93, 0.00), (8.04, 0.00), (8.15, 0.00), (8.26, 0.00), (8.37, 0.00), (8.48, 0.00), (8.59, 0.00), (8.70, 0.00), (8.81, 0.00), (8.92, 0.00), (9.03, 0.00), (9.14, 0.00), (9.25, 0.00), (9.36, 0.00), (9.47, 0.00), (9.58, 0.00), (9.69, 0.00), (9.80, 0.00), (9.91, 0.00), (10.02, 0.00), (10.13, 0.00), (10.24, 0.00), (10.35, 0.00), (10.46, 0.00), (10.57, 0.00), (10.68, 0.00), (10.79, 0.00), (10.90, 0.00), (11.01, 0.00), (11.12, 0.00), (11.23, 0.00), (11.34, 0.00), (11.45, 0.00), (11.56, 0.00), (11.67, 0.00), (11.78, 0.00), (11.89, 0.00), (12.00, 0.00)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.11009174311926606, 0.22018348623853212, 0.3302752293577982, 0.44036697247706424, 0.5504587155963303, 0.6605504587155964, 0.7706422018348624, 0.8807339449541285, 0.9908256880733946, 1.1009174311926606, 1.2110091743119267, 1.3211009174311927, 1.4311926605504588, 1.5412844036697249, 1.651376146788991, 1.761467889908257, 1.871559633027523, 1.981651376146789, 2.091743119266055, 2.2018348623853212, 2.3119266055045875, 2.4220183486238533, 2.532110091743119, 2.6422018348623855, 2.7522935779816518, 2.8623853211009176, 2.9724770642201834, 3.0825688073394497, 3.192660550458716, 3.302752293577982, 3.4128440366972477, 3.522935779816514, 3.6330275229357802, 3.743119266055046, 3.853211009174312, 3.963302752293578, 4.0733944954128445, 4.18348623853211, 4.293577981651376, 4.4036697247706424, 4.513761467889909, 4.623853211009175, 4.73394495412844, 4.844036697247707, 4.954128440366973, 5.064220183486238, 5.174311926605505, 5.284403669724771, 5.394495412844037, 5.5045871559633035, 5.614678899082569, 5.724770642201835, 5.8348623853211015, 5.944954128440367, 6.055045871559633, 6.165137614678899, 6.275229357798166, 6.385321100917432, 6.495412844036697, 6.605504587155964, 6.71559633027523, 6.825688073394495, 6.935779816513762, 7.045871559633028, 7.155963302752294, 7.2660550458715605, 7.376146788990826, 7.486238532110092, 7.596330275229358, 7.706422018348624, 7.81651376146789, 7.926605504587156, 8.036697247706423, 8.146788990825689, 8.256880733944955, 8.36697247706422, 8.477064220183486, 8.587155963302752, 8.697247706422019, 8.807339449541285, 8.917431192660551, 9.027522935779817, 9.137614678899084, 9.24770642201835, 9.357798165137615, 9.46788990825688, 9.577981651376147, 9.688073394495413, 9.79816513761468, 9.908256880733946, 10.018348623853212, 10.128440366972477, 10.238532110091743, 10.34862385321101, 10.458715596330276, 10.568807339449542, 10.678899082568808, 10.788990825688074, 10.89908256880734, 11.009174311926607, 11.119266055045872, 11.229357798165138, 11.339449541284404, 11.44954128440367, 11.559633027522937, 11.669724770642203, 11.77981651376147, 11.889908256880734, 12.0], "x": [2.1899237046523155, 1.9216801992442754, 1.6862937480048703, 1.4797398405719364, 1.2984866437317655, 1.1394351456407095, 0.9998658506237348, 0.87739241248034, 0.7699206698688691, 0.6756131695672549, 0.5928573748597187, 0.5202383333655092, 0.4565143900706225, 0.4005959867431681, 0.3515270193547997, 0.30846850509882323, 0.2706842249530441, 0.2375281377754108, 0.20843333687143878, 0.18290235563607452, 0.16049866196442125, 0.14083919466010714, 0.12358781242541388, 0.1084495591921275, 0.0951655862289661, 0.08350876391263444, 0.0732797839653497, 0.06430375107277679, 0.05642719072273191, 0.04951542990267844, 0.043450290097673344, 0.0381280685997799, 0.03345776644499734, 0.029359528299940683, 0.0257632830243354, 0.022607541461686056, 0.019838346106103865, 0.017408349472776488, 0.015276002644434414, 0.013404846664244836, 0.011762888636073953, 0.010322053726605855, 0.009057706442583646, 0.00794822904260602, 0.006974651361065838, 0.0061203270734676955, 0.005370648926626753, 0.004712798716332826, 0.004135528521775302, 0.003628968137302765, 0.0031844562050083124, 0.002794392512341911, 0.00245210771905147, 0.0021517492984430135, 0.0018881817627881686, 0.0016568986063691482, 0.0014539453881674811, 0.0012758521607129695, 0.0011195731167896975, 0.0009824366124072089, 0.0008620976128407215, 0.0007564988625096876, 0.0006638351675504174, 0.0005825218986730477, 0.0005111687157537369, 0.00044855562825782294, 0.0003936119405410269, 0.00034539843384430154, 0.0003030905320962195, 0.0002659650206645818, 0.0002333868727120156, 0.0002047993451292109, 0.00017971340296353552, 0.00015770034305844681, 0.00013838358711532414, 0.00012143286137127448, 0.00010655812731752285, 9.350592507972247e-05, 8.20529098581596e-05, 7.200260609326734e-05, 6.318358544998975e-05, 5.54445750355311e-05, 4.8653156052019265e-05, 4.2693752971124104e-05, 3.746408783780285e-05, 3.2875311147205046e-05, 2.8848357043679303e-05, 2.5314836542357377e-05, 2.221401312859101e-05, 1.9493267433802915e-05, 1.7105947442850363e-05, 1.5010495139355013e-05, 1.3171832756116841e-05, 1.155832486245004e-05, 1.0142314780335672e-05, 8.899960888492722e-06, 7.809706570271082e-06, 6.853072940977803e-06, 6.013715686801641e-06, 5.276991487609769e-06, 4.6305615939821755e-06, 4.063318575878381e-06, 3.5654946210486268e-06, 3.128779544162235e-06, 2.7455146709146083e-06, 2.4092891087455582e-06, 2.1143137606934927e-06, 1.855349225249729e-06, 1.6278446387519633e-06, 1.4279850472166945e-06], "k": 1.1868902378729242}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 2.40), (0.10, 2.25), (0.20, 2.12), (0.30, 1.98), (0.40, 1.86), (0.51, 1.75), (0.61, 1.64), (0.71, 1.54), (0.81, 1.44), (0.91, 1.35), (1.01, 1.27), (1.11, 1.19), (1.21, 1.12), (1.31, 1.05), (1.42, 0.99), (1.52, 0.92), (1.62, 0.87), (1.72, 0.81), (1.82, 0.76), (1.92, 0.72), (2.02, 0.67), (2.12, 0.63), (2.22, 0.59), (2.33, 0.56), (2.43, 0.52), (2.53, 0.49), (2.63, 0.46), (2.73, 0.43), (2.83, 0.40), (2.93, 0.38), (3.03, 0.36), (3.13, 0.33), (3.24, 0.31), (3.34, 0.29), (3.44, 0.28), (3.54, 0.26), (3.64, 0.24), (3.74, 0.23), (3.84, 0.21), (3.94, 0.20), (4.04, 0.19), (4.15, 0.18), (4.25, 0.17), (4.35, 0.16), (4.45, 0.15), (4.55, 0.14), (4.65, 0.13), (4.75, 0.12), (4.85, 0.11), (4.96, 0.11), (5.06, 0.10), (5.16, 0.09), (5.26, 0.09), (5.36, 0.08), (5.46, 0.08), (5.56, 0.07), (5.66, 0.07), (5.76, 0.06), (5.87, 0.06), (5.97, 0.06), (6.07, 0.05), (6.17, 0.05), (6.27, 0.05), (6.37, 0.04), (6.47, 0.04), (6.57, 0.04), (6.67, 0.04), (6.78, 0.03), (6.88, 0.03), (6.98, 0.03), (7.08, 0.03), (7.18, 0.03), (7.28, 0.02), (7.38, 0.02), (7.48, 0.02), (7.58, 0.02), (7.69, 0.02), (7.79, 0.02), (7.89, 0.02), (7.99, 0.02), (8.09, 0.01), (8.19, 0.01), (8.29, 0.01), (8.39, 0.01), (8.49, 0.01), (8.60, 0.01), (8.70, 0.01), (8.80, 0.01), (8.90, 0.01), (9.00, 0.01)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.10112359550561797, 0.20224719101123595, 0.3033707865168539, 0.4044943820224719, 0.5056179775280899, 0.6067415730337078, 0.7078651685393258, 0.8089887640449438, 0.9101123595505618, 1.0112359550561798, 1.1123595505617978, 1.2134831460674156, 1.3146067415730336, 1.4157303370786516, 1.5168539325842696, 1.6179775280898876, 1.7191011235955056, 1.8202247191011236, 1.9213483146067416, 2.0224719101123596, 2.1235955056179776, 2.2247191011235956, 2.3258426966292136, 2.426966292134831, 2.528089887640449, 2.629213483146067, 2.730337078651685, 2.831460674157303, 2.932584269662921, 3.033707865168539, 3.134831460674157, 3.235955056179775, 3.337078651685393, 3.438202247191011, 3.539325842696629, 3.640449438202247, 3.741573033707865, 3.842696629213483, 3.943820224719101, 4.044943820224719, 4.146067415730337, 4.247191011235955, 4.348314606741573, 4.449438202247191, 4.550561797752809, 4.651685393258427, 4.752808988764045, 4.853932584269662, 4.955056179775281, 5.056179775280898, 5.157303370786517, 5.258426966292134, 5.359550561797753, 5.46067415730337, 5.561797752808989, 5.662921348314606, 5.764044943820225, 5.865168539325842, 5.966292134831461, 6.067415730337078, 6.168539325842697, 6.269662921348314, 6.370786516853933, 6.47191011235955, 6.573033707865168, 6.674157303370786, 6.775280898876404, 6.876404494382022, 6.97752808988764, 7.078651685393258, 7.179775280898876, 7.280898876404494, 7.382022471910112, 7.48314606741573, 7.584269662921348, 7.685393258426966, 7.786516853932584, 7.887640449438202, 7.98876404494382, 8.089887640449438, 8.191011235955056, 8.292134831460674, 8.393258426966291, 8.49438202247191, 8.595505617977528, 8.696629213483146, 8.797752808988763, 8.898876404494382, 9.0], "x": [2.40228202790427, 2.2540923589306767, 2.1150440157027273, 1.9845731648259832, 1.8621506510147434, 1.7472800180505488, 1.6394955237239244, 1.5383598428705663, 1.4434629545534199, 1.354419969276362, 1.270869783739561, 1.1924735639486577, 1.1189133763259371, 1.0498909067950923, 0.9851262486708592, 0.9243566985420444, 0.867335823532261, 0.8138324290941307, 0.763629503553032, 0.716523438025561, 0.672323212237829, 0.6308495696677625, 0.5919343136301486, 0.5554196251390543, 0.521157419937665, 0.4890087501468524, 0.45884323734645005, 0.4305385460114468, 0.40397988664569334, 0.37905955031495325, 0.35567647968976923, 0.3337358398238609, 0.3131486559592855, 0.2938314329820213, 0.27570583445248065, 0.25869834965107547, 0.24274000756291522, 0.22776608844238297, 0.21371586649709462, 0.20053236176072683, 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0.009437879595080292, 0.008855684568127506, 0.008309403446837045], "k": 0.6296429780501015}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 1.52), (0.10, 1.40), (0.20, 1.29), (0.31, 1.19), (0.41, 1.09), (0.51, 1.00), (0.61, 0.92), (0.71, 0.85), (0.81, 0.78), (0.92, 0.72), (1.02, 0.66), (1.12, 0.61), (1.22, 0.56), (1.32, 0.52), (1.42, 0.47), (1.53, 0.44), (1.63, 0.40), (1.73, 0.37), (1.83, 0.34), (1.93, 0.31), (2.03, 0.29), (2.14, 0.26), (2.24, 0.24), (2.34, 0.22), (2.44, 0.21), (2.54, 0.19), (2.64, 0.17), (2.75, 0.16), (2.85, 0.15), (2.95, 0.14), (3.05, 0.12), (3.15, 0.11), (3.25, 0.11), (3.36, 0.10), (3.46, 0.09), (3.56, 0.08), (3.66, 0.08), (3.76, 0.07), (3.86, 0.06), (3.97, 0.06), (4.07, 0.05), (4.17, 0.05), (4.27, 0.05), (4.37, 0.04), (4.47, 0.04), (4.58, 0.04), (4.68, 0.03), (4.78, 0.03), (4.88, 0.03), (4.98, 0.03), (5.08, 0.02), (5.19, 0.02), (5.29, 0.02), (5.39, 0.02), (5.49, 0.02), (5.59, 0.02), (5.69, 0.01), (5.80, 0.01), (5.90, 0.01), (6.00, 0.01)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.1016949152542373, 0.2033898305084746, 0.3050847457627119, 0.4067796610169492, 0.5084745762711864, 0.6101694915254238, 0.7118644067796611, 0.8135593220338984, 0.9152542372881356, 1.0169491525423728, 1.1186440677966103, 1.2203389830508475, 1.3220338983050848, 1.4237288135593222, 1.5254237288135595, 1.6271186440677967, 1.728813559322034, 1.8305084745762712, 1.9322033898305087, 2.0338983050847457, 2.135593220338983, 2.2372881355932206, 2.3389830508474576, 2.440677966101695, 2.5423728813559325, 2.6440677966101696, 2.745762711864407, 2.8474576271186445, 2.9491525423728815, 3.050847457627119, 3.152542372881356, 3.2542372881355934, 3.355932203389831, 3.457627118644068, 3.5593220338983054, 3.6610169491525424, 3.76271186440678, 3.8644067796610173, 3.9661016949152543, 4.067796610169491, 4.169491525423729, 4.271186440677966, 4.372881355932203, 4.474576271186441, 4.576271186440678, 4.677966101694915, 4.779661016949153, 4.88135593220339, 4.983050847457627, 5.084745762711865, 5.186440677966102, 5.288135593220339, 5.389830508474577, 5.491525423728814, 5.593220338983051, 5.694915254237289, 5.796610169491526, 5.898305084745763, 6.0], "x": [1.5237010357142933, 1.4017814605173131, 1.2896172863976847, 1.186427978502293, 1.0914953806066316, 1.0041589548075323, 0.9238107166010466, 0.8498916005772782, 0.7818871497435017, 0.719324105550155, 0.6617670708821448, 0.608815504100972, 0.5601008561214619, 0.515284123098969, 0.47405342510296056, 0.4361218302052725, 0.40122534830536327, 0.3691211217731194, 0.3395857311612915, 0.31241362787073057, 0.28741571166349034, 0.26441801336961585, 0.24326048595515934, 0.22379588810440176, 0.20588876005119477, 0.18941447698257752, 0.17425839271868046, 0.16031502859601696, 0.14748734909993744, 0.13568608273504032, 0.12482909894080568, 0.11484084275482663, 0.10565180065862265, 0.09719802340472058, 0.08942067839532394, 0.0822656457844165, 0.07568312772828527, 0.06962731014914333, 0.0640560523082705, 0.058930578602239235, 0.054215222624065806, 0.049877167556866976, 0.045886224534287486, 0.04221461782770021, 0.03883679632824737, 0.03572925289891321, 0.03287036131502918, 0.030240224920541566, 0.02782054018506122, 0.025594467438907698, 0.0235465153403588, 0.02166243080955622, 0.019929102001311542, 0.018334466434459358, 0.01686742595523621, 0.01551777167412631, 0.014276110357246066, 0.013133801254664675, 0.012082894538592964, 0.011116076387541172], "k": 0.8200842096464255}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 1.39), (0.06, 1.36), (0.12, 1.32), (0.17, 1.29), (0.23, 1.26), (0.29, 1.22), (0.35, 1.19), (0.41, 1.16), (0.46, 1.13), (0.52, 1.10), (0.58, 1.07), (0.64, 1.05), (0.70, 1.02), (0.75, 0.99), (0.81, 0.97), (0.87, 0.94), (0.93, 0.92), (0.99, 0.89), (1.04, 0.87), (1.10, 0.85), (1.16, 0.83), (1.22, 0.80), (1.28, 0.78), (1.33, 0.76), (1.39, 0.74), (1.45, 0.72), (1.51, 0.71), (1.57, 0.69), (1.62, 0.67), (1.68, 0.65), (1.74, 0.64), (1.80, 0.62), (1.86, 0.60), (1.91, 0.59), (1.97, 0.57), (2.03, 0.56), (2.09, 0.54), (2.14, 0.53), (2.20, 0.52), (2.26, 0.50), (2.32, 0.49), (2.38, 0.48), (2.43, 0.46), (2.49, 0.45), (2.55, 0.44), (2.61, 0.43), (2.67, 0.42), (2.72, 0.41), (2.78, 0.40), (2.84, 0.39), (2.90, 0.38), (2.96, 0.37), (3.01, 0.36), (3.07, 0.35), (3.13, 0.34), (3.19, 0.33), (3.25, 0.32), (3.30, 0.31), (3.36, 0.31), (3.42, 0.30), (3.48, 0.29), (3.54, 0.28), (3.59, 0.28), (3.65, 0.27), (3.71, 0.26), (3.77, 0.25), (3.83, 0.25), (3.88, 0.24), (3.94, 0.24), (4.00, 0.23)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.057971014492753624, 0.11594202898550725, 0.17391304347826086, 0.2318840579710145, 0.2898550724637681, 0.34782608695652173, 0.4057971014492754, 0.463768115942029, 0.5217391304347826, 0.5797101449275363, 0.6376811594202899, 0.6956521739130435, 0.7536231884057971, 0.8115942028985508, 0.8695652173913043, 0.927536231884058, 0.9855072463768116, 1.0434782608695652, 1.1014492753623188, 1.1594202898550725, 1.2173913043478262, 1.2753623188405798, 1.3333333333333333, 1.391304347826087, 1.4492753623188406, 1.5072463768115942, 1.565217391304348, 1.6231884057971016, 1.681159420289855, 1.7391304347826086, 1.7971014492753623, 1.855072463768116, 1.9130434782608696, 1.9710144927536233, 2.028985507246377, 2.0869565217391304, 2.1449275362318843, 2.2028985507246377, 2.260869565217391, 2.318840579710145, 2.3768115942028984, 2.4347826086956523, 2.4927536231884058, 2.5507246376811596, 2.608695652173913, 2.6666666666666665, 2.7246376811594204, 2.782608695652174, 2.8405797101449277, 2.898550724637681, 2.956521739130435, 3.0144927536231885, 3.072463768115942, 3.130434782608696, 3.1884057971014492, 3.246376811594203, 3.3043478260869565, 3.36231884057971, 3.420289855072464, 3.4782608695652173, 3.536231884057971, 3.5942028985507246, 3.6521739130434785, 3.710144927536232, 3.7681159420289854, 3.8260869565217392, 3.8840579710144927, 3.9420289855072466, 4.0], "x": [1.393780197169281, 1.3578020985467456, 1.3227527077449481, 1.2886080507920168, 1.2553447759725873, 1.222940130412913, 1.1913719635230686, 1.1606186769159392, 1.1306592352565734, 1.101473145779572, 1.073040434960492, 1.0453416583281196, 1.0183578865492144, 0.9920706769122951, 0.9664620440894953, 0.9415144619986396, 0.9172108410280327, 0.893534561160694, 0.8704694427746266, 0.8479997213244986, 0.8261100230003474, 0.8047853701496311, 0.7840111744043575, 0.7637732301917304, 0.7440576945541801, 0.7248510829809747, 0.706140258448337, 0.6879124222155408, 0.670155107815173, 0.6528561688906557, 0.6360037727914888, 0.619586393811577, 0.6035928018834792, 0.5880120600514955, 0.5728335119648289, 0.5580467741851048, 0.5436417293343466, 0.529608521487332, 0.5159375545435874, 0.5026194781181558, 0.48964518481770103, 0.47700580516096164, 0.46469269240078115, 0.45269742062643337, 0.44101178573638494, 0.4296277965869559, 0.41853766920847263, 0.4077338155163895, 0.397208844964588, 0.3869555587322403, 0.3769669441850298, 0.3672361694751641, 0.3577565780304619, 0.3485216860069786, 0.3395251772475564, 0.3307608990536932, 0.3222228564270619, 0.3139052089474603, 0.30580226752927087, 0.29790849012129794, 0.2902184778276895, 0.2827269702650835, 0.275428843242173, 0.26831910508471263, 0.26139289322133896, 0.2546454701757689, 0.24807221999815784, 0.24166864670677493, 0.23543037064635247, 0.22935312561796364], "k": 0.4511280018103737}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 1.59), (0.06, 1.52), (0.12, 1.44), (0.17, 1.38), (0.23, 1.31), (0.29, 1.25), (0.35, 1.19), (0.41, 1.14), (0.46, 1.08), (0.52, 1.03), (0.58, 0.98), (0.64, 0.94), (0.70, 0.89), (0.75, 0.85), (0.81, 0.81), (0.87, 0.77), (0.93, 0.74), (0.99, 0.70), (1.04, 0.67), (1.10, 0.64), (1.16, 0.61), (1.22, 0.58), (1.28, 0.55), (1.33, 0.53), (1.39, 0.50), (1.45, 0.48), (1.51, 0.46), (1.57, 0.43), (1.62, 0.41), (1.68, 0.39), (1.74, 0.38), (1.80, 0.36), (1.86, 0.34), (1.91, 0.32), (1.97, 0.31), (2.03, 0.30), (2.09, 0.28), (2.14, 0.27), (2.20, 0.26), (2.26, 0.24), (2.32, 0.23), (2.38, 0.22), (2.43, 0.21), (2.49, 0.20), (2.55, 0.19), (2.61, 0.18), (2.67, 0.17), (2.72, 0.17), (2.78, 0.16), (2.84, 0.15), (2.90, 0.14), (2.96, 0.14), (3.01, 0.13), (3.07, 0.12), (3.13, 0.12), (3.19, 0.11), (3.25, 0.11), (3.30, 0.10), (3.36, 0.10), (3.42, 0.09), (3.48, 0.09), (3.54, 0.08), (3.59, 0.08), (3.65, 0.08), (3.71, 0.07), (3.77, 0.07), (3.83, 0.07), (3.88, 0.06), (3.94, 0.06), (4.00, 0.06)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.057971014492753624, 0.11594202898550725, 0.17391304347826086, 0.2318840579710145, 0.2898550724637681, 0.34782608695652173, 0.4057971014492754, 0.463768115942029, 0.5217391304347826, 0.5797101449275363, 0.6376811594202899, 0.6956521739130435, 0.7536231884057971, 0.8115942028985508, 0.8695652173913043, 0.927536231884058, 0.9855072463768116, 1.0434782608695652, 1.1014492753623188, 1.1594202898550725, 1.2173913043478262, 1.2753623188405798, 1.3333333333333333, 1.391304347826087, 1.4492753623188406, 1.5072463768115942, 1.565217391304348, 1.6231884057971016, 1.681159420289855, 1.7391304347826086, 1.7971014492753623, 1.855072463768116, 1.9130434782608696, 1.9710144927536233, 2.028985507246377, 2.0869565217391304, 2.1449275362318843, 2.2028985507246377, 2.260869565217391, 2.318840579710145, 2.3768115942028984, 2.4347826086956523, 2.4927536231884058, 2.5507246376811596, 2.608695652173913, 2.6666666666666665, 2.7246376811594204, 2.782608695652174, 2.8405797101449277, 2.898550724637681, 2.956521739130435, 3.0144927536231885, 3.072463768115942, 3.130434782608696, 3.1884057971014492, 3.246376811594203, 3.3043478260869565, 3.36231884057971, 3.420289855072464, 3.4782608695652173, 3.536231884057971, 3.5942028985507246, 3.6521739130434785, 3.710144927536232, 3.7681159420289854, 3.8260869565217392, 3.8840579710144927, 3.9420289855072466, 4.0], "x": [1.5902087363634578, 1.5154931505829727, 1.4442880328797214, 1.3764284574634227, 1.311757258327532, 1.2501246175036027, 1.1913877397324157, 1.1354106370853598, 1.082063659813042, 1.0312231334113902, 0.9827713215862427, 0.9365960280999833, 0.8925902645103851, 0.8506521015161757, 0.8106843949281706, 0.7725945622954923, 0.7362943721778191, 0.7016997390275854, 0.6687305326973841, 0.6373103844404998, 0.6073664925907383, 0.5788294957193765, 0.5516333037798928, 0.5257149268122107, 0.5010143150425955, 0.4774742627419473, 0.4550402359466355, 0.43366026662669865, 0.4132848309251283, 0.39386672910218723, 0.37536098403355345, 0.35772472748079015, 0.34091710647828616, 0.3248991885594339, 0.3096338682144398, 0.29508578627528315, 0.28122124152972566, 0.26800811800506785, 0.25541581275561603, 0.24341515411941264, 0.23197834303961834, 0.22107888964913824, 0.2106915439198821, 0.20079224464274203, 0.1913580634530919, 0.18236714445747432, 0.17379866138834194, 0.1656327680931328, 0.157850546780982, 0.15043397117863797, 0.1433658629105841, 0.13662984739380046, 0.13021032199487317, 0.1240924176019442, 0.1182619609104043, 0.11270544699449768, 0.10741000525022516, 0.10236336762676784, 0.09755384476759793, 0.0929702978683129, 0.08860210958083636, 0.08443916095803845, 0.08047180735360956, 0.07669085711218854, 0.07308755468118194, 0.06965355308051253, 0.06638089606659563, 0.06326200357792412, 0.0602896519404232, 0.057456955710163043], "k": 0.8301461116693228}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 0.74), (0.11, 0.65), (0.22, 0.58), (0.33, 0.52), (0.44, 0.46), (0.55, 0.41), (0.66, 0.36), (0.77, 0.32), (0.88, 0.29), (0.99, 0.25), (1.10, 0.23), (1.21, 0.20), (1.32, 0.18), (1.43, 0.16), (1.54, 0.14), (1.65, 0.13), (1.76, 0.11), (1.87, 0.10), (1.98, 0.09), (2.09, 0.08), (2.20, 0.07), (2.31, 0.06), (2.42, 0.05), (2.53, 0.05), (2.64, 0.04), (2.75, 0.04), (2.86, 0.03), (2.97, 0.03), (3.08, 0.03), (3.19, 0.02), (3.30, 0.02), (3.41, 0.02), (3.52, 0.02), (3.63, 0.02), (3.74, 0.01), (3.85, 0.01), (3.96, 0.01), (4.07, 0.01), (4.18, 0.01), (4.29, 0.01), (4.40, 0.01), (4.51, 0.01), (4.62, 0.01), (4.73, 0.00), (4.84, 0.00), (4.95, 0.00), (5.06, 0.00), (5.17, 0.00), (5.28, 0.00), (5.39, 0.00), (5.50, 0.00), (5.61, 0.00), (5.72, 0.00), (5.83, 0.00), (5.94, 0.00), (6.06, 0.00), (6.17, 0.00), (6.28, 0.00), (6.39, 0.00), (6.50, 0.00), (6.61, 0.00), (6.72, 0.00), (6.83, 0.00), (6.94, 0.00), (7.05, 0.00), (7.16, 0.00), (7.27, 0.00), (7.38, 0.00), (7.49, 0.00), (7.60, 0.00), (7.71, 0.00), (7.82, 0.00), (7.93, 0.00), (8.04, 0.00), (8.15, 0.00), (8.26, 0.00), (8.37, 0.00), (8.48, 0.00), (8.59, 0.00), (8.70, 0.00), (8.81, 0.00), (8.92, 0.00), (9.03, 0.00), (9.14, 0.00), (9.25, 0.00), (9.36, 0.00), (9.47, 0.00), (9.58, 0.00), (9.69, 0.00), (9.80, 0.00), (9.91, 0.00), (10.02, 0.00), (10.13, 0.00), (10.24, 0.00), (10.35, 0.00), (10.46, 0.00), (10.57, 0.00), (10.68, 0.00), (10.79, 0.00), (10.90, 0.00), (11.01, 0.00), (11.12, 0.00), (11.23, 0.00), (11.34, 0.00), (11.45, 0.00), (11.56, 0.00), (11.67, 0.00), (11.78, 0.00), (11.89, 0.00), (12.00, 0.00)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.11009174311926606, 0.22018348623853212, 0.3302752293577982, 0.44036697247706424, 0.5504587155963303, 0.6605504587155964, 0.7706422018348624, 0.8807339449541285, 0.9908256880733946, 1.1009174311926606, 1.2110091743119267, 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6.935779816513762, 7.045871559633028, 7.155963302752294, 7.2660550458715605, 7.376146788990826, 7.486238532110092, 7.596330275229358, 7.706422018348624, 7.81651376146789, 7.926605504587156, 8.036697247706423, 8.146788990825689, 8.256880733944955, 8.36697247706422, 8.477064220183486, 8.587155963302752, 8.697247706422019, 8.807339449541285, 8.917431192660551, 9.027522935779817, 9.137614678899084, 9.24770642201835, 9.357798165137615, 9.46788990825688, 9.577981651376147, 9.688073394495413, 9.79816513761468, 9.908256880733946, 10.018348623853212, 10.128440366972477, 10.238532110091743, 10.34862385321101, 10.458715596330276, 10.568807339449542, 10.678899082568808, 10.788990825688074, 10.89908256880734, 11.009174311926607, 11.119266055045872, 11.229357798165138, 11.339449541284404, 11.44954128440367, 11.559633027522937, 11.669724770642203, 11.77981651376147, 11.889908256880734, 12.0], "x": [0.7367770825505227, 0.654775100168611, 0.581899764990229, 0.5171352911918077, 0.4595790889918645, 0.4084287296174404, 0.36297132535747906, 0.3225732513006639, 0.2866714131297362, 0.25476539016877053, 0.22641043594753668, 0.20121134485658013, 0.17881687236395374, 0.15891486482501455, 0.14122791672871515, 0.12550949483715845, 0.11154050195236309, 0.09912623643371009, 0.08809365745778569, 0.0782889847249965, 0.0695755548133349, 0.06183191566035977, 0.05495013015903712, 0.04883427510741494, 0.04339910398608576, 0.038568857786655364, 0.0342762098466534, 0.03046133193145612, 0.027071040704045295, 0.02405808300226133, 0.021380459915432148, 0.019000851887143583, 0.016886090840078017, 0.015006698094072662, 0.013336478455598171, 0.011852151950673141, 0.01053302828827465, 0.009360720826225492, 0.008318888903067362, 0.007393011118367984, 0.006570182098432612, 0.005838932330468483, 0.00518906939396704, 0.004611535027221824, 0.004098279299005799, 0.0036421480370224238, 0.003236783326637088, 0.002876535019156785, 0.002556381700355313, 0.0022718609318621726, 0.002019006792508459, 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1.1230827854361707e-05, 9.98070618299436e-06, 8.869871462697103e-06, 7.882770430857262e-06, 7.005316734556092e-06, 6.225557767051719e-06, 5.53263132916823e-06, 4.916636636939245e-06, 4.3694674342793325e-06, 3.883168206103881e-06, 3.45095555242253e-06, 3.0669908940666037e-06, 2.725801557045118e-06, 2.4224404179971796e-06, 2.152561031771399e-06, 1.9124690409151067e-06], "k": 1.0717751782324982}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 1.26), (0.10, 1.18), (0.20, 1.12), (0.30, 1.05), (0.40, 0.99), (0.51, 0.94), (0.61, 0.88), (0.71, 0.83), (0.81, 0.79), (0.91, 0.74), (1.01, 0.70), (1.11, 0.66), (1.21, 0.62), (1.31, 0.59), (1.42, 0.55), (1.52, 0.52), (1.62, 0.49), (1.72, 0.46), (1.82, 0.44), (1.92, 0.41), (2.02, 0.39), (2.12, 0.37), (2.22, 0.34), (2.33, 0.33), (2.43, 0.31), (2.53, 0.29), (2.63, 0.27), (2.73, 0.26), (2.83, 0.24), (2.93, 0.23), (3.03, 0.22), (3.13, 0.20), (3.24, 0.19), (3.34, 0.18), (3.44, 0.17), (3.54, 0.16), (3.64, 0.15), (3.74, 0.14), (3.84, 0.13), (3.94, 0.13), (4.04, 0.12), (4.15, 0.11), (4.25, 0.11), (4.35, 0.10), (4.45, 0.09), (4.55, 0.09), (4.65, 0.08), (4.75, 0.08), (4.85, 0.07), (4.96, 0.07), (5.06, 0.07), (5.16, 0.06), (5.26, 0.06), (5.36, 0.06), (5.46, 0.05), (5.56, 0.05), (5.66, 0.05), (5.76, 0.04), (5.87, 0.04), (5.97, 0.04), (6.07, 0.04), (6.17, 0.03), (6.27, 0.03), (6.37, 0.03), (6.47, 0.03), (6.57, 0.03), (6.67, 0.03), (6.78, 0.02), (6.88, 0.02), (6.98, 0.02), (7.08, 0.02), (7.18, 0.02), (7.28, 0.02), (7.38, 0.02), (7.48, 0.02), (7.58, 0.02), (7.69, 0.01), (7.79, 0.01), (7.89, 0.01), (7.99, 0.01), (8.09, 0.01), (8.19, 0.01), (8.29, 0.01), (8.39, 0.01), (8.49, 0.01), (8.60, 0.01), (8.70, 0.01), (8.80, 0.01), (8.90, 0.01), (9.00, 0.01)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.10112359550561797, 0.20224719101123595, 0.3033707865168539, 0.4044943820224719, 0.5056179775280899, 0.6067415730337078, 0.7078651685393258, 0.8089887640449438, 0.9101123595505618, 1.0112359550561798, 1.1123595505617978, 1.2134831460674156, 1.3146067415730336, 1.4157303370786516, 1.5168539325842696, 1.6179775280898876, 1.7191011235955056, 1.8202247191011236, 1.9213483146067416, 2.0224719101123596, 2.1235955056179776, 2.2247191011235956, 2.3258426966292136, 2.426966292134831, 2.528089887640449, 2.629213483146067, 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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 1.10), (0.06, 1.09), (0.12, 1.07), (0.17, 1.05), (0.23, 1.04), (0.29, 1.02), (0.35, 1.01), (0.41, 0.99), (0.46, 0.98), (0.52, 0.96), (0.58, 0.95), (0.64, 0.93), (0.70, 0.92), (0.75, 0.91), (0.81, 0.89), (0.87, 0.88), (0.93, 0.87), (0.99, 0.85), (1.04, 0.84), (1.10, 0.83), (1.16, 0.82), (1.22, 0.80), (1.28, 0.79), (1.33, 0.78), (1.39, 0.77), (1.45, 0.76), (1.51, 0.75), (1.57, 0.73), (1.62, 0.72), (1.68, 0.71), (1.74, 0.70), (1.80, 0.69), (1.86, 0.68), (1.91, 0.67), (1.97, 0.66), (2.03, 0.65), (2.09, 0.64), (2.14, 0.63), (2.20, 0.62), (2.26, 0.61), (2.32, 0.60), (2.38, 0.59), (2.43, 0.59), (2.49, 0.58), (2.55, 0.57), (2.61, 0.56), (2.67, 0.55), (2.72, 0.54), (2.78, 0.53), (2.84, 0.53), (2.90, 0.52), (2.96, 0.51), (3.01, 0.50), (3.07, 0.50), (3.13, 0.49), (3.19, 0.48), (3.25, 0.47), (3.30, 0.47), (3.36, 0.46), (3.42, 0.45), (3.48, 0.45), (3.54, 0.44), (3.59, 0.43), (3.65, 0.43), (3.71, 0.42), (3.77, 0.41), (3.83, 0.41), (3.88, 0.40), (3.94, 0.40), (4.00, 0.39)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.057971014492753624, 0.11594202898550725, 0.17391304347826086, 0.2318840579710145, 0.2898550724637681, 0.34782608695652173, 0.4057971014492754, 0.463768115942029, 0.5217391304347826, 0.5797101449275363, 0.6376811594202899, 0.6956521739130435, 0.7536231884057971, 0.8115942028985508, 0.8695652173913043, 0.927536231884058, 0.9855072463768116, 1.0434782608695652, 1.1014492753623188, 1.1594202898550725, 1.2173913043478262, 1.2753623188405798, 1.3333333333333333, 1.391304347826087, 1.4492753623188406, 1.5072463768115942, 1.565217391304348, 1.6231884057971016, 1.681159420289855, 1.7391304347826086, 1.7971014492753623, 1.855072463768116, 1.9130434782608696, 1.9710144927536233, 2.028985507246377, 2.0869565217391304, 2.1449275362318843, 2.2028985507246377, 2.260869565217391, 2.318840579710145, 2.3768115942028984, 2.4347826086956523, 2.4927536231884058, 2.5507246376811596, 2.608695652173913, 2.6666666666666665, 2.7246376811594204, 2.782608695652174, 2.8405797101449277, 2.898550724637681, 2.956521739130435, 3.0144927536231885, 3.072463768115942, 3.130434782608696, 3.1884057971014492, 3.246376811594203, 3.3043478260869565, 3.36231884057971, 3.420289855072464, 3.4782608695652173, 3.536231884057971, 3.5942028985507246, 3.6521739130434785, 3.710144927536232, 3.7681159420289854, 3.8260869565217392, 3.8840579710144927, 3.9420289855072466, 4.0], "x": [1.1034496422618914, 1.0869115326090812, 1.0706213800312374, 1.0545753235860105, 1.0387697591559921, 1.023201082383008, 1.00786574115534, 0.9927602381708881, 0.9778811295034538, 0.963225020479233, 0.9487885760454745, 0.9345684994905693, 0.9205615482232998, 0.9067645274101253, 0.8931742913470659, 0.8797877401263917, 0.8666018210141447, 0.8536135232887083, 0.8408198850665936, 0.8282179903938011, 0.8158049679117677, 0.8035779900253748, 0.791534271895648, 0.7796710662064478, 0.76798566661917, 0.7564754076207004, 0.7451376623073431, 0.7339698414681325, 0.7229693926681435, 0.7121338059661804, 0.7014606160215977, 0.6909473901059577, 0.6805917327941609, 0.6703912854254424, 0.6603437209965508, 0.6504467468022455, 0.6406981053419742, 0.631095572322757, 0.6216369565203181, 0.6123201024605314, 0.6031428858771392, 0.5941032138979465, 0.5851990249363455, 0.5764282883823222, 0.5677890044038032, 0.559279202842371, 0.5508969429498822, 0.5426403129115454, 0.5345074299594539, 0.5264964397204863, 0.5186055152588039, 0.5108328568936337, 0.5031766918663997, 0.49563527437054095, 0.48820688493310765, 0.4808898294358854, 0.47368243905019103, 0.4665830700922089, 0.45959010439149395, 0.4527019473418615, 0.44591702805138617, 0.43923379903630794, 0.4326507358463436, 0.4261663366985552, 0.4197791221197788, 0.41348763500015845, 0.4072904414395865, 0.40118612822227984, 0.3951733032896274, 0.38925059558607944], "k": 0.26049332555443483}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 1.85), (0.10, 1.79), (0.20, 1.73), (0.30, 1.68), (0.40, 1.63), (0.51, 1.58), (0.61, 1.53), (0.71, 1.48), (0.81, 1.43), (0.91, 1.39), (1.01, 1.34), (1.11, 1.30), (1.21, 1.26), (1.31, 1.22), (1.42, 1.18), (1.52, 1.14), (1.62, 1.11), (1.72, 1.07), (1.82, 1.04), (1.92, 1.01), (2.02, 0.98), (2.12, 0.95), (2.22, 0.92), (2.33, 0.89), (2.43, 0.86), (2.53, 0.83), (2.63, 0.81), (2.73, 0.78), (2.83, 0.76), (2.93, 0.73), (3.03, 0.71), (3.13, 0.69), (3.24, 0.67), (3.34, 0.64), (3.44, 0.62), (3.54, 0.60), (3.64, 0.59), (3.74, 0.57), (3.84, 0.55), (3.94, 0.53), (4.04, 0.52), (4.15, 0.50), (4.25, 0.48), (4.35, 0.47), (4.45, 0.45), (4.55, 0.44), (4.65, 0.43), (4.75, 0.41), (4.85, 0.40), (4.96, 0.39), (5.06, 0.37), (5.16, 0.36), (5.26, 0.35), (5.36, 0.34), (5.46, 0.33), (5.56, 0.32), (5.66, 0.31), (5.76, 0.30), (5.87, 0.29), (5.97, 0.28), (6.07, 0.27), (6.17, 0.26), (6.27, 0.26), (6.37, 0.25), (6.47, 0.24), (6.57, 0.23), (6.67, 0.22), (6.78, 0.22), (6.88, 0.21), (6.98, 0.20), (7.08, 0.20), (7.18, 0.19), (7.28, 0.19), (7.38, 0.18), (7.48, 0.17), (7.58, 0.17), (7.69, 0.16), (7.79, 0.16), (7.89, 0.15), (7.99, 0.15), (8.09, 0.14), (8.19, 0.14), (8.29, 0.13), (8.39, 0.13), (8.49, 0.13), (8.60, 0.12), (8.70, 0.12), (8.80, 0.11), (8.90, 0.11), (9.00, 0.11)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.10112359550561797, 0.20224719101123595, 0.3033707865168539, 0.4044943820224719, 0.5056179775280899, 0.6067415730337078, 0.7078651685393258, 0.8089887640449438, 0.9101123595505618, 1.0112359550561798, 1.1123595505617978, 1.2134831460674156, 1.3146067415730336, 1.4157303370786516, 1.5168539325842696, 1.6179775280898876, 1.7191011235955056, 1.8202247191011236, 1.9213483146067416, 2.0224719101123596, 2.1235955056179776, 2.2247191011235956, 2.3258426966292136, 2.426966292134831, 2.528089887640449, 2.629213483146067, 2.730337078651685, 2.831460674157303, 2.932584269662921, 3.033707865168539, 3.134831460674157, 3.235955056179775, 3.337078651685393, 3.438202247191011, 3.539325842696629, 3.640449438202247, 3.741573033707865, 3.842696629213483, 3.943820224719101, 4.044943820224719, 4.146067415730337, 4.247191011235955, 4.348314606741573, 4.449438202247191, 4.550561797752809, 4.651685393258427, 4.752808988764045, 4.853932584269662, 4.955056179775281, 5.056179775280898, 5.157303370786517, 5.258426966292134, 5.359550561797753, 5.46067415730337, 5.561797752808989, 5.662921348314606, 5.764044943820225, 5.865168539325842, 5.966292134831461, 6.067415730337078, 6.168539325842697, 6.269662921348314, 6.370786516853933, 6.47191011235955, 6.573033707865168, 6.674157303370786, 6.775280898876404, 6.876404494382022, 6.97752808988764, 7.078651685393258, 7.179775280898876, 7.280898876404494, 7.382022471910112, 7.48314606741573, 7.584269662921348, 7.685393258426966, 7.786516853932584, 7.887640449438202, 7.98876404494382, 8.089887640449438, 8.191011235955056, 8.292134831460674, 8.393258426966291, 8.49438202247191, 8.595505617977528, 8.696629213483146, 8.797752808988763, 8.898876404494382, 9.0], "x": [1.8485835787757297, 1.7904565121923914, 1.7341571744341275, 1.6796281142201974, 1.62681366134169, 1.5756599216855331, 1.5261146673034092, 1.4781273196017457, 1.4316488756094354, 1.3866318927729415, 1.3430304538893572, 1.3008000568935658, 1.2598975708356774, 1.220281192919887, 1.1819105004047081, 1.1447463509741567, 1.1087508051388058, 1.0738871048425027, 1.0401196608647698, 1.0074140045332354, 0.9757367494567787, 0.9450555581145803, 0.9153391101091124, 0.8865570702785999, 0.8586800559025712, 0.8316796105132421, 0.8055281720059677, 0.780199048469229, 0.7556663800636158, 0.7319051143053119, 0.7088909921425965, 0.6866005233191604, 0.6650109561840926, 0.6441002614356307, 0.6238470913740917, 0.604230766212163, 0.585231257987852, 0.5668291701181183, 0.5490057182730007, 0.53174270976808, 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0.11112472791944486, 0.10763050653955981], "k": 0.3159411941405646}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 1.25), (0.10, 1.20), (0.20, 1.15), (0.31, 1.10), (0.41, 1.06), (0.51, 1.01), (0.61, 0.97), (0.71, 0.93), (0.81, 0.89), (0.92, 0.86), (1.02, 0.82), (1.12, 0.79), (1.22, 0.76), (1.32, 0.72), (1.42, 0.70), (1.53, 0.67), (1.63, 0.64), (1.73, 0.61), (1.83, 0.59), (1.93, 0.56), (2.03, 0.54), (2.14, 0.52), (2.24, 0.50), (2.34, 0.48), (2.44, 0.46), (2.54, 0.44), (2.64, 0.42), (2.75, 0.40), (2.85, 0.39), (2.95, 0.37), (3.05, 0.36), (3.15, 0.34), (3.25, 0.33), (3.36, 0.31), (3.46, 0.30), (3.56, 0.29), (3.66, 0.28), (3.76, 0.27), (3.86, 0.25), (3.97, 0.24), (4.07, 0.23), (4.17, 0.22), (4.27, 0.22), (4.37, 0.21), (4.47, 0.20), (4.58, 0.19), (4.68, 0.18), (4.78, 0.17), (4.88, 0.17), (4.98, 0.16), (5.08, 0.15), (5.19, 0.15), (5.29, 0.14), (5.39, 0.14), (5.49, 0.13), (5.59, 0.12), (5.69, 0.12), (5.80, 0.11), (5.90, 0.11), (6.00, 0.11)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.1016949152542373, 0.2033898305084746, 0.3050847457627119, 0.4067796610169492, 0.5084745762711864, 0.6101694915254238, 0.7118644067796611, 0.8135593220338984, 0.9152542372881356, 1.0169491525423728, 1.1186440677966103, 1.2203389830508475, 1.3220338983050848, 1.4237288135593222, 1.5254237288135595, 1.6271186440677967, 1.728813559322034, 1.8305084745762712, 1.9322033898305087, 2.0338983050847457, 2.135593220338983, 2.2372881355932206, 2.3389830508474576, 2.440677966101695, 2.5423728813559325, 2.6440677966101696, 2.745762711864407, 2.8474576271186445, 2.9491525423728815, 3.050847457627119, 3.152542372881356, 3.2542372881355934, 3.355932203389831, 3.457627118644068, 3.5593220338983054, 3.6610169491525424, 3.76271186440678, 3.8644067796610173, 3.9661016949152543, 4.067796610169491, 4.169491525423729, 4.271186440677966, 4.372881355932203, 4.474576271186441, 4.576271186440678, 4.677966101694915, 4.779661016949153, 4.88135593220339, 4.983050847457627, 5.084745762711865, 5.186440677966102, 5.288135593220339, 5.389830508474577, 5.491525423728814, 5.593220338983051, 5.694915254237289, 5.796610169491526, 5.898305084745763, 6.0], "x": [1.249578561442826, 1.1983039570094651, 1.1491333093910066, 1.1019802952332756, 1.056762138815086, 1.0133994461325606, 0.9718160730808154, 0.9319389882923252, 0.893698220505502, 0.8570266494213092, 0.8218598423880342, 0.7881360120843633, 0.7557959954074216, 0.7247830166863795, 0.6950426047948749, 0.6665225465727002, 0.6391727674533892, 0.6129452466083344, 0.58779393432898, 0.5636746687537281, 0.5405451024422988, 0.5183646265558407, 0.4970942995644082, 0.4766967656903959, 0.4571362055503117, 0.43837827875395635, 0.4203900605623367, 0.4031399652698694, 0.38659770001165383, 0.37073422613058055, 0.35552168844204757, 0.3409333743231677, 0.3269436708865145, 0.31352801385341567, 0.30066284805455257, 0.28832558667934716, 0.2764945667009496, 0.26514901512119204, 0.2542690122139318, 0.24383545389101133, 0.23383002120540386, 0.224235147196733, 0.2150339833905362, 0.2062103750129576, 0.19774883230037882, 0.18963449709265642, 0.18185312090666314, 0.17439104230420593, 0.16723516036142355, 0.16037290864717488, 0.15379223884510257, 0.1474815983868221, 0.14142990576383466, 0.1356265347494918, 0.13006129686868464, 0.12472442132240054, 0.11960653599331345, 0.1146986552878309, 0.10999216317699015, 0.10547879489705732], "k": 0.4120085931097105}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 0.82), (0.11, 0.73), (0.22, 0.65), (0.33, 0.58), (0.44, 0.51), (0.55, 0.46), (0.66, 0.41), (0.77, 0.36), (0.88, 0.32), (0.99, 0.29), (1.10, 0.25), (1.21, 0.23), (1.32, 0.20), (1.43, 0.18), (1.54, 0.16), (1.65, 0.14), (1.76, 0.13), (1.87, 0.11), (1.98, 0.10), (2.09, 0.09), (2.20, 0.08), (2.31, 0.07), (2.42, 0.06), (2.53, 0.06), (2.64, 0.05), (2.75, 0.04), (2.86, 0.04), (2.97, 0.03), (3.08, 0.03), (3.19, 0.03), (3.30, 0.02), (3.41, 0.02), (3.52, 0.02), (3.63, 0.02), (3.74, 0.02), (3.85, 0.01), (3.96, 0.01), (4.07, 0.01), (4.18, 0.01), (4.29, 0.01), (4.40, 0.01), (4.51, 0.01), (4.62, 0.01), (4.73, 0.01), (4.84, 0.00), (4.95, 0.00), (5.06, 0.00), (5.17, 0.00), (5.28, 0.00), (5.39, 0.00), (5.50, 0.00), (5.61, 0.00), (5.72, 0.00), (5.83, 0.00), (5.94, 0.00), (6.06, 0.00), (6.17, 0.00), (6.28, 0.00), (6.39, 0.00), (6.50, 0.00), (6.61, 0.00), (6.72, 0.00), (6.83, 0.00), (6.94, 0.00), (7.05, 0.00), (7.16, 0.00), (7.27, 0.00), (7.38, 0.00), (7.49, 0.00), (7.60, 0.00), (7.71, 0.00), (7.82, 0.00), (7.93, 0.00), (8.04, 0.00), (8.15, 0.00), (8.26, 0.00), (8.37, 0.00), (8.48, 0.00), (8.59, 0.00), (8.70, 0.00), (8.81, 0.00), (8.92, 0.00), (9.03, 0.00), (9.14, 0.00), (9.25, 0.00), (9.36, 0.00), (9.47, 0.00), (9.58, 0.00), (9.69, 0.00), (9.80, 0.00), (9.91, 0.00), (10.02, 0.00), (10.13, 0.00), (10.24, 0.00), (10.35, 0.00), (10.46, 0.00), (10.57, 0.00), (10.68, 0.00), (10.79, 0.00), (10.90, 0.00), (11.01, 0.00), (11.12, 0.00), (11.23, 0.00), (11.34, 0.00), (11.45, 0.00), (11.56, 0.00), (11.67, 0.00), (11.78, 0.00), (11.89, 0.00), (12.00, 0.00)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.11009174311926606, 0.22018348623853212, 0.3302752293577982, 0.44036697247706424, 0.5504587155963303, 0.6605504587155964, 0.7706422018348624, 0.8807339449541285, 0.9908256880733946, 1.1009174311926606, 1.2110091743119267, 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6.935779816513762, 7.045871559633028, 7.155963302752294, 7.2660550458715605, 7.376146788990826, 7.486238532110092, 7.596330275229358, 7.706422018348624, 7.81651376146789, 7.926605504587156, 8.036697247706423, 8.146788990825689, 8.256880733944955, 8.36697247706422, 8.477064220183486, 8.587155963302752, 8.697247706422019, 8.807339449541285, 8.917431192660551, 9.027522935779817, 9.137614678899084, 9.24770642201835, 9.357798165137615, 9.46788990825688, 9.577981651376147, 9.688073394495413, 9.79816513761468, 9.908256880733946, 10.018348623853212, 10.128440366972477, 10.238532110091743, 10.34862385321101, 10.458715596330276, 10.568807339449542, 10.678899082568808, 10.788990825688074, 10.89908256880734, 11.009174311926607, 11.119266055045872, 11.229357798165138, 11.339449541284404, 11.44954128440367, 11.559633027522937, 11.669724770642203, 11.77981651376147, 11.889908256880734, 12.0], "x": [0.8195858513744911, 0.7290611571910404, 0.6485350449476759, 0.5769031492784326, 0.5131832209216627, 0.4565012135833629, 0.40607984192835506, 0.361227601444264, 0.3213293724747994, 0.28583797554251944, 0.2542666506346936, 0.22618244140501487, 0.2012001870164251, 0.17897726629834063, 0.15920890753781916, 0.14162399892071179, 0.12598137079841543, 0.11206650174335435, 0.09968855522943205, 0.08867777442173995, 0.07888315374251818, 0.0701703675169454, 0.0624199242826214, 0.05552553108826313, 0.04939263577429551, 0.043937129217860325, 0.03908419415064079, 0.03476728005783245, 0.030927173795428833, 0.027511213945409754, 0.024472551124849046, 0.021769514144725312, 0.019365033150046534, 0.01722613038984402, 0.015323473360268146, 0.013630968799047904, 0.012125404161512523, 0.010786131829548302, 0.009594784429086024, 0.008535023456639257, 0.007592315175081972, 0.006753730445219891, 0.006007768949728935, 0.005344200209582092, 0.004753923845458062, 0.0042288445816359215, 0.0037617611681511993, 0.0033462679980848496, 0.0029766667557496553, 0.0026478886614873074, 0.0023554246707532893, 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1.5359304860070595e-05, 1.3662540451892136e-05, 1.215368644569839e-05, 1.0811365306884943e-05, 9.61716476569006e-06, 8.555026944801793e-06, 7.610171219825007e-06, 6.769404926596971e-06, 6.0211182961414385e-06, 5.3553254781538e-06, 4.763569332539196e-06, 4.237268893719732e-06, 3.7689973637971293e-06, 3.3527627781302497e-06, 2.982698850467037e-06, 2.653344442220544e-06, 2.360368605761367e-06], "k": 1.0631275604129622}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 1.00), (0.10, 0.94), (0.20, 0.89), (0.30, 0.84), (0.40, 0.79), (0.51, 0.75), (0.61, 0.71), (0.71, 0.67), (0.81, 0.63), (0.91, 0.60), (1.01, 0.56), (1.11, 0.53), (1.21, 0.50), (1.31, 0.47), (1.42, 0.45), (1.52, 0.42), (1.62, 0.40), (1.72, 0.38), (1.82, 0.36), (1.92, 0.34), (2.02, 0.32), (2.12, 0.30), (2.22, 0.28), (2.33, 0.27), (2.43, 0.25), (2.53, 0.24), (2.63, 0.23), (2.73, 0.21), (2.83, 0.20), (2.93, 0.19), (3.03, 0.18), (3.13, 0.17), (3.24, 0.16), (3.34, 0.15), (3.44, 0.14), (3.54, 0.13), (3.64, 0.13), (3.74, 0.12), (3.84, 0.11), (3.94, 0.11), (4.04, 0.10), (4.15, 0.10), (4.25, 0.09), (4.35, 0.09), (4.45, 0.08), (4.55, 0.08), (4.65, 0.07), (4.75, 0.07), (4.85, 0.06), (4.96, 0.06), (5.06, 0.06), (5.16, 0.05), (5.26, 0.05), (5.36, 0.05), (5.46, 0.05), (5.56, 0.04), (5.66, 0.04), (5.76, 0.04), (5.87, 0.04), (5.97, 0.03), (6.07, 0.03), (6.17, 0.03), (6.27, 0.03), (6.37, 0.03), (6.47, 0.03), (6.57, 0.02), (6.67, 0.02), (6.78, 0.02), (6.88, 0.02), (6.98, 0.02), (7.08, 0.02), (7.18, 0.02), (7.28, 0.02), (7.38, 0.02), (7.48, 0.01), (7.58, 0.01), (7.69, 0.01), (7.79, 0.01), (7.89, 0.01), (7.99, 0.01), (8.09, 0.01), (8.19, 0.01), (8.29, 0.01), (8.39, 0.01), (8.49, 0.01), (8.60, 0.01), (8.70, 0.01), (8.80, 0.01), (8.90, 0.01), (9.00, 0.01)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.10112359550561797, 0.20224719101123595, 0.3033707865168539, 0.4044943820224719, 0.5056179775280899, 0.6067415730337078, 0.7078651685393258, 0.8089887640449438, 0.9101123595505618, 1.0112359550561798, 1.1123595505617978, 1.2134831460674156, 1.3146067415730336, 1.4157303370786516, 1.5168539325842696, 1.6179775280898876, 1.7191011235955056, 1.8202247191011236, 1.9213483146067416, 2.0224719101123596, 2.1235955056179776, 2.2247191011235956, 2.3258426966292136, 2.426966292134831, 2.528089887640449, 2.629213483146067, 2.730337078651685, 2.831460674157303, 2.932584269662921, 3.033707865168539, 3.134831460674157, 3.235955056179775, 3.337078651685393, 3.438202247191011, 3.539325842696629, 3.640449438202247, 3.741573033707865, 3.842696629213483, 3.943820224719101, 4.044943820224719, 4.146067415730337, 4.247191011235955, 4.348314606741573, 4.449438202247191, 4.550561797752809, 4.651685393258427, 4.752808988764045, 4.853932584269662, 4.955056179775281, 5.056179775280898, 5.157303370786517, 5.258426966292134, 5.359550561797753, 5.46067415730337, 5.561797752808989, 5.662921348314606, 5.764044943820225, 5.865168539325842, 5.966292134831461, 6.067415730337078, 6.168539325842697, 6.269662921348314, 6.370786516853933, 6.47191011235955, 6.573033707865168, 6.674157303370786, 6.775280898876404, 6.876404494382022, 6.97752808988764, 7.078651685393258, 7.179775280898876, 7.280898876404494, 7.382022471910112, 7.48314606741573, 7.584269662921348, 7.685393258426966, 7.786516853932584, 7.887640449438202, 7.98876404494382, 8.089887640449438, 8.191011235955056, 8.292134831460674, 8.393258426966291, 8.49438202247191, 8.595505617977528, 8.696629213483146, 8.797752808988763, 8.898876404494382, 9.0], "x": [0.9990645807261991, 0.9434310476438139, 0.890895479857204, 0.8412853798738317, 0.7944378565860061, 0.7501990473061133, 0.7084237031024212, 0.6689747106340959, 0.6317224330684198, 0.5965445475374537, 0.5633255850081708, 0.5319564350382597, 0.502334096498992, 0.47436129738839194, 0.4479461820286136, 0.42300200938064486, 0.3994468723704938, 0.37720342304365484, 0.3561986025566984, 0.3363634416805953, 0.31763282244366897, 0.2999452275049271, 0.28324258236705174, 0.26747003502899824, 0.25257579245827844, 0.23851094443423296, 0.22522930718038667, 0.2126872666444315, 0.2008436379063984, 0.18965952912491302, 0.17909821465287837, 0.16912501280441197, 0.15970717341633042, 0.15081377508581567, 0.14241561080019935, 0.13448510357564014, 0.12699621302240316, 0.11992434472228053, 0.11324627905350887, 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0.007664851518841805, 0.00723802936255813, 0.006834975119483336, 0.006454365101117337, 0.006094949612573914], "k": 0.5665954483751449}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 1.19), (0.10, 1.07), (0.20, 0.96), (0.30, 0.86), (0.40, 0.77), (0.51, 0.69), (0.61, 0.62), (0.71, 0.56), (0.81, 0.50), (0.91, 0.45), (1.01, 0.40), (1.11, 0.36), (1.21, 0.32), (1.31, 0.29), (1.42, 0.26), (1.52, 0.23), (1.62, 0.21), (1.72, 0.19), (1.82, 0.17), (1.92, 0.15), (2.02, 0.14), (2.12, 0.12), (2.22, 0.11), (2.33, 0.10), (2.43, 0.09), (2.53, 0.08), (2.63, 0.07), (2.73, 0.06), (2.83, 0.06), (2.93, 0.05), (3.03, 0.05), (3.13, 0.04), (3.24, 0.04), (3.34, 0.03), (3.44, 0.03), (3.54, 0.03), (3.64, 0.02), (3.74, 0.02), (3.84, 0.02), (3.94, 0.02), (4.04, 0.02), (4.15, 0.01), (4.25, 0.01), (4.35, 0.01), (4.45, 0.01), (4.55, 0.01), (4.65, 0.01), (4.75, 0.01), (4.85, 0.01), (4.96, 0.01), (5.06, 0.01), (5.16, 0.00), (5.26, 0.00), (5.36, 0.00), (5.46, 0.00), (5.56, 0.00), (5.66, 0.00), (5.76, 0.00), (5.87, 0.00), (5.97, 0.00), (6.07, 0.00), (6.17, 0.00), (6.27, 0.00), (6.37, 0.00), (6.47, 0.00), (6.57, 0.00), (6.67, 0.00), (6.78, 0.00), (6.88, 0.00), (6.98, 0.00), (7.08, 0.00), (7.18, 0.00), (7.28, 0.00), (7.38, 0.00), (7.48, 0.00), (7.58, 0.00), (7.69, 0.00), (7.79, 0.00), (7.89, 0.00), (7.99, 0.00), (8.09, 0.00), (8.19, 0.00), (8.29, 0.00), (8.39, 0.00), (8.49, 0.00), (8.60, 0.00), (8.70, 0.00), (8.80, 0.00), (8.90, 0.00), (9.00, 0.00)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.10112359550561797, 0.20224719101123595, 0.3033707865168539, 0.4044943820224719, 0.5056179775280899, 0.6067415730337078, 0.7078651685393258, 0.8089887640449438, 0.9101123595505618, 1.0112359550561798, 1.1123595505617978, 1.2134831460674156, 1.3146067415730336, 1.4157303370786516, 1.5168539325842696, 1.6179775280898876, 1.7191011235955056, 1.8202247191011236, 1.9213483146067416, 2.0224719101123596, 2.1235955056179776, 2.2247191011235956, 2.3258426966292136, 2.426966292134831, 2.528089887640449, 2.629213483146067, 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7.98876404494382, 8.089887640449438, 8.191011235955056, 8.292134831460674, 8.393258426966291, 8.49438202247191, 8.595505617977528, 8.696629213483146, 8.797752808988763, 8.898876404494382, 9.0], "x": [1.188187598267351, 1.0662186684847608, 0.9567699647704395, 0.8585562694149458, 0.7704244415558206, 0.6913393889029832, 0.6203725289516995, 0.5566905065001106, 0.49954552425860765, 0.448266558976338, 0.40225141202222564, 0.36095978701542425, 0.32390680769311325, 0.29065736273659837, 0.260821015532287, 0.2340474074947141, 0.21002214349059065, 0.1884630997759651, 0.16911712175436786, 0.15175703372143057, 0.13617898015734087, 0.12220003308387864, 0.10965604360904277, 0.09839971093005243, 0.08829885475081563, 0.07923486403359013, 0.07110130318746065, 0.06380266308430504, 0.057253243779174186, 0.05137612795706023, 0.046102305786587264, 0.041369845511557805, 0.03712317856661967, 0.03331243796469754, 0.02989287393836495, 0.0268243323779197, 0.02407078099072477, 0.0215998851184295, 0.019382629861279078, 0.017392978510565378, 0.015607567704111638, 0.014005431257683236, 0.012567756263030902, 0.01127766026982742, 0.010119994285716001, 0.009081164240924314, 0.008148971321772967, 0.007312469234043388, 0.006561835034591287, 0.005888254511367647, 0.005283817753890205, 0.0047414272965777575, 0.004254713791323527, 0.003817962105663029, 0.0034260434952764407, 0.003074355849674983, 0.0027587693655695285, 0.002475578220329395, 0.002221457025503526, 0.0019934217003000315, 0.0017887947735067337, 0.001605172895914556, 0.0014403998222150256, 0.0012925408578982407, 0.0011598595121314103, 0.001040797930036674, 0.0009339585897846923, 0.0008380862088981162, 0.0007520556254561002, 0.0006748559129796916, 0.0006055810920633629, 0.0005434172573151437, 0.0004876347428570935, 0.00043757837192650873, 0.0003926603394396153, 0.000352353178874844, 0.0003161834525006194, 0.00028372684972619825, 0.0002546018347782929, 0.00022846666690419217, 0.00020501422482065984, 0.0001839692244158663, 0.000165084526081929, 0.00014813831442030958, 0.00013293175502229062, 0.00011928610331709745, 0.00010704125024122518, 9.605329368042794e-05, 8.61932687826519e-05, 7.734542648164995e-05], "k": 1.0710726063036837}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 1.74), (0.11, 1.65), (0.22, 1.57), (0.33, 1.49), (0.44, 1.41), (0.55, 1.34), (0.66, 1.28), (0.77, 1.21), (0.88, 1.15), (0.99, 1.10), (1.10, 1.04), (1.21, 0.99), (1.32, 0.94), (1.43, 0.89), (1.54, 0.85), (1.65, 0.81), (1.76, 0.77), (1.87, 0.73), (1.98, 0.69), (2.09, 0.66), (2.20, 0.62), (2.31, 0.59), (2.42, 0.56), (2.53, 0.53), (2.64, 0.51), (2.75, 0.48), (2.86, 0.46), (2.97, 0.44), (3.08, 0.41), (3.19, 0.39), (3.30, 0.37), (3.41, 0.36), (3.52, 0.34), (3.63, 0.32), (3.74, 0.30), (3.85, 0.29), (3.96, 0.27), (4.07, 0.26), (4.18, 0.25), (4.29, 0.24), (4.40, 0.22), (4.51, 0.21), (4.62, 0.20), (4.73, 0.19), (4.84, 0.18), (4.95, 0.17), (5.06, 0.16), (5.17, 0.16), (5.28, 0.15), (5.39, 0.14), (5.50, 0.13), (5.61, 0.13), (5.72, 0.12), (5.83, 0.12), (5.94, 0.11), (6.06, 0.10), (6.17, 0.10), (6.28, 0.09), (6.39, 0.09), (6.50, 0.08), (6.61, 0.08), (6.72, 0.08), (6.83, 0.07), (6.94, 0.07), (7.05, 0.07), (7.16, 0.06), (7.27, 0.06), (7.38, 0.06), (7.49, 0.05), (7.60, 0.05), (7.71, 0.05), (7.82, 0.05), (7.93, 0.04), (8.04, 0.04), (8.15, 0.04), (8.26, 0.04), (8.37, 0.04), (8.48, 0.03), (8.59, 0.03), (8.70, 0.03), (8.81, 0.03), (8.92, 0.03), (9.03, 0.03), (9.14, 0.02), (9.25, 0.02), (9.36, 0.02), (9.47, 0.02), (9.58, 0.02), (9.69, 0.02), (9.80, 0.02), (9.91, 0.02), (10.02, 0.02), (10.13, 0.02), (10.24, 0.01), (10.35, 0.01), (10.46, 0.01), (10.57, 0.01), (10.68, 0.01), (10.79, 0.01), (10.90, 0.01), (11.01, 0.01), (11.12, 0.01), (11.23, 0.01), (11.34, 0.01), (11.45, 0.01), (11.56, 0.01), (11.67, 0.01), (11.78, 0.01), (11.89, 0.01), (12.00, 0.01)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.11009174311926606, 0.22018348623853212, 0.3302752293577982, 0.44036697247706424, 0.5504587155963303, 0.6605504587155964, 0.7706422018348624, 0.8807339449541285, 0.9908256880733946, 1.1009174311926606, 1.2110091743119267, 1.3211009174311927, 1.4311926605504588, 1.5412844036697249, 1.651376146788991, 1.761467889908257, 1.871559633027523, 1.981651376146789, 2.091743119266055, 2.2018348623853212, 2.3119266055045875, 2.4220183486238533, 2.532110091743119, 2.6422018348623855, 2.7522935779816518, 2.8623853211009176, 2.9724770642201834, 3.0825688073394497, 3.192660550458716, 3.302752293577982, 3.4128440366972477, 3.522935779816514, 3.6330275229357802, 3.743119266055046, 3.853211009174312, 3.963302752293578, 4.0733944954128445, 4.18348623853211, 4.293577981651376, 4.4036697247706424, 4.513761467889909, 4.623853211009175, 4.73394495412844, 4.844036697247707, 4.954128440366973, 5.064220183486238, 5.174311926605505, 5.284403669724771, 5.394495412844037, 5.5045871559633035, 5.614678899082569, 5.724770642201835, 5.8348623853211015, 5.944954128440367, 6.055045871559633, 6.165137614678899, 6.275229357798166, 6.385321100917432, 6.495412844036697, 6.605504587155964, 6.71559633027523, 6.825688073394495, 6.935779816513762, 7.045871559633028, 7.155963302752294, 7.2660550458715605, 7.376146788990826, 7.486238532110092, 7.596330275229358, 7.706422018348624, 7.81651376146789, 7.926605504587156, 8.036697247706423, 8.146788990825689, 8.256880733944955, 8.36697247706422, 8.477064220183486, 8.587155963302752, 8.697247706422019, 8.807339449541285, 8.917431192660551, 9.027522935779817, 9.137614678899084, 9.24770642201835, 9.357798165137615, 9.46788990825688, 9.577981651376147, 9.688073394495413, 9.79816513761468, 9.908256880733946, 10.018348623853212, 10.128440366972477, 10.238532110091743, 10.34862385321101, 10.458715596330276, 10.568807339449542, 10.678899082568808, 10.788990825688074, 10.89908256880734, 11.009174311926607, 11.119266055045872, 11.229357798165138, 11.339449541284404, 11.44954128440367, 11.559633027522937, 11.669724770642203, 11.77981651376147, 11.889908256880734, 12.0], "x": [1.7358227045779662, 1.6492008112030705, 1.5669015365154855, 1.488709189494093, 1.4144188462248526, 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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 0.60), (0.10, 0.59), (0.20, 0.58), (0.30, 0.57), (0.41, 0.56), (0.51, 0.55), (0.61, 0.55), (0.71, 0.54), (0.81, 0.53), (0.91, 0.52), (1.01, 0.52), (1.11, 0.51), (1.22, 0.50), (1.32, 0.49), (1.42, 0.49), (1.52, 0.48), (1.62, 0.47), (1.72, 0.47), (1.82, 0.46), (1.92, 0.45), (2.03, 0.45), (2.13, 0.44), (2.23, 0.43), (2.33, 0.43), (2.43, 0.42), (2.53, 0.42), (2.63, 0.41), (2.73, 0.40), (2.84, 0.40), (2.94, 0.39), (3.04, 0.39), (3.14, 0.38), (3.24, 0.38), (3.34, 0.37), (3.44, 0.37), (3.54, 0.36), (3.65, 0.36), (3.75, 0.35), (3.85, 0.35), (3.95, 0.34), (4.05, 0.34), (4.15, 0.33), (4.25, 0.33), (4.35, 0.32), (4.46, 0.32), (4.56, 0.31), (4.66, 0.31), (4.76, 0.30), (4.86, 0.30), (4.96, 0.30), (5.06, 0.29), (5.16, 0.29), (5.27, 0.28), (5.37, 0.28), (5.47, 0.28), (5.57, 0.27), (5.67, 0.27), (5.77, 0.26), (5.87, 0.26), (5.97, 0.26), (6.08, 0.25), (6.18, 0.25), (6.28, 0.25), (6.38, 0.24), (6.48, 0.24), (6.58, 0.24), (6.68, 0.23), (6.78, 0.23), (6.89, 0.23), (6.99, 0.22), (7.09, 0.22), (7.19, 0.22), (7.29, 0.21), (7.39, 0.21), (7.49, 0.21), (7.59, 0.20), (7.70, 0.20), (7.80, 0.20), (7.90, 0.20), (8.00, 0.19)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.10126582278481013, 0.20253164556962025, 0.3037974683544304, 0.4050632911392405, 0.5063291139240507, 0.6075949367088608, 0.7088607594936709, 0.810126582278481, 0.9113924050632911, 1.0126582278481013, 1.1139240506329113, 1.2151898734177216, 1.3164556962025316, 1.4177215189873418, 1.5189873417721518, 1.620253164556962, 1.7215189873417722, 1.8227848101265822, 1.9240506329113924, 2.0253164556962027, 2.1265822784810124, 2.2278481012658227, 2.329113924050633, 2.430379746835443, 2.5316455696202533, 2.632911392405063, 2.7341772151898733, 2.8354430379746836, 2.9367088607594938, 3.0379746835443036, 3.1392405063291138, 3.240506329113924, 3.3417721518987342, 3.4430379746835444, 3.5443037974683542, 3.6455696202531644, 3.7468354430379747, 3.848101265822785, 3.9493670886075947, 4.050632911392405, 4.151898734177215, 4.253164556962025, 4.3544303797468356, 4.455696202531645, 4.556962025316456, 4.658227848101266, 4.7594936708860756, 4.860759493670886, 4.962025316455696, 5.063291139240507, 5.1645569620253164, 5.265822784810126, 5.367088607594937, 5.468354430379747, 5.5696202531645564, 5.670886075949367, 5.772151898734177, 5.8734177215189876, 5.974683544303797, 6.075949367088607, 6.177215189873418, 6.2784810126582276, 6.379746835443038, 6.481012658227848, 6.582278481012658, 6.6835443037974684, 6.784810126582278, 6.886075949367089, 6.987341772151899, 7.0886075949367084, 7.189873417721519, 7.291139240506329, 7.3924050632911396, 7.493670886075949, 7.594936708860759, 7.69620253164557, 7.7974683544303796, 7.898734177215189, 8.0], "x": [0.5953198653556546, 0.5868744911086354, 0.5785489734258906, 0.5703415464456087, 0.5622505428339531, 0.5542743212914397, 0.5464112507001494, 0.5386597270638057, 0.5310181671632789, 0.5234850121110303, 0.5160587217803282, 0.5087377841231062, 0.5015207048430547, 0.49440600869422546, 0.48739224359204486, 0.4804779772304599, 0.47366179864124813, 0.4669423157481528, 0.46031815714619745, 0.45378796944960603, 0.4473504175706396, 0.4410041877046184, 0.43474798517798985, 0.4285805341090927, 0.4225005770752832, 0.41650687478006077, 0.4105982054167202, 0.40477336162006916, 0.3990311539119822, 0.39337040974839216, 0.3877899726072509, 0.38228870162358214, 0.3768654712245345, 0.3715191707644339, 0.3662487079283526, 0.36105301085481467, 0.35593101961943346, 0.35088168975714235, 0.34590399216912104, 0.3409969125118175, 0.3361594474110587, 0.3313906086948773, 0.3266894224887526, 0.3220549283906414, 0.31748617920842653, 0.31298224242765277, 0.30854219962421375, 0.3041651443820454, 0.29985018312415884, 0.29559643491674387, 0.29140303133189127, 0.28726911648108155, 0.2831938464762936, 0.2791763893383842, 0.2752159248308703, 0.2713116442786094, 0.2674627507883112, 0.2636684587845817, 0.2599279936529784, 0.2562405917105468, 0.2526055000300445, 0.24902197648113197, 0.24548928969771325, 0.24200671860152478, 0.23857355218384024, 0.2351890894744512, 0.2318526394096522, 0.22856352122411874, 0.2253210636300607, 0.2221246046791382, 0.21897349176364936, 0.21586708147540482, 0.21280473946785983, 0.2097858403215035, 0.20680976741250587, 0.20387591312738673, 0.2009836788502869, 0.19813247411685755, 0.19532171688001607, 0.1925508334147531], "k": 0.14109234205774512}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 1.39), (0.10, 1.27), (0.20, 1.16), (0.31, 1.07), (0.41, 0.98), (0.51, 0.89), (0.61, 0.82), (0.71, 0.75), (0.81, 0.68), (0.92, 0.63), (1.02, 0.57), (1.12, 0.53), (1.22, 0.48), (1.32, 0.44), (1.42, 0.40), (1.53, 0.37), (1.63, 0.34), (1.73, 0.31), (1.83, 0.28), (1.93, 0.26), (2.03, 0.24), (2.14, 0.22), (2.24, 0.20), (2.34, 0.18), (2.44, 0.17), (2.54, 0.15), (2.64, 0.14), (2.75, 0.13), (2.85, 0.12), (2.95, 0.11), (3.05, 0.10), (3.15, 0.09), (3.25, 0.08), (3.36, 0.08), (3.46, 0.07), (3.56, 0.06), (3.66, 0.06), (3.76, 0.05), (3.86, 0.05), (3.97, 0.04), (4.07, 0.04), (4.17, 0.04), (4.27, 0.03), (4.37, 0.03), (4.47, 0.03), (4.58, 0.03), (4.68, 0.02), (4.78, 0.02), (4.88, 0.02), (4.98, 0.02), (5.08, 0.02), (5.19, 0.02), (5.29, 0.01), (5.39, 0.01), (5.49, 0.01), (5.59, 0.01), (5.69, 0.01), (5.80, 0.01), (5.90, 0.01), (6.00, 0.01)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.1016949152542373, 0.2033898305084746, 0.3050847457627119, 0.4067796610169492, 0.5084745762711864, 0.6101694915254238, 0.7118644067796611, 0.8135593220338984, 0.9152542372881356, 1.0169491525423728, 1.1186440677966103, 1.2203389830508475, 1.3220338983050848, 1.4237288135593222, 1.5254237288135595, 1.6271186440677967, 1.728813559322034, 1.8305084745762712, 1.9322033898305087, 2.0338983050847457, 2.135593220338983, 2.2372881355932206, 2.3389830508474576, 2.440677966101695, 2.5423728813559325, 2.6440677966101696, 2.745762711864407, 2.8474576271186445, 2.9491525423728815, 3.050847457627119, 3.152542372881356, 3.2542372881355934, 3.355932203389831, 3.457627118644068, 3.5593220338983054, 3.6610169491525424, 3.76271186440678, 3.8644067796610173, 3.9661016949152543, 4.067796610169491, 4.169491525423729, 4.271186440677966, 4.372881355932203, 4.474576271186441, 4.576271186440678, 4.677966101694915, 4.779661016949153, 4.88135593220339, 4.983050847457627, 5.084745762711865, 5.186440677966102, 5.288135593220339, 5.389830508474577, 5.491525423728814, 5.593220338983051, 5.694915254237289, 5.796610169491526, 5.898305084745763, 6.0], "x": [1.3893926321713086, 1.271831133094406, 1.1642168922666898, 1.0657082732878753, 0.9755348255764695, 0.8929913378662229, 0.8174321073984047, 0.7482662241486542, 0.684952714938681, 0.626996391146334, 0.5739439670456301, 0.5253805037406767, 0.48092614046556165, 0.440233233009918, 0.4029835040661284, 0.36888561199212855, 0.337672864228245, 0.3091011414592548, 0.28294697547869413, 0.2590058074312857, 0.23709038609598826, 0.21702930868113085, 0.19866567139531902, 0.18185584951303282, 0.16646836637585077, 0.1523828739868264, 0.1394892070512223, 0.12768651895011104, 0.11688249997464503, 0.10699264792219487, 0.09793961165953342, 0.08965258609666521, 0.08206675371102735, 0.07512279016020867, 0.06876638385074352, 0.0629478128598759, 0.05762157330340428, 0.05274600335754123, 0.04828297361584316, 0.04419757659005213, 0.04045786044628557, 0.03703457440691004, 0.03390094496794471, 0.031032463513623158, 0.02840669495984386, 0.026003101902504502, 0.023802885641716065, 0.021788837586846656, 0.019945205818281003, 0.018257569907547115, 0.01671273123546121, 0.015298606672689724, 0.014004136402462444, 0.012819195923787692, 0.011734517505047061, 0.010741617791103051, 0.009832730658260114, 0.009000747917653876, 0.008239162086967157, 0.007542016940544727], "k": 0.8693554105706675}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 1.69), (0.10, 1.59), (0.20, 1.50), (0.31, 1.42), (0.41, 1.34), (0.51, 1.26), (0.61, 1.19), (0.71, 1.12), (0.81, 1.06), (0.92, 1.00), (1.02, 0.94), (1.12, 0.89), (1.22, 0.83), (1.32, 0.79), (1.42, 0.74), (1.53, 0.70), (1.63, 0.66), (1.73, 0.62), (1.83, 0.59), (1.93, 0.55), (2.03, 0.52), (2.14, 0.49), (2.24, 0.46), (2.34, 0.44), (2.44, 0.41), (2.54, 0.39), (2.64, 0.37), (2.75, 0.35), (2.85, 0.33), (2.95, 0.31), (3.05, 0.29), (3.15, 0.27), (3.25, 0.26), (3.36, 0.24), (3.46, 0.23), (3.56, 0.22), (3.66, 0.20), (3.76, 0.19), (3.86, 0.18), (3.97, 0.17), (4.07, 0.16), (4.17, 0.15), (4.27, 0.14), (4.37, 0.14), (4.47, 0.13), (4.58, 0.12), (4.68, 0.11), (4.78, 0.11), (4.88, 0.10), (4.98, 0.09), (5.08, 0.09), (5.19, 0.08), (5.29, 0.08), (5.39, 0.08), (5.49, 0.07), (5.59, 0.07), (5.69, 0.06), (5.80, 0.06), (5.90, 0.06), (6.00, 0.05)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.1016949152542373, 0.2033898305084746, 0.3050847457627119, 0.4067796610169492, 0.5084745762711864, 0.6101694915254238, 0.7118644067796611, 0.8135593220338984, 0.9152542372881356, 1.0169491525423728, 1.1186440677966103, 1.2203389830508475, 1.3220338983050848, 1.4237288135593222, 1.5254237288135595, 1.6271186440677967, 1.728813559322034, 1.8305084745762712, 1.9322033898305087, 2.0338983050847457, 2.135593220338983, 2.2372881355932206, 2.3389830508474576, 2.440677966101695, 2.5423728813559325, 2.6440677966101696, 2.745762711864407, 2.8474576271186445, 2.9491525423728815, 3.050847457627119, 3.152542372881356, 3.2542372881355934, 3.355932203389831, 3.457627118644068, 3.5593220338983054, 3.6610169491525424, 3.76271186440678, 3.8644067796610173, 3.9661016949152543, 4.067796610169491, 4.169491525423729, 4.271186440677966, 4.372881355932203, 4.474576271186441, 4.576271186440678, 4.677966101694915, 4.779661016949153, 4.88135593220339, 4.983050847457627, 5.084745762711865, 5.186440677966102, 5.288135593220339, 5.389830508474577, 5.491525423728814, 5.593220338983051, 5.694915254237289, 5.796610169491526, 5.898305084745763, 6.0], "x": [1.6894754236156584, 1.5930737897611862, 1.502172800636095, 1.4164586316034693, 1.3356353255399434, 1.2594237645301603, 1.1875609091272255, 1.1197985833968869, 1.0559027214041832, 0.9956527921022756, 0.9388407237956115, 0.8852703586777604, 0.8347567254475511, 0.7871254063774812, 0.7422119364436749, 0.6998612454632267, 0.6599270883374136, 0.6222715567629287, 0.5867646516546917, 0.5532837829828877, 0.5217133350059446, 0.49194430892612934, 0.4638739057491017, 0.4374052034588814, 0.41244680675813317, 0.3889125413425195, 0.3667211431440044, 0.34579598966718667, 0.3260648268827016, 0.3074595271948752, 0.28991584534420856, 0.27337321015674565, 0.25777450005435, 0.243065853792899, 0.22919648595792036, 0.2161185041800167, 0.20378675542778252, 0.19215865665369342, 0.18119405917726453, 0.1708551032791876, 0.16110608869593157, 0.1519133553315955, 0.14324515928856388, 0.13507157256327235, 0.12736437124186592, 0.1200969437834967, 0.11324419676375229, 0.10678246692961335, 0.10068944540198696, 0.09494409504919399, 0.08952657681516313, 0.08441818108033693, 0.0796012705117142, 0.07505921425843008, 0.07077632657865075, 0.06673782066465711, 0.06292975281013527, 0.059338973340900235, 0.055953084512686324, 0.052760395157939656], "k": 0.5777354169737321}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 1.06), (0.10, 1.03), (0.20, 1.01), (0.30, 0.98), (0.41, 0.96), (0.51, 0.93), (0.61, 0.91), (0.71, 0.88), (0.81, 0.86), (0.91, 0.84), (1.01, 0.81), (1.11, 0.79), (1.22, 0.77), (1.32, 0.75), (1.42, 0.73), (1.52, 0.71), (1.62, 0.70), (1.72, 0.68), (1.82, 0.66), (1.92, 0.64), (2.03, 0.63), (2.13, 0.61), (2.23, 0.59), (2.33, 0.58), (2.43, 0.56), (2.53, 0.55), (2.63, 0.53), (2.73, 0.52), (2.84, 0.51), (2.94, 0.49), (3.04, 0.48), (3.14, 0.47), (3.24, 0.46), (3.34, 0.44), (3.44, 0.43), (3.54, 0.42), (3.65, 0.41), (3.75, 0.40), (3.85, 0.39), (3.95, 0.38), (4.05, 0.37), (4.15, 0.36), (4.25, 0.35), (4.35, 0.34), (4.46, 0.33), (4.56, 0.32), (4.66, 0.31), (4.76, 0.31), (4.86, 0.30), (4.96, 0.29), (5.06, 0.28), (5.16, 0.28), (5.27, 0.27), (5.37, 0.26), (5.47, 0.25), (5.57, 0.25), (5.67, 0.24), (5.77, 0.24), (5.87, 0.23), (5.97, 0.22), (6.08, 0.22), (6.18, 0.21), (6.28, 0.21), (6.38, 0.20), (6.48, 0.20), (6.58, 0.19), (6.68, 0.19), (6.78, 0.18), (6.89, 0.18), (6.99, 0.17), (7.09, 0.17), (7.19, 0.16), (7.29, 0.16), (7.39, 0.15), (7.49, 0.15), (7.59, 0.15), (7.70, 0.14), (7.80, 0.14), (7.90, 0.13), (8.00, 0.13)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.10126582278481013, 0.20253164556962025, 0.3037974683544304, 0.4050632911392405, 0.5063291139240507, 0.6075949367088608, 0.7088607594936709, 0.810126582278481, 0.9113924050632911, 1.0126582278481013, 1.1139240506329113, 1.2151898734177216, 1.3164556962025316, 1.4177215189873418, 1.5189873417721518, 1.620253164556962, 1.7215189873417722, 1.8227848101265822, 1.9240506329113924, 2.0253164556962027, 2.1265822784810124, 2.2278481012658227, 2.329113924050633, 2.430379746835443, 2.5316455696202533, 2.632911392405063, 2.7341772151898733, 2.8354430379746836, 2.9367088607594938, 3.0379746835443036, 3.1392405063291138, 3.240506329113924, 3.3417721518987342, 3.4430379746835444, 3.5443037974683542, 3.6455696202531644, 3.7468354430379747, 3.848101265822785, 3.9493670886075947, 4.050632911392405, 4.151898734177215, 4.253164556962025, 4.3544303797468356, 4.455696202531645, 4.556962025316456, 4.658227848101266, 4.7594936708860756, 4.860759493670886, 4.962025316455696, 5.063291139240507, 5.1645569620253164, 5.265822784810126, 5.367088607594937, 5.468354430379747, 5.5696202531645564, 5.670886075949367, 5.772151898734177, 5.8734177215189876, 5.974683544303797, 6.075949367088607, 6.177215189873418, 6.2784810126582276, 6.379746835443038, 6.481012658227848, 6.582278481012658, 6.6835443037974684, 6.784810126582278, 6.886075949367089, 6.987341772151899, 7.0886075949367084, 7.189873417721519, 7.291139240506329, 7.3924050632911396, 7.493670886075949, 7.594936708860759, 7.69620253164557, 7.7974683544303796, 7.898734177215189, 8.0], "x": [1.0617613450606933, 1.034040729987301, 1.0070438489114506, 0.9807517974669567, 0.9551461781809094, 0.9302090688527201, 0.9059230256746753, 0.8822710475438895, 0.859236578879368, 0.8368034974104672, 0.8149560942702877, 0.7936790764130657, 0.7729575636227514, 0.7527770679353678, 0.7331234635462954, 0.7139829889373168, 0.6953422300460637, 0.6771881251639602, 0.6595079841569255, 0.642289443508146, 0.6255204543506542, 0.609189274712214, 0.5932844687377794, 0.5777949069359417, 0.5627097490289985, 0.5480184365045143, 0.5337106874996769, 0.5197764872950049, 0.5062060832029622, 0.4929899777689054, 0.4801189200067453, 0.46758390181544573, 0.4553761500783881, 0.4434871200839592, 0.43190849274989374, 0.42063216393738656, 0.4096502396306539, 0.39895503031902413, 0.3885390497003069, 0.378395008776943, 0.3685158081987969, 0.3588945357287926, 0.34952446081538036, 0.34039902116071075, 0.3315118287917419, 0.32285666417259273, 0.31442747123945497, 0.30621835076676246, 0.2982235550300839, 0.29043748836787975, 0.28285470143505304, 0.2754698874140028, 0.2682778771041548, 0.26127363651432783, 0.2544522634801752, 0.24780898411684635, 0.24133914904714324, 0.23503822929919282, 0.22890181477826907, 0.22292561066853428, 0.2171054344529263, 0.2114372123226841, 0.20591697680145318, 0.20054086428389498, 0.1953051122043084, 0.19020605619644354, 0.1852401266517984, 0.180403847767594, 0.1756938347543733, 0.17110679149550015, 0.16663950836463592, 0.16228885839746293, 0.1580517955233053, 0.15392535418298853, 0.14990664639847429, 0.14599285983579494, 0.14218125575196716, 0.13846916553569696, 0.13485399075239823, 0.13133320116702651], "k": 0.26124334508536695}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 1.69), (0.11, 1.56), (0.22, 1.44), (0.33, 1.33), (0.44, 1.23), (0.55, 1.14), (0.66, 1.05), (0.77, 0.97), (0.88, 0.90), (0.99, 0.83), (1.10, 0.77), (1.21, 0.71), (1.32, 0.66), (1.43, 0.61), (1.54, 0.56), (1.65, 0.52), (1.76, 0.48), (1.87, 0.44), (1.98, 0.41), (2.09, 0.38), (2.20, 0.35), (2.31, 0.32), (2.42, 0.30), (2.53, 0.28), (2.64, 0.26), (2.75, 0.24), (2.86, 0.22), (2.97, 0.20), (3.08, 0.19), (3.19, 0.17), (3.30, 0.16), (3.41, 0.15), (3.52, 0.14), (3.63, 0.13), (3.74, 0.12), (3.85, 0.11), (3.96, 0.10), (4.07, 0.09), (4.18, 0.08), (4.29, 0.08), (4.40, 0.07), (4.51, 0.07), (4.62, 0.06), (4.73, 0.06), (4.84, 0.05), (4.95, 0.05), (5.06, 0.05), (5.17, 0.04), (5.28, 0.04), (5.39, 0.04), (5.50, 0.03), (5.61, 0.03), (5.72, 0.03), (5.83, 0.03), (5.94, 0.02), (6.06, 0.02), (6.17, 0.02), (6.28, 0.02), (6.39, 0.02), (6.50, 0.02), (6.61, 0.02), (6.72, 0.01), (6.83, 0.01), (6.94, 0.01), (7.05, 0.01), (7.16, 0.01), (7.27, 0.01), (7.38, 0.01), (7.49, 0.01), (7.60, 0.01), (7.71, 0.01), (7.82, 0.01), (7.93, 0.01), (8.04, 0.01), (8.15, 0.00), (8.26, 0.00), (8.37, 0.00), (8.48, 0.00), (8.59, 0.00), (8.70, 0.00), (8.81, 0.00), (8.92, 0.00), (9.03, 0.00), (9.14, 0.00), (9.25, 0.00), (9.36, 0.00), (9.47, 0.00), (9.58, 0.00), (9.69, 0.00), (9.80, 0.00), (9.91, 0.00), (10.02, 0.00), (10.13, 0.00), (10.24, 0.00), (10.35, 0.00), (10.46, 0.00), (10.57, 0.00), (10.68, 0.00), (10.79, 0.00), (10.90, 0.00), (11.01, 0.00), (11.12, 0.00), (11.23, 0.00), (11.34, 0.00), (11.45, 0.00), (11.56, 0.00), (11.67, 0.00), (11.78, 0.00), (11.89, 0.00), (12.00, 0.00)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.11009174311926606, 0.22018348623853212, 0.3302752293577982, 0.44036697247706424, 0.5504587155963303, 0.6605504587155964, 0.7706422018348624, 0.8807339449541285, 0.9908256880733946, 1.1009174311926606, 1.2110091743119267, 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6.935779816513762, 7.045871559633028, 7.155963302752294, 7.2660550458715605, 7.376146788990826, 7.486238532110092, 7.596330275229358, 7.706422018348624, 7.81651376146789, 7.926605504587156, 8.036697247706423, 8.146788990825689, 8.256880733944955, 8.36697247706422, 8.477064220183486, 8.587155963302752, 8.697247706422019, 8.807339449541285, 8.917431192660551, 9.027522935779817, 9.137614678899084, 9.24770642201835, 9.357798165137615, 9.46788990825688, 9.577981651376147, 9.688073394495413, 9.79816513761468, 9.908256880733946, 10.018348623853212, 10.128440366972477, 10.238532110091743, 10.34862385321101, 10.458715596330276, 10.568807339449542, 10.678899082568808, 10.788990825688074, 10.89908256880734, 11.009174311926607, 11.119266055045872, 11.229357798165138, 11.339449541284404, 11.44954128440367, 11.559633027522937, 11.669724770642203, 11.77981651376147, 11.889908256880734, 12.0], "x": [1.6895550239056685, 1.5617001505114465, 1.443520480561475, 1.3342839118535013, 1.233313634099903, 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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 0.94), (0.10, 0.93), (0.20, 0.92), (0.30, 0.91), (0.41, 0.90), (0.51, 0.89), (0.61, 0.88), (0.71, 0.87), (0.81, 0.86), (0.91, 0.85), (1.01, 0.84), (1.11, 0.83), (1.22, 0.82), (1.32, 0.81), (1.42, 0.80), (1.52, 0.79), (1.62, 0.79), (1.72, 0.78), (1.82, 0.77), (1.92, 0.76), (2.03, 0.75), (2.13, 0.74), (2.23, 0.74), (2.33, 0.73), (2.43, 0.72), (2.53, 0.71), (2.63, 0.70), (2.73, 0.70), (2.84, 0.69), (2.94, 0.68), (3.04, 0.67), (3.14, 0.67), (3.24, 0.66), (3.34, 0.65), (3.44, 0.64), (3.54, 0.64), (3.65, 0.63), (3.75, 0.62), (3.85, 0.62), (3.95, 0.61), (4.05, 0.60), (4.15, 0.60), (4.25, 0.59), (4.35, 0.58), (4.46, 0.58), (4.56, 0.57), (4.66, 0.57), (4.76, 0.56), (4.86, 0.55), (4.96, 0.55), (5.06, 0.54), (5.16, 0.54), (5.27, 0.53), (5.37, 0.52), (5.47, 0.52), (5.57, 0.51), (5.67, 0.51), (5.77, 0.50), (5.87, 0.50), (5.97, 0.49), (6.08, 0.49), (6.18, 0.48), (6.28, 0.47), (6.38, 0.47), (6.48, 0.46), (6.58, 0.46), (6.68, 0.45), (6.78, 0.45), (6.89, 0.44), (6.99, 0.44), (7.09, 0.43), (7.19, 0.43), (7.29, 0.43), (7.39, 0.42), (7.49, 0.42), (7.59, 0.41), (7.70, 0.41), (7.80, 0.40), (7.90, 0.40), (8.00, 0.39)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.10126582278481013, 0.20253164556962025, 0.3037974683544304, 0.4050632911392405, 0.5063291139240507, 0.6075949367088608, 0.7088607594936709, 0.810126582278481, 0.9113924050632911, 1.0126582278481013, 1.1139240506329113, 1.2151898734177216, 1.3164556962025316, 1.4177215189873418, 1.5189873417721518, 1.620253164556962, 1.7215189873417722, 1.8227848101265822, 1.9240506329113924, 2.0253164556962027, 2.1265822784810124, 2.2278481012658227, 2.329113924050633, 2.430379746835443, 2.5316455696202533, 2.632911392405063, 2.7341772151898733, 2.8354430379746836, 2.9367088607594938, 3.0379746835443036, 3.1392405063291138, 3.240506329113924, 3.3417721518987342, 3.4430379746835444, 3.5443037974683542, 3.6455696202531644, 3.7468354430379747, 3.848101265822785, 3.9493670886075947, 4.050632911392405, 4.151898734177215, 4.253164556962025, 4.3544303797468356, 4.455696202531645, 4.556962025316456, 4.658227848101266, 4.7594936708860756, 4.860759493670886, 4.962025316455696, 5.063291139240507, 5.1645569620253164, 5.265822784810126, 5.367088607594937, 5.468354430379747, 5.5696202531645564, 5.670886075949367, 5.772151898734177, 5.8734177215189876, 5.974683544303797, 6.075949367088607, 6.177215189873418, 6.2784810126582276, 6.379746835443038, 6.481012658227848, 6.582278481012658, 6.6835443037974684, 6.784810126582278, 6.886075949367089, 6.987341772151899, 7.0886075949367084, 7.189873417721519, 7.291139240506329, 7.3924050632911396, 7.493670886075949, 7.594936708860759, 7.69620253164557, 7.7974683544303796, 7.898734177215189, 8.0], "x": [0.935765221762535, 0.9255723941700941, 0.9154905974849437, 0.9055186525170179, 0.8956552958982903, 0.8858993751540485, 0.8762497222158572, 0.8667051761924691, 0.8572645938396644, 0.8479268423366775, 0.8386908013349201, 0.8295553636533536, 0.8205194314817303, 0.8115819240688094, 0.8027417708248487, 0.7939979087184978, 0.7853492891923746, 0.776794874806476, 0.76833363913982, 0.7599645677701966, 0.7516866561886278, 0.7434989116854759, 0.7354003523092983, 0.7273900051362377, 0.7194669084298301, 0.7116301120281993, 0.7038786763705347, 0.6962116723562121, 0.688628181203914, 0.6811272943107506, 0.6737081131113798, 0.6663697488673856, 0.6591113205997605, 0.651931957140529, 0.6448307972683134, 0.6378069888726592, 0.6308596887989836, 0.6239880626935251, 0.6171912848482924, 0.6104685380460141, 0.6038190136191797, 0.5972419161327678, 0.5907364582390577, 0.5843018599685551, 0.5779373500587989, 0.5716421658804968, 0.5654155533636605, 0.5592567663342487, 0.553165064684027, 0.5471397174949809, 0.5411800018618628, 0.5352852026100563, 0.5294546121851947, 0.5236875305427808, 0.5179832660976312, 0.5123411353625009, 0.5067604615483849, 0.5012405752283167, 0.4957808142516047, 0.49038052365804097, 0.4850390556094974, 0.4797557695126085, 0.4745300316793023, 0.46936121526216346, 0.4642487002176386, 0.45919187322368277, 0.4541901275974065, 0.44924286333014407, 0.44434948720564305, 0.4395094122642782, 0.4347220579047519, 0.4299868498210233, 0.4253032199253092, 0.4206706063658451, 0.41608845331004385, 0.4115562114562974, 0.4070733371272719, 0.40263929255607195, 0.3982535458114545, 0.3939155707238966], "k": 0.10815350729791984}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 1.27), (0.10, 1.25), (0.20, 1.23), (0.30, 1.21), (0.41, 1.19), (0.51, 1.17), (0.61, 1.15), (0.71, 1.13), (0.81, 1.11), (0.91, 1.09), (1.01, 1.07), (1.11, 1.06), (1.22, 1.04), (1.32, 1.02), (1.42, 1.00), (1.52, 0.99), (1.62, 0.97), (1.72, 0.96), (1.82, 0.94), (1.92, 0.92), (2.03, 0.91), (2.13, 0.89), (2.23, 0.88), (2.33, 0.86), (2.43, 0.85), (2.53, 0.84), (2.63, 0.82), (2.73, 0.81), (2.84, 0.79), (2.94, 0.78), (3.04, 0.77), (3.14, 0.76), (3.24, 0.74), (3.34, 0.73), (3.44, 0.72), (3.54, 0.71), (3.65, 0.69), (3.75, 0.68), (3.85, 0.67), (3.95, 0.66), (4.05, 0.65), (4.15, 0.64), (4.25, 0.63), (4.35, 0.62), (4.46, 0.61), (4.56, 0.60), (4.66, 0.59), (4.76, 0.58), (4.86, 0.57), (4.96, 0.56), (5.06, 0.55), (5.16, 0.54), (5.27, 0.53), (5.37, 0.52), (5.47, 0.51), (5.57, 0.51), (5.67, 0.50), (5.77, 0.49), (5.87, 0.48), (5.97, 0.47), (6.08, 0.46), (6.18, 0.46), (6.28, 0.45), (6.38, 0.44), (6.48, 0.43), (6.58, 0.43), (6.68, 0.42), (6.78, 0.41), (6.89, 0.41), (6.99, 0.40), (7.09, 0.39), (7.19, 0.39), (7.29, 0.38), (7.39, 0.37), (7.49, 0.37), (7.59, 0.36), (7.70, 0.36), (7.80, 0.35), (7.90, 0.34), (8.00, 0.34)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.10126582278481013, 0.20253164556962025, 0.3037974683544304, 0.4050632911392405, 0.5063291139240507, 0.6075949367088608, 0.7088607594936709, 0.810126582278481, 0.9113924050632911, 1.0126582278481013, 1.1139240506329113, 1.2151898734177216, 1.3164556962025316, 1.4177215189873418, 1.5189873417721518, 1.620253164556962, 1.7215189873417722, 1.8227848101265822, 1.9240506329113924, 2.0253164556962027, 2.1265822784810124, 2.2278481012658227, 2.329113924050633, 2.430379746835443, 2.5316455696202533, 2.632911392405063, 2.7341772151898733, 2.8354430379746836, 2.9367088607594938, 3.0379746835443036, 3.1392405063291138, 3.240506329113924, 3.3417721518987342, 3.4430379746835444, 3.5443037974683542, 3.6455696202531644, 3.7468354430379747, 3.848101265822785, 3.9493670886075947, 4.050632911392405, 4.151898734177215, 4.253164556962025, 4.3544303797468356, 4.455696202531645, 4.556962025316456, 4.658227848101266, 4.7594936708860756, 4.860759493670886, 4.962025316455696, 5.063291139240507, 5.1645569620253164, 5.265822784810126, 5.367088607594937, 5.468354430379747, 5.5696202531645564, 5.670886075949367, 5.772151898734177, 5.8734177215189876, 5.974683544303797, 6.075949367088607, 6.177215189873418, 6.2784810126582276, 6.379746835443038, 6.481012658227848, 6.582278481012658, 6.6835443037974684, 6.784810126582278, 6.886075949367089, 6.987341772151899, 7.0886075949367084, 7.189873417721519, 7.291139240506329, 7.3924050632911396, 7.493670886075949, 7.594936708860759, 7.69620253164557, 7.7974683544303796, 7.898734177215189, 8.0], "x": [1.2708454632675015, 1.2497120455732809, 1.228930155002043, 1.208493798952476, 1.1883972873990618, 1.1686349672069474, 1.1492012796161932, 1.1300907607645312, 1.1112980347465076, 1.0928178256959535, 1.0746449312478503, 1.0567742410490737, 1.039200729633887, 1.0219194546665196, 1.004925556665364, 0.9882142521311476, 0.9717808409555715, 0.9556207043332358, 0.9397293017711239, 0.9241021694644143, 0.9087349159103111, 0.8936232170773348, 0.8787628226155937, 0.8641495508054142, 0.8497792866320353, 0.8356479804573286, 0.8217516613939215, 0.8080864266043012, 0.7946484356987408, 0.7814339137067698, 0.7684391450552852, 0.7556604730829074, 0.7430943034338998, 0.7307371004478177, 0.7185853882478868, 0.7066357516794608, 0.6948848303569184, 0.6833293196214534, 0.6719659697924811, 0.6607915857549089, 0.6498030251255109, 0.6389971975531875, 0.6283710639612082, 0.6179216366549679, 0.6076459771987508, 0.5975411957245715, 0.5876044502818152, 0.5778329467494094, 0.5682239376288376, 0.558774720558468, 0.5494826379372536, 0.5403450774503703, 0.5313594701384459, 0.5225232890739543, 0.5138340491212556, 0.5052893061928729, 0.49688665652431246, 0.488623735967425, 0.4804982207141386, 0.4725078267687247, 0.46465030705821114, 0.45692345207613116, 0.4493250893562692, 0.4418530829650384, 0.43450533301730493, 0.42727977386474614, 0.42017437100730565, 0.41318712608196934, 0.40631607424722904, 0.3995592834857395, 0.3929148541090641, 0.3863809182772788, 0.37995563922819203, 0.3736372088588288, 0.3674238500076827, 0.3613138153793355, 0.3553053867680882, 0.34939687458928664, 0.3435866174210645, 0.3378729815349782], "k": 0.16559595577852176}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 0.63), (0.06, 0.59), (0.12, 0.55), (0.17, 0.51), (0.23, 0.48), (0.29, 0.45), (0.35, 0.42), (0.41, 0.39), (0.46, 0.37), (0.52, 0.34), (0.58, 0.32), (0.64, 0.30), (0.70, 0.28), (0.75, 0.26), (0.81, 0.25), (0.87, 0.23), (0.93, 0.22), (0.99, 0.20), (1.04, 0.19), (1.10, 0.18), (1.16, 0.16), (1.22, 0.15), (1.28, 0.14), (1.33, 0.13), (1.39, 0.13), (1.45, 0.12), (1.51, 0.11), (1.57, 0.10), (1.62, 0.10), (1.68, 0.09), (1.74, 0.08), (1.80, 0.08), (1.86, 0.07), (1.91, 0.07), (1.97, 0.06), (2.03, 0.06), (2.09, 0.06), (2.14, 0.05), (2.20, 0.05), (2.26, 0.05), (2.32, 0.04), (2.38, 0.04), (2.43, 0.04), (2.49, 0.04), (2.55, 0.03), (2.61, 0.03), (2.67, 0.03), (2.72, 0.03), (2.78, 0.03), (2.84, 0.02), (2.90, 0.02), (2.96, 0.02), (3.01, 0.02), (3.07, 0.02), (3.13, 0.02), (3.19, 0.02), (3.25, 0.01), (3.30, 0.01), (3.36, 0.01), (3.42, 0.01), (3.48, 0.01), (3.54, 0.01), (3.59, 0.01), (3.65, 0.01), (3.71, 0.01), (3.77, 0.01), (3.83, 0.01), (3.88, 0.01), (3.94, 0.01), (4.00, 0.01)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.057971014492753624, 0.11594202898550725, 0.17391304347826086, 0.2318840579710145, 0.2898550724637681, 0.34782608695652173, 0.4057971014492754, 0.463768115942029, 0.5217391304347826, 0.5797101449275363, 0.6376811594202899, 0.6956521739130435, 0.7536231884057971, 0.8115942028985508, 0.8695652173913043, 0.927536231884058, 0.9855072463768116, 1.0434782608695652, 1.1014492753623188, 1.1594202898550725, 1.2173913043478262, 1.2753623188405798, 1.3333333333333333, 1.391304347826087, 1.4492753623188406, 1.5072463768115942, 1.565217391304348, 1.6231884057971016, 1.681159420289855, 1.7391304347826086, 1.7971014492753623, 1.855072463768116, 1.9130434782608696, 1.9710144927536233, 2.028985507246377, 2.0869565217391304, 2.1449275362318843, 2.2028985507246377, 2.260869565217391, 2.318840579710145, 2.3768115942028984, 2.4347826086956523, 2.4927536231884058, 2.5507246376811596, 2.608695652173913, 2.6666666666666665, 2.7246376811594204, 2.782608695652174, 2.8405797101449277, 2.898550724637681, 2.956521739130435, 3.0144927536231885, 3.072463768115942, 3.130434782608696, 3.1884057971014492, 3.246376811594203, 3.3043478260869565, 3.36231884057971, 3.420289855072464, 3.4782608695652173, 3.536231884057971, 3.5942028985507246, 3.6521739130434785, 3.710144927536232, 3.7681159420289854, 3.8260869565217392, 3.8840579710144927, 3.9420289855072466, 4.0], "x": [0.6277252862023092, 0.5870895995216436, 0.5490844362346483, 0.5135395280370565, 0.480295616869856, 0.44920371290945776, 0.42012457899800226, 0.3929279191224842, 0.36749176921595494, 0.3437022464510852, 0.3214527320835226, 0.3006435352161375, 0.2811814191978446, 0.26297918073249854, 0.24595526145269955, 0.23003338679577193, 0.21514221071183134, 0.20121500332519957, 0.18818937516268616, 0.17600695917189382, 0.16461317329468686, 0.1539569623699368, 0.14399057979276694, 0.134669369180618, 0.12595156631686563, 0.11779810919691054, 0.11017246476096376, 0.10304046529789278, 0.09637015270818419, 0.09013164225320575, 0.08429698222439143, 0.07884002697424337, 0.07373632868507818, 0.06896301620734191, 0.0644987043073979, 0.060323388809473216, 0.05641836133069906, 0.05276612643034898, 0.04935031743835039, 0.046155631322496865, 0.043167752141782284, 0.04037329311069346, 0.037759733263402095, 0.03531536131447707, 0.03302922609767005, 0.030891082368108926, 0.028891351065284804, 0.027021074367044186, 0.025271871461914803, 0.02363590292181848, 0.022105836686729295, 0.02067481989116807, 0.019336439247225393, 0.018084697138511692, 0.01691398677639714, 0.01581906219005936, 0.014795017373272346, 0.01383726442306203, 0.012941511258567275, 0.012103744160213493, 0.011320209751334007, 0.010587397414544664, 0.009902023790504458, 0.009261017934891886, 0.008661507365752476, 0.008100806010024563, 0.007576401643551961, 0.0070859443524201576, 0.006627236707020966, 0.006198223483459198], "k": 1.1544599879234256}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 1.10), (0.06, 1.03), (0.12, 0.97), (0.17, 0.91), (0.23, 0.86), (0.29, 0.81), (0.35, 0.76), (0.41, 0.71), (0.46, 0.67), (0.52, 0.63), (0.58, 0.59), (0.64, 0.56), (0.70, 0.52), (0.75, 0.49), (0.81, 0.46), (0.87, 0.43), (0.93, 0.41), (0.99, 0.38), (1.04, 0.36), (1.10, 0.34), (1.16, 0.32), (1.22, 0.30), (1.28, 0.28), (1.33, 0.26), (1.39, 0.25), (1.45, 0.23), (1.51, 0.22), (1.57, 0.21), (1.62, 0.19), (1.68, 0.18), (1.74, 0.17), (1.80, 0.16), (1.86, 0.15), (1.91, 0.14), (1.97, 0.13), (2.03, 0.13), (2.09, 0.12), (2.14, 0.11), (2.20, 0.10), (2.26, 0.10), (2.32, 0.09), (2.38, 0.09), (2.43, 0.08), (2.49, 0.08), (2.55, 0.07), (2.61, 0.07), (2.67, 0.06), (2.72, 0.06), (2.78, 0.06), (2.84, 0.05), (2.90, 0.05), (2.96, 0.05), (3.01, 0.04), (3.07, 0.04), (3.13, 0.04), (3.19, 0.04), (3.25, 0.03), (3.30, 0.03), (3.36, 0.03), (3.42, 0.03), (3.48, 0.03), (3.54, 0.03), (3.59, 0.02), (3.65, 0.02), (3.71, 0.02), (3.77, 0.02), (3.83, 0.02), (3.88, 0.02), (3.94, 0.02), (4.00, 0.02)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.057971014492753624, 0.11594202898550725, 0.17391304347826086, 0.2318840579710145, 0.2898550724637681, 0.34782608695652173, 0.4057971014492754, 0.463768115942029, 0.5217391304347826, 0.5797101449275363, 0.6376811594202899, 0.6956521739130435, 0.7536231884057971, 0.8115942028985508, 0.8695652173913043, 0.927536231884058, 0.9855072463768116, 1.0434782608695652, 1.1014492753623188, 1.1594202898550725, 1.2173913043478262, 1.2753623188405798, 1.3333333333333333, 1.391304347826087, 1.4492753623188406, 1.5072463768115942, 1.565217391304348, 1.6231884057971016, 1.681159420289855, 1.7391304347826086, 1.7971014492753623, 1.855072463768116, 1.9130434782608696, 1.9710144927536233, 2.028985507246377, 2.0869565217391304, 2.1449275362318843, 2.2028985507246377, 2.260869565217391, 2.318840579710145, 2.3768115942028984, 2.4347826086956523, 2.4927536231884058, 2.5507246376811596, 2.608695652173913, 2.6666666666666665, 2.7246376811594204, 2.782608695652174, 2.8405797101449277, 2.898550724637681, 2.956521739130435, 3.0144927536231885, 3.072463768115942, 3.130434782608696, 3.1884057971014492, 3.246376811594203, 3.3043478260869565, 3.36231884057971, 3.420289855072464, 3.4782608695652173, 3.536231884057971, 3.5942028985507246, 3.6521739130434785, 3.710144927536232, 3.7681159420289854, 3.8260869565217392, 3.8840579710144927, 3.9420289855072466, 4.0], "x": [1.0972322583938154, 1.0313639438207225, 0.9694497594019961, 0.9112523664556837, 0.8565486439762333, 0.8051288239683819, 0.7567958591320044, 0.7113644148111482, 0.668660224445187, 0.6285196489646545, 0.590788760576123, 0.5553229082884739, 0.5219861196834006, 0.4906505839369351, 0.46119616319552176, 0.43350993878897326, 0.4074857526548959, 0.3830238187754037, 0.3600303708431425, 0.33841725253809846, 0.318101602124787, 0.2990055298899971, 0.2810558208834247, 0.26418365619409295, 0.24832435127750016, 0.23341710198053794, 0.21940475551117705, 0.20623358867933314, 0.19385310511984022, 0.18221583643187275, 0.17127716962409195, 0.16099516713018477, 0.1513304062052231, 0.1422458357132439, 0.13370662272257983, 0.12568003149174023, 0.1181352870003772, 0.11104346360117451, 0.10437737300428344, 0.09811145586028137, 0.09222169140238674, 0.08668549666530209, 0.08148164770584031, 0.07659019294441574, 0.07199237843035274, 0.06767057759127215, 0.063608218947118, 0.059789729552052195, 0.056200471871936046, 0.05282668401849716, 0.04965542865003026, 0.04667454648807907, 0.04387261168000392, 0.04123887989075053, 0.03876325351207446, 0.036436242810065494, 0.03424892556036352, 0.032192916006538674, 0.03026033192518594, 0.02844376314111188, 0.026736245177258824, 0.025131231834781442, 0.023622569704475502, 0.022204474827061477, 0.020871510288864477, 0.019618565214616357, 0.01844083617664831, 0.01733380786393413, 0.016293235799606405, 0.015315130822997122], "k": 1.0679262206897344}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 1.47), (0.10, 1.44), (0.20, 1.40), (0.31, 1.36), (0.41, 1.33), (0.51, 1.30), (0.61, 1.26), (0.71, 1.23), (0.81, 1.20), (0.92, 1.17), (1.02, 1.14), (1.12, 1.11), (1.22, 1.08), (1.32, 1.05), (1.42, 1.03), (1.53, 1.00), (1.63, 0.97), (1.73, 0.95), (1.83, 0.92), (1.93, 0.90), (2.03, 0.88), (2.14, 0.86), (2.24, 0.83), (2.34, 0.81), (2.44, 0.79), (2.54, 0.77), (2.64, 0.75), (2.75, 0.73), (2.85, 0.71), (2.95, 0.70), (3.05, 0.68), (3.15, 0.66), (3.25, 0.64), (3.36, 0.63), (3.46, 0.61), (3.56, 0.60), (3.66, 0.58), (3.76, 0.57), (3.86, 0.55), (3.97, 0.54), (4.07, 0.52), (4.17, 0.51), (4.27, 0.50), (4.37, 0.48), (4.47, 0.47), (4.58, 0.46), (4.68, 0.45), (4.78, 0.44), (4.88, 0.43), (4.98, 0.41), (5.08, 0.40), (5.19, 0.39), (5.29, 0.38), (5.39, 0.37), (5.49, 0.36), (5.59, 0.35), (5.69, 0.35), (5.80, 0.34), (5.90, 0.33), (6.00, 0.32)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.1016949152542373, 0.2033898305084746, 0.3050847457627119, 0.4067796610169492, 0.5084745762711864, 0.6101694915254238, 0.7118644067796611, 0.8135593220338984, 0.9152542372881356, 1.0169491525423728, 1.1186440677966103, 1.2203389830508475, 1.3220338983050848, 1.4237288135593222, 1.5254237288135595, 1.6271186440677967, 1.728813559322034, 1.8305084745762712, 1.9322033898305087, 2.0338983050847457, 2.135593220338983, 2.2372881355932206, 2.3389830508474576, 2.440677966101695, 2.5423728813559325, 2.6440677966101696, 2.745762711864407, 2.8474576271186445, 2.9491525423728815, 3.050847457627119, 3.152542372881356, 3.2542372881355934, 3.355932203389831, 3.457627118644068, 3.5593220338983054, 3.6610169491525424, 3.76271186440678, 3.8644067796610173, 3.9661016949152543, 4.067796610169491, 4.169491525423729, 4.271186440677966, 4.372881355932203, 4.474576271186441, 4.576271186440678, 4.677966101694915, 4.779661016949153, 4.88135593220339, 4.983050847457627, 5.084745762711865, 5.186440677966102, 5.288135593220339, 5.389830508474577, 5.491525423728814, 5.593220338983051, 5.694915254237289, 5.796610169491526, 5.898305084745763, 6.0], "x": [1.474354136395516, 1.4366584388830916, 1.3999265236699276, 1.3641337474888073, 1.3292561016263345, 1.2952701869494672, 1.262153217672685, 1.2298829709333212, 1.1984377973957618, 1.1677966010290461, 1.1379388152626915, 1.1088444124101704, 1.0804938905418178, 1.0528682451093017, 1.0259489381340698, 0.9997179007880685, 0.9741575098693972, 0.9492506197115514, 0.9249805364658802, 0.9013309904566994, 0.8782861118968481, 0.8558304356353778, 0.8339488937500409, 0.8126268109033228, 0.79184988255934, 0.7716041709317111, 0.7518760942137928, 0.7326524167994563, 0.7139202434617442, 0.6956670070600441, 0.6778804619000572, 0.6605486767419049, 0.6436600236827111, 0.6272031751002671, 0.611167091861137, 0.5955410146945488, 0.5803144574577883, 0.5654772014598176, 0.55101929536108, 0.5369310404459808, 0.5232029871542244, 0.5098259302709189, 0.4967908967932252, 0.48408913645146995, 0.4717121284646122, 0.45965157104263044, 0.44789937611335573, 0.4364476581204859, 0.42528873285708274, 0.4144151143276409, 0.4038195082573965, 0.3934948070630486, 0.38343408348437424, 0.37363058806726746, 0.36407774435171514, 0.35476914443084323, 0.34569854390927934, 0.3368598567950293, 0.3282471535997431, 0.31985465661027956], "k": 0.25468476503970305}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 0.68), (0.10, 0.62), (0.20, 0.57), (0.30, 0.53), (0.40, 0.49), (0.51, 0.45), (0.61, 0.41), (0.71, 0.38), (0.81, 0.35), (0.91, 0.32), (1.01, 0.30), (1.11, 0.28), (1.21, 0.25), (1.31, 0.23), (1.42, 0.22), (1.52, 0.20), (1.62, 0.18), (1.72, 0.17), (1.82, 0.16), (1.92, 0.14), (2.02, 0.13), (2.12, 0.12), (2.22, 0.11), (2.33, 0.10), (2.43, 0.10), (2.53, 0.09), (2.63, 0.08), (2.73, 0.07), (2.83, 0.07), (2.93, 0.06), (3.03, 0.06), (3.13, 0.05), (3.24, 0.05), (3.34, 0.05), (3.44, 0.04), (3.54, 0.04), (3.64, 0.04), (3.74, 0.03), (3.84, 0.03), (3.94, 0.03), (4.04, 0.03), (4.15, 0.02), (4.25, 0.02), (4.35, 0.02), (4.45, 0.02), (4.55, 0.02), (4.65, 0.02), (4.75, 0.01), (4.85, 0.01), (4.96, 0.01), (5.06, 0.01), (5.16, 0.01), (5.26, 0.01), (5.36, 0.01), (5.46, 0.01), (5.56, 0.01), (5.66, 0.01), (5.76, 0.01), (5.87, 0.01), (5.97, 0.01), (6.07, 0.01), (6.17, 0.00), (6.27, 0.00), (6.37, 0.00), (6.47, 0.00), (6.57, 0.00), (6.67, 0.00), (6.78, 0.00), (6.88, 0.00), (6.98, 0.00), (7.08, 0.00), (7.18, 0.00), (7.28, 0.00), (7.38, 0.00), (7.48, 0.00), (7.58, 0.00), (7.69, 0.00), (7.79, 0.00), (7.89, 0.00), (7.99, 0.00), (8.09, 0.00), (8.19, 0.00), (8.29, 0.00), (8.39, 0.00), (8.49, 0.00), (8.60, 0.00), (8.70, 0.00), (8.80, 0.00), (8.90, 0.00), (9.00, 0.00)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.10112359550561797, 0.20224719101123595, 0.3033707865168539, 0.4044943820224719, 0.5056179775280899, 0.6067415730337078, 0.7078651685393258, 0.8089887640449438, 0.9101123595505618, 1.0112359550561798, 1.1123595505617978, 1.2134831460674156, 1.3146067415730336, 1.4157303370786516, 1.5168539325842696, 1.6179775280898876, 1.7191011235955056, 1.8202247191011236, 1.9213483146067416, 2.0224719101123596, 2.1235955056179776, 2.2247191011235956, 2.3258426966292136, 2.426966292134831, 2.528089887640449, 2.629213483146067, 2.730337078651685, 2.831460674157303, 2.932584269662921, 3.033707865168539, 3.134831460674157, 3.235955056179775, 3.337078651685393, 3.438202247191011, 3.539325842696629, 3.640449438202247, 3.741573033707865, 3.842696629213483, 3.943820224719101, 4.044943820224719, 4.146067415730337, 4.247191011235955, 4.348314606741573, 4.449438202247191, 4.550561797752809, 4.651685393258427, 4.752808988764045, 4.853932584269662, 4.955056179775281, 5.056179775280898, 5.157303370786517, 5.258426966292134, 5.359550561797753, 5.46067415730337, 5.561797752808989, 5.662921348314606, 5.764044943820225, 5.865168539325842, 5.966292134831461, 6.067415730337078, 6.168539325842697, 6.269662921348314, 6.370786516853933, 6.47191011235955, 6.573033707865168, 6.674157303370786, 6.775280898876404, 6.876404494382022, 6.97752808988764, 7.078651685393258, 7.179775280898876, 7.280898876404494, 7.382022471910112, 7.48314606741573, 7.584269662921348, 7.685393258426966, 7.786516853932584, 7.887640449438202, 7.98876404494382, 8.089887640449438, 8.191011235955056, 8.292134831460674, 8.393258426966291, 8.49438202247191, 8.595505617977528, 8.696629213483146, 8.797752808988763, 8.898876404494382, 9.0], "x": [0.6756995789091247, 0.6226953632624115, 0.5738489532526226, 0.5288342318494152, 0.4873505900359201, 0.44912111731424254, 0.4138905159551097, 0.3814234857808752, 0.3515032983647719, 0.32393015040917167, 0.29851993725087284, 0.27510299000966754, 0.25352295276148024, 0.233635729404419, 0.21530851616537688, 0.19841895972975687, 0.18285428006078305, 0.16851055016001631, 0.15529199246257602, 0.14311034454740834, 0.1318842679020313, 0.12153880409670394, 0.11200487435571237, 0.10321881657608645, 0.09512196996703061, 0.08766026760187644, 0.08078388881310633, 0.07444691583894511, 0.0686070386478385, 0.0632252605729314, 0.05826564948140086, 0.05369508659091793, 0.049483055761321296, 0.04560143035803923, 0.042024294286923655, 0.038727760490101994, 0.035689818850986196, 0.0328901824562008, 0.03031016150993302, 0.027932529319906314, 0.025741406512770813, 0.023722161655870877, 0.021861314046490745, 0.020146435662534438, 0.01856607874652145, 0.017109690422366666, 0.01576754671594796, 0.014530685566355348, 0.013390847516731372, 0.012340422310937292, 0.01137239633271526, 0.010480306034708814, 0.009658194331149618, 0.008900571921230723, 0.008202380066596108, 0.00755895662497556, 0.006966005654862111, 0.0064195677984983926, 0.005915994588641574, 0.005451923418965219, 0.005024255460173891, 0.004630135314480813, 0.004266931278681362, 0.003932218317462348, 0.0036237614043241433, 0.003339500912465919, 0.0030775388563893166, 0.002836125928467169, 0.0026136502995067878, 0.002408626427880994, 0.0022196853703554723, 0.0020455655439228127, 0.0018851042232168377, 0.0017372300743696007, 0.001600955678590974, 0.0014753712422296025, 0.0013596382144738823, 0.0012529835069559506, 0.0011546950708717567, 0.0010641166995121755, 0.0009806435711314768, 0.0009037181690072344, 0.0008328268804845668, 0.0007674968542234649, 0.0007072915989136305, 0.0006518089048424198, 0.0006006787020515214, 0.0005535593523323305, 0.0005101360314777471, 0.0004701191480368614], "k": 0.8078350978188267}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 1.80), (0.10, 1.68), (0.20, 1.57), (0.31, 1.47), (0.41, 1.38), (0.51, 1.29), (0.61, 1.20), (0.71, 1.13), (0.81, 1.05), (0.92, 0.98), (1.02, 0.92), (1.12, 0.86), (1.22, 0.81), (1.32, 0.75), (1.42, 0.70), (1.53, 0.66), (1.63, 0.62), (1.73, 0.58), (1.83, 0.54), (1.93, 0.50), (2.03, 0.47), (2.14, 0.44), (2.24, 0.41), (2.34, 0.39), (2.44, 0.36), (2.54, 0.34), (2.64, 0.32), (2.75, 0.30), (2.85, 0.28), (2.95, 0.26), (3.05, 0.24), (3.15, 0.23), (3.25, 0.21), (3.36, 0.20), (3.46, 0.18), (3.56, 0.17), (3.66, 0.16), (3.76, 0.15), (3.86, 0.14), (3.97, 0.13), (4.07, 0.12), (4.17, 0.12), (4.27, 0.11), (4.37, 0.10), (4.47, 0.09), (4.58, 0.09), (4.68, 0.08), (4.78, 0.08), (4.88, 0.07), (4.98, 0.07), (5.08, 0.06), (5.19, 0.06), (5.29, 0.06), (5.39, 0.05), (5.49, 0.05), (5.59, 0.05), (5.69, 0.04), (5.80, 0.04), (5.90, 0.04), (6.00, 0.03)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.1016949152542373, 0.2033898305084746, 0.3050847457627119, 0.4067796610169492, 0.5084745762711864, 0.6101694915254238, 0.7118644067796611, 0.8135593220338984, 0.9152542372881356, 1.0169491525423728, 1.1186440677966103, 1.2203389830508475, 1.3220338983050848, 1.4237288135593222, 1.5254237288135595, 1.6271186440677967, 1.728813559322034, 1.8305084745762712, 1.9322033898305087, 2.0338983050847457, 2.135593220338983, 2.2372881355932206, 2.3389830508474576, 2.440677966101695, 2.5423728813559325, 2.6440677966101696, 2.745762711864407, 2.8474576271186445, 2.9491525423728815, 3.050847457627119, 3.152542372881356, 3.2542372881355934, 3.355932203389831, 3.457627118644068, 3.5593220338983054, 3.6610169491525424, 3.76271186440678, 3.8644067796610173, 3.9661016949152543, 4.067796610169491, 4.169491525423729, 4.271186440677966, 4.372881355932203, 4.474576271186441, 4.576271186440678, 4.677966101694915, 4.779661016949153, 4.88135593220339, 4.983050847457627, 5.084745762711865, 5.186440677966102, 5.288135593220339, 5.389830508474577, 5.491525423728814, 5.593220338983051, 5.694915254237289, 5.796610169491526, 5.898305084745763, 6.0], "x": [1.7969082775345462, 1.6806581517587973, 1.5719287258288217, 1.470233508260439, 1.3751173889866128, 1.2861547752785076, 1.2029476365318144, 1.1251234653374214, 1.0523341224594494, 0.9842538447782417, 0.920577990293504, 0.8610216166047284, 0.8053182152152908, 0.753218530230062, 0.7044894127948698, 0.6589127743170925, 0.6162847000121741, 0.5764144464003387, 0.5391235737659513, 0.5042452158883528, 0.471623300410987, 0.441111844961422, 0.4125743139782164, 0.3858830050237895, 0.36091847883834577, 0.33756902130795446, 0.3157301461241208, 0.2953041264607553, 0.27619955598783347, 0.25833094987791133, 0.24161834351290032, 0.22598695351835998, 0.21136682779288785, 0.1976925457106492, 0.1849029142924971, 0.17294070299154254, 0.16175238136681927, 0.1512878832812706, 0.1415003813040421, 0.13234607709188384, 0.12378400695957661, 0.11577585551748415, 0.10828578832496628, 0.10128028614659255, 0.09472800382270927, 0.08859962127564391, 0.08286771215581334, 0.07750662392619559, 0.07249237002213013, 0.06780250938003997, 0.06341605677715056, 0.059313384062996265, 0.05547613149853254, 0.05188712877547598, 0.0485303146236084, 0.04539066779247361, 0.042454139023134614, 0.03970758777435431, 0.037138723691720894, 0.03473605096011935], "k": 0.6576741272023088}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 2.27), (0.11, 1.85), (0.22, 1.50), (0.33, 1.22), (0.44, 0.99), (0.55, 0.81), (0.66, 0.66), (0.77, 0.54), (0.88, 0.44), (0.99, 0.35), (1.10, 0.29), (1.21, 0.23), (1.32, 0.19), (1.43, 0.16), (1.54, 0.13), (1.65, 0.10), (1.76, 0.08), (1.87, 0.07), (1.98, 0.06), (2.09, 0.05), (2.20, 0.04), (2.31, 0.03), (2.42, 0.02), (2.53, 0.02), (2.64, 0.02), (2.75, 0.01), (2.86, 0.01), (2.97, 0.01), (3.08, 0.01), (3.19, 0.01), (3.30, 0.00), (3.41, 0.00), (3.52, 0.00), (3.63, 0.00), (3.74, 0.00), (3.85, 0.00), (3.96, 0.00), (4.07, 0.00), (4.18, 0.00), (4.29, 0.00), (4.40, 0.00), (4.51, 0.00), (4.62, 0.00), (4.73, 0.00), (4.84, 0.00), (4.95, 0.00), (5.06, 0.00), (5.17, 0.00), (5.28, 0.00), (5.39, 0.00), (5.50, 0.00), (5.61, 0.00), (5.72, 0.00), (5.83, 0.00), (5.94, 0.00), (6.06, 0.00), (6.17, 0.00), (6.28, 0.00), (6.39, 0.00), (6.50, 0.00), (6.61, 0.00), (6.72, 0.00), (6.83, 0.00), (6.94, 0.00), (7.05, 0.00), (7.16, 0.00), (7.27, 0.00), (7.38, 0.00), (7.49, 0.00), (7.60, 0.00), (7.71, 0.00), (7.82, 0.00), (7.93, 0.00), (8.04, 0.00), (8.15, 0.00), (8.26, 0.00), (8.37, 0.00), (8.48, 0.00), (8.59, 0.00), (8.70, 0.00), (8.81, 0.00), (8.92, 0.00), (9.03, 0.00), (9.14, 0.00), (9.25, 0.00), (9.36, 0.00), (9.47, 0.00), (9.58, 0.00), (9.69, 0.00), (9.80, 0.00), (9.91, 0.00), (10.02, 0.00), (10.13, 0.00), (10.24, 0.00), (10.35, 0.00), (10.46, 0.00), (10.57, 0.00), (10.68, 0.00), (10.79, 0.00), (10.90, 0.00), (11.01, 0.00), (11.12, 0.00), (11.23, 0.00), (11.34, 0.00), (11.45, 0.00), (11.56, 0.00), (11.67, 0.00), (11.78, 0.00), (11.89, 0.00), (12.00, 0.00)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.11009174311926606, 0.22018348623853212, 0.3302752293577982, 0.44036697247706424, 0.5504587155963303, 0.6605504587155964, 0.7706422018348624, 0.8807339449541285, 0.9908256880733946, 1.1009174311926606, 1.2110091743119267, 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6.935779816513762, 7.045871559633028, 7.155963302752294, 7.2660550458715605, 7.376146788990826, 7.486238532110092, 7.596330275229358, 7.706422018348624, 7.81651376146789, 7.926605504587156, 8.036697247706423, 8.146788990825689, 8.256880733944955, 8.36697247706422, 8.477064220183486, 8.587155963302752, 8.697247706422019, 8.807339449541285, 8.917431192660551, 9.027522935779817, 9.137614678899084, 9.24770642201835, 9.357798165137615, 9.46788990825688, 9.577981651376147, 9.688073394495413, 9.79816513761468, 9.908256880733946, 10.018348623853212, 10.128440366972477, 10.238532110091743, 10.34862385321101, 10.458715596330276, 10.568807339449542, 10.678899082568808, 10.788990825688074, 10.89908256880734, 11.009174311926607, 11.119266055045872, 11.229357798165138, 11.339449541284404, 11.44954128440367, 11.559633027522937, 11.669724770642203, 11.77981651376147, 11.889908256880734, 12.0], "x": [2.2700654584630824, 1.8468363317215903, 1.5025136839222195, 1.222386252594223, 0.9944855643895242, 0.8090744754295147, 0.6582312904251195, 0.5355111843455183, 0.43567091352125376, 0.35444477632179244, 0.28836237577197904, 0.23460032315592294, 0.19086162668400022, 0.15527753646022252, 0.12632771588395786, 0.10277528612552289, 0.0836139475359191, 0.06802503191330873, 0.05534250007489727, 0.04502448996253902, 0.036630161663769686, 0.029800865210814313, 0.024244816708747702, 0.019724633401278422, 0.016047189131231578, 0.01305536460008266, 0.010621333331572428, 0.008641100768377166, 0.007030061180930953, 0.005719382410831795, 0.004653065527576573, 0.003785551871660453, 0.0030797767212077465, 0.0025055857224077064, 0.0020384463955598455, 0.001658400155019187, 0.001349209887788457, 0.0010976642185451567, 0.000893016008693657, 0.0007265223429589625, 0.0005910698675359185, 0.0004808710550426695, 0.000391217624089576, 0.0003182792799029873, 0.0002589395020792025, 0.00021066297601978696, 0.00017138708960114058, 0.00013943376249723536, 0.0001134372852622938, 9.228853483847945e-05, 7.508295862982001e-05, 6.108537462817388e-05, 4.969671374015153e-05, 4.043124038422979e-05, 3.289342237849854e-05, 2.6760923771712216e-05, 2.1771797661467153e-05, 1.7713171607661913e-05, 1.4410603497248786e-05, 1.1723638544120851e-05, 9.537788060949736e-06, 7.759429963332043e-06, 6.3128481199189085e-06, 5.13574243357229e-06, 4.178012220579113e-06, 3.399128684395326e-06, 2.765404775056246e-06, 2.2500369756809468e-06, 1.8303708992044463e-06, 1.4883549053876764e-06, 1.210390906908044e-06, 9.845533486464115e-07, 8.010633208146432e-07, 6.521648542249476e-07, 5.308794585277731e-07, 4.3195728319162967e-07, 3.5156151968315506e-07, 2.861409095732815e-07, 2.3304457851429393e-07, 1.8992393675946293e-07, 1.5489826459470998e-07, 1.2643739020984373e-07, 1.0282145292054626e-07, 8.345744584091298e-08, 6.76747667750571e-08, 5.4017689449592414e-08, 4.4175656441246535e-08, 3.584315439098916e-08, 2.8908206761496142e-08, 2.3258407563444056e-08, 1.8880005435505132e-08, 1.536588024283536e-08, 1.2526741067794129e-08, 1.0330091767625886e-08, 8.508779660935156e-09, 7.003599407474144e-09, 5.7863088281154146e-09, 4.755772235231823e-09, 3.9029628764178955e-09, 3.203909038020035e-09, 2.6172735347155596e-09, 2.1422375311983467e-09, 1.7534193512421103e-09, 1.4310610357959132e-09, 1.1740272714428476e-09, 9.618153640034879e-10, 7.868153077016097e-10, 6.470501569012772e-10, 5.3026506174016e-10, 4.3435058562507224e-10], "k": 1.8742059421119255}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 1.98), (0.11, 1.76), (0.22, 1.56), (0.33, 1.39), (0.44, 1.24), (0.55, 1.10), (0.66, 0.98), (0.77, 0.87), (0.88, 0.77), (0.99, 0.69), (1.10, 0.61), (1.21, 0.54), (1.32, 0.48), (1.43, 0.43), (1.54, 0.38), (1.65, 0.34), (1.76, 0.30), (1.87, 0.27), (1.98, 0.24), (2.09, 0.21), (2.20, 0.19), (2.31, 0.17), (2.42, 0.15), (2.53, 0.13), (2.64, 0.12), (2.75, 0.11), (2.86, 0.09), (2.97, 0.08), (3.08, 0.07), (3.19, 0.07), (3.30, 0.06), (3.41, 0.05), (3.52, 0.05), (3.63, 0.04), (3.74, 0.04), (3.85, 0.03), (3.96, 0.03), (4.07, 0.03), (4.18, 0.02), (4.29, 0.02), (4.40, 0.02), (4.51, 0.02), (4.62, 0.01), (4.73, 0.01), (4.84, 0.01), (4.95, 0.01), (5.06, 0.01), (5.17, 0.01), (5.28, 0.01), (5.39, 0.01), (5.50, 0.01), (5.61, 0.00), (5.72, 0.00), (5.83, 0.00), (5.94, 0.00), (6.06, 0.00), (6.17, 0.00), (6.28, 0.00), (6.39, 0.00), (6.50, 0.00), (6.61, 0.00), (6.72, 0.00), (6.83, 0.00), (6.94, 0.00), (7.05, 0.00), (7.16, 0.00), (7.27, 0.00), (7.38, 0.00), (7.49, 0.00), (7.60, 0.00), (7.71, 0.00), (7.82, 0.00), (7.93, 0.00), (8.04, 0.00), (8.15, 0.00), (8.26, 0.00), (8.37, 0.00), (8.48, 0.00), (8.59, 0.00), (8.70, 0.00), (8.81, 0.00), (8.92, 0.00), (9.03, 0.00), (9.14, 0.00), (9.25, 0.00), (9.36, 0.00), (9.47, 0.00), (9.58, 0.00), (9.69, 0.00), (9.80, 0.00), (9.91, 0.00), (10.02, 0.00), (10.13, 0.00), (10.24, 0.00), (10.35, 0.00), (10.46, 0.00), (10.57, 0.00), (10.68, 0.00), (10.79, 0.00), (10.90, 0.00), (11.01, 0.00), (11.12, 0.00), (11.23, 0.00), (11.34, 0.00), (11.45, 0.00), (11.56, 0.00), (11.67, 0.00), (11.78, 0.00), (11.89, 0.00), (12.00, 0.00)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.11009174311926606, 0.22018348623853212, 0.3302752293577982, 0.44036697247706424, 0.5504587155963303, 0.6605504587155964, 0.7706422018348624, 0.8807339449541285, 0.9908256880733946, 1.1009174311926606, 1.2110091743119267, 1.3211009174311927, 1.4311926605504588, 1.5412844036697249, 1.651376146788991, 1.761467889908257, 1.871559633027523, 1.981651376146789, 2.091743119266055, 2.2018348623853212, 2.3119266055045875, 2.4220183486238533, 2.532110091743119, 2.6422018348623855, 2.7522935779816518, 2.8623853211009176, 2.9724770642201834, 3.0825688073394497, 3.192660550458716, 3.302752293577982, 3.4128440366972477, 3.522935779816514, 3.6330275229357802, 3.743119266055046, 3.853211009174312, 3.963302752293578, 4.0733944954128445, 4.18348623853211, 4.293577981651376, 4.4036697247706424, 4.513761467889909, 4.623853211009175, 4.73394495412844, 4.844036697247707, 4.954128440366973, 5.064220183486238, 5.174311926605505, 5.284403669724771, 5.394495412844037, 5.5045871559633035, 5.614678899082569, 5.724770642201835, 5.8348623853211015, 5.944954128440367, 6.055045871559633, 6.165137614678899, 6.275229357798166, 6.385321100917432, 6.495412844036697, 6.605504587155964, 6.71559633027523, 6.825688073394495, 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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 1.57), (0.06, 1.48), (0.12, 1.40), (0.17, 1.32), (0.23, 1.24), (0.29, 1.17), (0.35, 1.11), (0.41, 1.05), (0.46, 0.99), (0.52, 0.93), (0.58, 0.88), (0.64, 0.83), (0.70, 0.79), (0.75, 0.74), (0.81, 0.70), (0.87, 0.66), (0.93, 0.62), (0.99, 0.59), (1.04, 0.56), (1.10, 0.52), (1.16, 0.50), (1.22, 0.47), (1.28, 0.44), (1.33, 0.42), (1.39, 0.39), (1.45, 0.37), (1.51, 0.35), (1.57, 0.33), (1.62, 0.31), (1.68, 0.30), (1.74, 0.28), (1.80, 0.26), (1.86, 0.25), (1.91, 0.23), (1.97, 0.22), (2.03, 0.21), (2.09, 0.20), (2.14, 0.19), (2.20, 0.18), (2.26, 0.17), (2.32, 0.16), (2.38, 0.15), (2.43, 0.14), (2.49, 0.13), (2.55, 0.12), (2.61, 0.12), (2.67, 0.11), (2.72, 0.10), (2.78, 0.10), (2.84, 0.09), (2.90, 0.09), (2.96, 0.08), (3.01, 0.08), (3.07, 0.07), (3.13, 0.07), (3.19, 0.07), (3.25, 0.06), (3.30, 0.06), (3.36, 0.06), (3.42, 0.05), (3.48, 0.05), (3.54, 0.05), (3.59, 0.04), (3.65, 0.04), (3.71, 0.04), (3.77, 0.04), (3.83, 0.04), (3.88, 0.03), (3.94, 0.03), (4.00, 0.03)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.057971014492753624, 0.11594202898550725, 0.17391304347826086, 0.2318840579710145, 0.2898550724637681, 0.34782608695652173, 0.4057971014492754, 0.463768115942029, 0.5217391304347826, 0.5797101449275363, 0.6376811594202899, 0.6956521739130435, 0.7536231884057971, 0.8115942028985508, 0.8695652173913043, 0.927536231884058, 0.9855072463768116, 1.0434782608695652, 1.1014492753623188, 1.1594202898550725, 1.2173913043478262, 1.2753623188405798, 1.3333333333333333, 1.391304347826087, 1.4492753623188406, 1.5072463768115942, 1.565217391304348, 1.6231884057971016, 1.681159420289855, 1.7391304347826086, 1.7971014492753623, 1.855072463768116, 1.9130434782608696, 1.9710144927536233, 2.028985507246377, 2.0869565217391304, 2.1449275362318843, 2.2028985507246377, 2.260869565217391, 2.318840579710145, 2.3768115942028984, 2.4347826086956523, 2.4927536231884058, 2.5507246376811596, 2.608695652173913, 2.6666666666666665, 2.7246376811594204, 2.782608695652174, 2.8405797101449277, 2.898550724637681, 2.956521739130435, 3.0144927536231885, 3.072463768115942, 3.130434782608696, 3.1884057971014492, 3.246376811594203, 3.3043478260869565, 3.36231884057971, 3.420289855072464, 3.4782608695652173, 3.536231884057971, 3.5942028985507246, 3.6521739130434785, 3.710144927536232, 3.7681159420289854, 3.8260869565217392, 3.8840579710144927, 3.9420289855072466, 4.0], "x": [1.5650122842637484, 1.4775706440182264, 1.395014581001013, 1.3170711525698442, 1.24348264953696, 1.1740057065049847, 1.1084106786286145, 1.0464806843703967, 0.9880108238869608, 0.9328078601923941, 0.8806892429527203, 0.8314826377358757, 0.7850253456744463, 0.7411637547354514, 0.6997528347305839, 0.66065566448593, 0.6237429739030251, 0.588892682646955, 0.5559895619291376, 0.5249248424283345, 0.49559579408027654, 0.4679054491420378, 0.4417622440814163, 0.4170797341504294, 0.39377630474486275, 0.3717749043420746, 0.3510027852888247, 0.33139126335213615, 0.31287549286491384, 0.29539425051729046, 0.2788897344254327, 0.2633073700634756, 0.24859563951939978, 0.23470589435635136, 0.22159220891707107, 0.20921122288768262, 0.19752199620946254, 0.18648588158560173, 0.17606638480955594, 0.1662290554351362, 0.1569413659218671, 0.14817260512206548, 0.13989378113422277, 0.13207751748307445, 0.12469797131177955, 0.11773074128569608, 0.1111527896974378, 0.10494236765906743, 0.09907893810055694, 0.09354311507236518, 0.0883165968255248, 0.08338210086642144, 0.07872330924849177, 0.07432481532829535, 0.0701720787276845, 0.06625136703441795, 0.06254971491168698, 0.059054885042046076, 0.055755321323059256, 0.05264011327253036, 0.04969896119938787, 0.04692213961091541, 0.04430046644973245, 0.041825273602210084, 0.039488376832154656, 0.03728204923794222, 0.03519899565151294, 0.033232328147569185, 0.03137554376966784, 0.029622503313432684], "k": 0.9917786519569769}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 0.66), (0.10, 0.65), (0.20, 0.64), (0.30, 0.62), (0.41, 0.61), (0.51, 0.60), (0.61, 0.58), (0.71, 0.57), (0.81, 0.56), (0.91, 0.55), (1.01, 0.54), (1.11, 0.53), (1.22, 0.51), (1.32, 0.50), (1.42, 0.49), (1.52, 0.48), (1.62, 0.47), (1.72, 0.46), (1.82, 0.45), (1.92, 0.44), (2.03, 0.43), (2.13, 0.43), (2.23, 0.42), (2.33, 0.41), (2.43, 0.40), (2.53, 0.39), (2.63, 0.38), (2.73, 0.37), (2.84, 0.37), (2.94, 0.36), (3.04, 0.35), (3.14, 0.34), (3.24, 0.34), (3.34, 0.33), (3.44, 0.32), (3.54, 0.32), (3.65, 0.31), (3.75, 0.30), (3.85, 0.30), (3.95, 0.29), (4.05, 0.28), (4.15, 0.28), (4.25, 0.27), (4.35, 0.27), (4.46, 0.26), (4.56, 0.26), (4.66, 0.25), (4.76, 0.24), (4.86, 0.24), (4.96, 0.23), (5.06, 0.23), (5.16, 0.22), (5.27, 0.22), (5.37, 0.22), (5.47, 0.21), (5.57, 0.21), (5.67, 0.20), (5.77, 0.20), (5.87, 0.19), (5.97, 0.19), (6.08, 0.19), (6.18, 0.18), (6.28, 0.18), (6.38, 0.17), (6.48, 0.17), (6.58, 0.17), (6.68, 0.16), (6.78, 0.16), (6.89, 0.16), (6.99, 0.15), (7.09, 0.15), (7.19, 0.15), (7.29, 0.14), (7.39, 0.14), (7.49, 0.14), (7.59, 0.13), (7.70, 0.13), (7.80, 0.13), (7.90, 0.13), (8.00, 0.12)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.10126582278481013, 0.20253164556962025, 0.3037974683544304, 0.4050632911392405, 0.5063291139240507, 0.6075949367088608, 0.7088607594936709, 0.810126582278481, 0.9113924050632911, 1.0126582278481013, 1.1139240506329113, 1.2151898734177216, 1.3164556962025316, 1.4177215189873418, 1.5189873417721518, 1.620253164556962, 1.7215189873417722, 1.8227848101265822, 1.9240506329113924, 2.0253164556962027, 2.1265822784810124, 2.2278481012658227, 2.329113924050633, 2.430379746835443, 2.5316455696202533, 2.632911392405063, 2.7341772151898733, 2.8354430379746836, 2.9367088607594938, 3.0379746835443036, 3.1392405063291138, 3.240506329113924, 3.3417721518987342, 3.4430379746835444, 3.5443037974683542, 3.6455696202531644, 3.7468354430379747, 3.848101265822785, 3.9493670886075947, 4.050632911392405, 4.151898734177215, 4.253164556962025, 4.3544303797468356, 4.455696202531645, 4.556962025316456, 4.658227848101266, 4.7594936708860756, 4.860759493670886, 4.962025316455696, 5.063291139240507, 5.1645569620253164, 5.265822784810126, 5.367088607594937, 5.468354430379747, 5.5696202531645564, 5.670886075949367, 5.772151898734177, 5.8734177215189876, 5.974683544303797, 6.075949367088607, 6.177215189873418, 6.2784810126582276, 6.379746835443038, 6.481012658227848, 6.582278481012658, 6.6835443037974684, 6.784810126582278, 6.886075949367089, 6.987341772151899, 7.0886075949367084, 7.189873417721519, 7.291139240506329, 7.3924050632911396, 7.493670886075949, 7.594936708860759, 7.69620253164557, 7.7974683544303796, 7.898734177215189, 8.0], "x": [0.6639193788797724, 0.6499663773785014, 0.6363066669142962, 0.6229339966624801, 0.6098423670373375, 0.5970258699746908, 0.5844787235243712, 0.5721952655756385, 0.560169962505214, 0.5483973842782236, 0.5368722193514825, 0.5255892684826166, 0.5145434408297895, 0.5037297494846468, 0.49314331318897897, 0.4827793588404995, 0.47263321582878853, 0.46270031323119026, 0.4529761706255997, 0.4434563990332022, 0.4341367011809473, 0.42501286622072565, 0.4160807671930882, 0.4073363761748081, 0.3987757544674886, 0.39039504422497573, 0.38219046944743973, 0.3741583253872313, 0.36629498677172734, 0.3585969033312853, 0.35106060152294916, 0.3436826833213589, 0.3364598200572072, 0.3293887529012384, 0.3224662920246715, 0.31568931438514186, 0.3090547622038282, 0.30255964208195946, 0.2962010242345197, 0.28997603976805725, 0.2838818798019568, 0.2779157950502082, 0.2720750942951867, 0.26635714218542167, 0.2607593588476647, 0.25527921976116946, 0.24991425255987504, 0.24466203647235138, 0.2395202012503846, 0.23448642605387274, 0.22955843959920294, 0.22473401916612892, 0.22001098820945852, 0.2153872162891762, 0.21086061828235073, 0.20642915342705945, 0.2020908210003532, 0.19784366289393848, 0.19368576304583707, 0.18961524586044196, 0.1856302754410098, 0.18172905441331805, 0.17790982179228035, 0.17417085436539398, 0.17051046527754735, 0.16692700318373652, 0.16341885153098507, 0.15998442756237158, 0.15662218158041508, 0.15333059669264837, 0.15010818793497244, 0.14695350162286336, 0.14386511469756308, 0.14084163363019966, 0.13788169423012822, 0.13498396110337335, 0.13214712694706782, 0.1293699119740374, 0.1266510632888567, 0.12398935410154556], "k": 0.20974562789164614}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 0.61), (0.10, 0.57), (0.20, 0.54), (0.31, 0.50), (0.41, 0.47), (0.51, 0.44), (0.61, 0.41), (0.71, 0.38), (0.81, 0.36), (0.92, 0.33), (1.02, 0.31), (1.12, 0.29), (1.22, 0.27), (1.32, 0.26), (1.42, 0.24), (1.53, 0.22), (1.63, 0.21), (1.73, 0.20), (1.83, 0.18), (1.93, 0.17), (2.03, 0.16), (2.14, 0.15), (2.24, 0.14), (2.34, 0.13), (2.44, 0.12), (2.54, 0.11), (2.64, 0.11), (2.75, 0.10), (2.85, 0.09), (2.95, 0.09), (3.05, 0.08), (3.15, 0.08), (3.25, 0.07), (3.36, 0.07), (3.46, 0.06), (3.56, 0.06), (3.66, 0.05), (3.76, 0.05), (3.86, 0.05), (3.97, 0.04), (4.07, 0.04), (4.17, 0.04), (4.27, 0.04), (4.37, 0.03), (4.47, 0.03), (4.58, 0.03), (4.68, 0.03), (4.78, 0.03), (4.88, 0.02), (4.98, 0.02), (5.08, 0.02), (5.19, 0.02), (5.29, 0.02), (5.39, 0.02), (5.49, 0.02), (5.59, 0.02), (5.69, 0.01), (5.80, 0.01), (5.90, 0.01), (6.00, 0.01)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.1016949152542373, 0.2033898305084746, 0.3050847457627119, 0.4067796610169492, 0.5084745762711864, 0.6101694915254238, 0.7118644067796611, 0.8135593220338984, 0.9152542372881356, 1.0169491525423728, 1.1186440677966103, 1.2203389830508475, 1.3220338983050848, 1.4237288135593222, 1.5254237288135595, 1.6271186440677967, 1.728813559322034, 1.8305084745762712, 1.9322033898305087, 2.0338983050847457, 2.135593220338983, 2.2372881355932206, 2.3389830508474576, 2.440677966101695, 2.5423728813559325, 2.6440677966101696, 2.745762711864407, 2.8474576271186445, 2.9491525423728815, 3.050847457627119, 3.152542372881356, 3.2542372881355934, 3.355932203389831, 3.457627118644068, 3.5593220338983054, 3.6610169491525424, 3.76271186440678, 3.8644067796610173, 3.9661016949152543, 4.067796610169491, 4.169491525423729, 4.271186440677966, 4.372881355932203, 4.474576271186441, 4.576271186440678, 4.677966101694915, 4.779661016949153, 4.88135593220339, 4.983050847457627, 5.084745762711865, 5.186440677966102, 5.288135593220339, 5.389830508474577, 5.491525423728814, 5.593220338983051, 5.694915254237289, 5.796610169491526, 5.898305084745763, 6.0], "x": [0.6118974879887868, 0.5722477735825777, 0.5351672598275886, 0.5004894853064579, 0.46805876398261126, 0.4377294563056708, 0.4093654649437207, 0.3828394469188257, 0.358032199182854, 0.3348324319103079, 0.31313596134981003, 0.29284537671830574, 0.27386958189674165, 0.2561233809474864, 0.23952709818010018, 0.22400622459119968, 0.20949107167277697, 0.19591646226625414, 0.18322146321849522, 0.1713490750695991, 0.16024599685717283, 0.1498623758912949, 0.1401515928970433, 0.13107004878660344, 0.12257697113543137, 0.11463422793090149, 0.10720615844842912, 0.10025941299135242, 0.09376280074053403, 0.08768715614199236, 0.08200520272358525, 0.07669142732970458, 0.07172197569848021, 0.06707453333014074, 0.0627282366390457, 0.05866357129175485, 0.054862287523304964, 0.0513073206494886, 0.04798270752117842, 0.04487352355449058, 0.04196580801804897, 0.03924650667843089, 0.03670341107842677, 0.03432510237929316, 0.03210090402496579, 0.030020828219272325, 0.028075536951335914, 0.026256298857288623, 0.02455494549592148, 0.022963836744388046, 0.02147582658486368, 0.020084237248605016, 0.01878281989178633, 0.01756573021693292, 0.016427505881502703, 0.015363036316553516, 0.014367542120234611, 0.013436554453047004, 0.012565892832145414, 0.011751647885072847], "k": 0.6587618814966604}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 1.04), (0.10, 1.00), (0.20, 0.96), (0.30, 0.93), (0.41, 0.89), (0.51, 0.86), (0.61, 0.83), (0.71, 0.80), (0.81, 0.77), (0.91, 0.74), (1.01, 0.71), (1.11, 0.69), (1.22, 0.66), (1.32, 0.64), (1.42, 0.62), (1.52, 0.59), (1.62, 0.57), (1.72, 0.55), (1.82, 0.53), (1.92, 0.51), (2.03, 0.49), (2.13, 0.48), (2.23, 0.46), (2.33, 0.44), (2.43, 0.43), (2.53, 0.41), (2.63, 0.39), (2.73, 0.38), (2.84, 0.37), (2.94, 0.35), (3.04, 0.34), (3.14, 0.33), (3.24, 0.32), (3.34, 0.30), (3.44, 0.29), (3.54, 0.28), (3.65, 0.27), (3.75, 0.26), (3.85, 0.25), (3.95, 0.24), (4.05, 0.23), (4.15, 0.23), (4.25, 0.22), (4.35, 0.21), (4.46, 0.20), (4.56, 0.20), (4.66, 0.19), (4.76, 0.18), (4.86, 0.17), (4.96, 0.17), (5.06, 0.16), (5.16, 0.16), (5.27, 0.15), (5.37, 0.14), (5.47, 0.14), (5.57, 0.13), (5.67, 0.13), (5.77, 0.12), (5.87, 0.12), (5.97, 0.12), (6.08, 0.11), (6.18, 0.11), (6.28, 0.10), (6.38, 0.10), (6.48, 0.10), (6.58, 0.09), (6.68, 0.09), (6.78, 0.09), (6.89, 0.08), (6.99, 0.08), (7.09, 0.08), (7.19, 0.07), (7.29, 0.07), (7.39, 0.07), (7.49, 0.07), (7.59, 0.06), (7.70, 0.06), (7.80, 0.06), (7.90, 0.06), (8.00, 0.06)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.10126582278481013, 0.20253164556962025, 0.3037974683544304, 0.4050632911392405, 0.5063291139240507, 0.6075949367088608, 0.7088607594936709, 0.810126582278481, 0.9113924050632911, 1.0126582278481013, 1.1139240506329113, 1.2151898734177216, 1.3164556962025316, 1.4177215189873418, 1.5189873417721518, 1.620253164556962, 1.7215189873417722, 1.8227848101265822, 1.9240506329113924, 2.0253164556962027, 2.1265822784810124, 2.2278481012658227, 2.329113924050633, 2.430379746835443, 2.5316455696202533, 2.632911392405063, 2.7341772151898733, 2.8354430379746836, 2.9367088607594938, 3.0379746835443036, 3.1392405063291138, 3.240506329113924, 3.3417721518987342, 3.4430379746835444, 3.5443037974683542, 3.6455696202531644, 3.7468354430379747, 3.848101265822785, 3.9493670886075947, 4.050632911392405, 4.151898734177215, 4.253164556962025, 4.3544303797468356, 4.455696202531645, 4.556962025316456, 4.658227848101266, 4.7594936708860756, 4.860759493670886, 4.962025316455696, 5.063291139240507, 5.1645569620253164, 5.265822784810126, 5.367088607594937, 5.468354430379747, 5.5696202531645564, 5.670886075949367, 5.772151898734177, 5.8734177215189876, 5.974683544303797, 6.075949367088607, 6.177215189873418, 6.2784810126582276, 6.379746835443038, 6.481012658227848, 6.582278481012658, 6.6835443037974684, 6.784810126582278, 6.886075949367089, 6.987341772151899, 7.0886075949367084, 7.189873417721519, 7.291139240506329, 7.3924050632911396, 7.493670886075949, 7.594936708860759, 7.69620253164557, 7.7974683544303796, 7.898734177215189, 8.0], "x": [1.0355651910858565, 0.9978470174135022, 0.9615026281633725, 0.9264819973191712, 0.8927369094585771, 0.8602209190948895, 0.82888925248548, 0.7986987679981211, 0.769607886778626, 0.7415765862997923, 0.7145662971541482, 0.6885398173526875, 0.6634612681946026, 0.6392961301725885, 0.6160111643238823, 0.5935743106555483, 0.5719546659646668, 0.5511224685789698, 0.5310490381369887, 0.5117067391552246, 0.49306894065292756, 0.47510998383541486, 0.4578051420640778, 0.44113059178616115, 0.42506337626501006, 0.4095813778969228, 0.3946632781354569, 0.38028853132832563, 0.3664373483562783, 0.3530906616438174, 0.34023010346351046, 0.3278379639724806, 0.3158971793791107, 0.3043913134620397, 0.2933045258257447, 0.2826215496584681, 0.27232767739288066, 0.2624087372866025, 0.252851072187866, 0.24364152385181737, 0.23476741400302545, 0.22621652412607704, 0.2179770814923238, 0.2100377428396718, 0.20238757718149245, 0.19501605173624711, 0.18791301815299835, 0.1810686969105196, 0.17447366397783026, 0.1681188400165234, 0.16199547763398695, 0.15609514644809316, 0.15040972123622043, 0.14493137474338968, 0.13965256566701092, 0.134566026288391, 0.1296647522482544, 0.12494199589340217, 0.12039125617832236, 0.11600626785167038, 0.11178099250877763, 0.10770961316306087, 0.10378652540575549, 0.10000632813950303, 0.09636381578680486, 0.09285397362912273, 0.08947197017764194, 0.08621314927392301, 0.08307302333014589, 0.08004726928573214, 0.07713172205919414, 0.07432236772341377, 0.07161533757990923, 0.06900690482273704, 0.066493478806635, 0.06407159912064528, 0.06173793055034637, 0.05948926028417871, 0.05732249284778393, 0.055234645961795295], "k": 0.3663889982023882}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 0.33), (0.10, 0.32), (0.20, 0.32), (0.30, 0.31), (0.40, 0.30), (0.51, 0.30), (0.61, 0.29), (0.71, 0.29), (0.81, 0.28), (0.91, 0.27), (1.01, 0.27), (1.11, 0.26), (1.21, 0.26), (1.31, 0.25), (1.42, 0.25), (1.52, 0.24), (1.62, 0.24), (1.72, 0.23), (1.82, 0.23), (1.92, 0.22), (2.02, 0.22), (2.12, 0.21), (2.22, 0.21), (2.33, 0.20), (2.43, 0.20), (2.53, 0.19), (2.63, 0.19), (2.73, 0.19), (2.83, 0.18), (2.93, 0.18), (3.03, 0.18), (3.13, 0.17), (3.24, 0.17), (3.34, 0.16), (3.44, 0.16), (3.54, 0.16), (3.64, 0.15), (3.74, 0.15), (3.84, 0.15), (3.94, 0.14), (4.04, 0.14), (4.15, 0.14), (4.25, 0.14), (4.35, 0.13), (4.45, 0.13), (4.55, 0.13), (4.65, 0.12), (4.75, 0.12), (4.85, 0.12), (4.96, 0.12), (5.06, 0.11), (5.16, 0.11), (5.26, 0.11), (5.36, 0.11), (5.46, 0.11), (5.56, 0.10), (5.66, 0.10), (5.76, 0.10), (5.87, 0.10), (5.97, 0.09), (6.07, 0.09), (6.17, 0.09), (6.27, 0.09), (6.37, 0.09), (6.47, 0.09), (6.57, 0.08), (6.67, 0.08), (6.78, 0.08), (6.88, 0.08), (6.98, 0.08), (7.08, 0.08), (7.18, 0.07), (7.28, 0.07), (7.38, 0.07), (7.48, 0.07), (7.58, 0.07), (7.69, 0.07), (7.79, 0.06), (7.89, 0.06), (7.99, 0.06), (8.09, 0.06), (8.19, 0.06), (8.29, 0.06), (8.39, 0.06), (8.49, 0.06), (8.60, 0.05), (8.70, 0.05), (8.80, 0.05), (8.90, 0.05), (9.00, 0.05)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.10112359550561797, 0.20224719101123595, 0.3033707865168539, 0.4044943820224719, 0.5056179775280899, 0.6067415730337078, 0.7078651685393258, 0.8089887640449438, 0.9101123595505618, 1.0112359550561798, 1.1123595505617978, 1.2134831460674156, 1.3146067415730336, 1.4157303370786516, 1.5168539325842696, 1.6179775280898876, 1.7191011235955056, 1.8202247191011236, 1.9213483146067416, 2.0224719101123596, 2.1235955056179776, 2.2247191011235956, 2.3258426966292136, 2.426966292134831, 2.528089887640449, 2.629213483146067, 2.730337078651685, 2.831460674157303, 2.932584269662921, 3.033707865168539, 3.134831460674157, 3.235955056179775, 3.337078651685393, 3.438202247191011, 3.539325842696629, 3.640449438202247, 3.741573033707865, 3.842696629213483, 3.943820224719101, 4.044943820224719, 4.146067415730337, 4.247191011235955, 4.348314606741573, 4.449438202247191, 4.550561797752809, 4.651685393258427, 4.752808988764045, 4.853932584269662, 4.955056179775281, 5.056179775280898, 5.157303370786517, 5.258426966292134, 5.359550561797753, 5.46067415730337, 5.561797752808989, 5.662921348314606, 5.764044943820225, 5.865168539325842, 5.966292134831461, 6.067415730337078, 6.168539325842697, 6.269662921348314, 6.370786516853933, 6.47191011235955, 6.573033707865168, 6.674157303370786, 6.775280898876404, 6.876404494382022, 6.97752808988764, 7.078651685393258, 7.179775280898876, 7.280898876404494, 7.382022471910112, 7.48314606741573, 7.584269662921348, 7.685393258426966, 7.786516853932584, 7.887640449438202, 7.98876404494382, 8.089887640449438, 8.191011235955056, 8.292134831460674, 8.393258426966291, 8.49438202247191, 8.595505617977528, 8.696629213483146, 8.797752808988763, 8.898876404494382, 9.0], "x": [0.3305742038112963, 0.32365845453807485, 0.31688743855537127, 0.31025804319494116, 0.30376733747242735, 0.2974124186171157, 0.2911904451676149, 0.285098636589636, 0.2791342681265258, 0.2732946799585312, 0.26757725815772926, 0.26197944702734, 0.2564987441092976, 0.25113269917623826, 0.2458789138936943, 0.24073503733759283, 0.2356987692404205, 0.23076786011701722, 0.22594010858632615, 0.22121335993767158, 0.21658550137924312, 0.21205446337146253, 0.20761821904978042, 0.2032747818463024, 0.1990222044540562, 0.1948585879589958, 0.19078207424550156, 0.186790842651098, 0.18288311131160814, 0.1790571326558066, 0.17531119564377032, 0.1716436249946435, 0.16805278001389787, 0.16453705657171397, 0.16109488340470696, 0.1577247216886891, 0.15442506474319032, 0.15119443790071754, 0.14803139705966842, 0.14493452812956126, 0.14190244659314227, 0.1389337974389418, 0.1360272536179201, 0.1331815156381632, 0.13039531128690518, 0.12766739542796707, 0.12499654865493198, 0.12238157684557693, 0.11982131121812582, 0.11731460791201045, 0.11486034636897598, 0.11245742930181363, 0.11010478217368584, 0.10780135269080698, 0.10554611045315562, 0.10333804782473491, 0.10117617791572406, 0.0990595343893956, 0.09698717134261041, 0.09495816297114333, 0.09297160325666963, 0.09102660419109208, 0.08912229488153196, 0.08725782405649164, 0.08543235835981146, 0.08364508200207903, 0.08189519643931978, 0.08018191993766562, 0.07850448597541695, 0.07686214444854826, 0.07525416119554026, 0.07367981744126967, 0.07213840948886921, 0.07062924842066132, 0.06915165961206857, 0.0677049823514055, 0.06628856995346319, 0.06490178929354759, 0.0635440205336263, 0.06221465685885835, 0.060913104184337104, 0.059638780492692986, 0.058391116058422336, 0.057169553160229536, 0.055973545758423754, 0.054802559257952736, 0.05365607027803716, 0.052533566319796936, 0.05143454548450857, 0.050358516488826846], "k": 0.20907370767539557}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 0.57), (0.10, 0.55), (0.20, 0.54), (0.30, 0.52), (0.41, 0.50), (0.51, 0.48), (0.61, 0.47), (0.71, 0.45), (0.81, 0.44), (0.91, 0.42), (1.01, 0.41), (1.11, 0.40), (1.22, 0.38), (1.32, 0.37), (1.42, 0.36), (1.52, 0.35), (1.62, 0.34), (1.72, 0.33), (1.82, 0.32), (1.92, 0.31), (2.03, 0.30), (2.13, 0.29), (2.23, 0.28), (2.33, 0.27), (2.43, 0.26), (2.53, 0.25), (2.63, 0.24), (2.73, 0.23), (2.84, 0.23), (2.94, 0.22), (3.04, 0.21), (3.14, 0.21), (3.24, 0.20), (3.34, 0.19), (3.44, 0.19), (3.54, 0.18), (3.65, 0.17), (3.75, 0.17), (3.85, 0.16), (3.95, 0.16), (4.05, 0.15), (4.15, 0.15), (4.25, 0.14), (4.35, 0.14), (4.46, 0.13), (4.56, 0.13), (4.66, 0.13), (4.76, 0.12), (4.86, 0.12), (4.96, 0.11), (5.06, 0.11), (5.16, 0.11), (5.27, 0.10), (5.37, 0.10), (5.47, 0.10), (5.57, 0.09), (5.67, 0.09), (5.77, 0.09), (5.87, 0.08), (5.97, 0.08), (6.08, 0.08), (6.18, 0.08), (6.28, 0.07), (6.38, 0.07), (6.48, 0.07), (6.58, 0.07), (6.68, 0.06), (6.78, 0.06), (6.89, 0.06), (6.99, 0.06), (7.09, 0.06), (7.19, 0.06), (7.29, 0.05), (7.39, 0.05), (7.49, 0.05), (7.59, 0.05), (7.70, 0.05), (7.80, 0.05), (7.90, 0.04), (8.00, 0.04)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.10126582278481013, 0.20253164556962025, 0.3037974683544304, 0.4050632911392405, 0.5063291139240507, 0.6075949367088608, 0.7088607594936709, 0.810126582278481, 0.9113924050632911, 1.0126582278481013, 1.1139240506329113, 1.2151898734177216, 1.3164556962025316, 1.4177215189873418, 1.5189873417721518, 1.620253164556962, 1.7215189873417722, 1.8227848101265822, 1.9240506329113924, 2.0253164556962027, 2.1265822784810124, 2.2278481012658227, 2.329113924050633, 2.430379746835443, 2.5316455696202533, 2.632911392405063, 2.7341772151898733, 2.8354430379746836, 2.9367088607594938, 3.0379746835443036, 3.1392405063291138, 3.240506329113924, 3.3417721518987342, 3.4430379746835444, 3.5443037974683542, 3.6455696202531644, 3.7468354430379747, 3.848101265822785, 3.9493670886075947, 4.050632911392405, 4.151898734177215, 4.253164556962025, 4.3544303797468356, 4.455696202531645, 4.556962025316456, 4.658227848101266, 4.7594936708860756, 4.860759493670886, 4.962025316455696, 5.063291139240507, 5.1645569620253164, 5.265822784810126, 5.367088607594937, 5.468354430379747, 5.5696202531645564, 5.670886075949367, 5.772151898734177, 5.8734177215189876, 5.974683544303797, 6.075949367088607, 6.177215189873418, 6.2784810126582276, 6.379746835443038, 6.481012658227848, 6.582278481012658, 6.6835443037974684, 6.784810126582278, 6.886075949367089, 6.987341772151899, 7.0886075949367084, 7.189873417721519, 7.291139240506329, 7.3924050632911396, 7.493670886075949, 7.594936708860759, 7.69620253164557, 7.7974683544303796, 7.898734177215189, 8.0], "x": [0.5715431190217124, 0.553020426360689, 0.5350980097312412, 0.5177564253257321, 0.5009768464511396, 0.48474106145455204, 0.46903145415924863, 0.4538309676962359, 0.43912310206976707, 0.42489188379866516, 0.41112186362478015, 0.39779811062418635, 0.38490617778598796, 0.37243206669964823, 0.36036222434760795, 0.3486835212799164, 0.3373832905641946, 0.32644928394364414, 0.31586963870737617, 0.30563286314032384, 0.2957278391323192, 0.28614381935516453, 0.276870400621526, 0.26789751744031876, 0.25921542971247, 0.25081471310758224, 0.24268624939296773, 0.23482121435263664, 0.22721107162244836, 0.21984756006311745, 0.2127226879979937, 0.20582872197540564, 0.19915817706270614, 0.19270381003230092, 0.18645861558593144, 0.18041581541090773, 0.17456885299681543, 0.1689113824681578, 0.16343725980346585, 0.15814054353755094, 0.15301548580576796, 0.14805652266306174, 0.14325827058443397, 0.13861552135881086, 0.1341232356905138, 0.1297765368660565, 0.12557070670323803, 0.1215011802829585, 0.11756354032878893, 0.11375351225783883, 0.11006696044983356, 0.10649988345809458, 0.1030484091262088, 0.09970879087284962, 0.09647740378295287, 0.09335074036858558, 0.0903254060473494, 0.08739811686384578, 0.08456569566112658, 0.08182506877695199, 0.07917326187356098, 0.07660739503113576, 0.07412468299253856, 0.07172243108586154, 0.069398032382029, 0.06714896405858413, 0.06497278369426965, 0.06286712908229217, 0.060829714840995926, 0.058858330047106354, 0.056950834927743374, 0.055105158001746736, 0.05331929585770556, 0.05159131023685668, 0.04991932604219865, 0.048301528355514406, 0.04673616035392071, 0.045221522896929045, 0.043755972089531504, 0.04233791759658596], "k": 0.32533207881898174}}
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{"data_source": "LinearODE", "prompt": "下面给出变量 x(t) 的观测数据点：\n(0.00, 2.71), (0.11, 2.51), (0.22, 2.32), (0.33, 2.14), (0.44, 1.98), (0.55, 1.83), (0.66, 1.69), (0.77, 1.56), (0.88, 1.44), (0.99, 1.33), (1.10, 1.23), (1.21, 1.14), (1.32, 1.05), (1.43, 0.97), (1.54, 0.90), (1.65, 0.83), (1.76, 0.77), (1.87, 0.71), (1.98, 0.66), (2.09, 0.61), (2.20, 0.56), (2.31, 0.52), (2.42, 0.48), (2.53, 0.44), (2.64, 0.41), (2.75, 0.38), (2.86, 0.35), (2.97, 0.32), (3.08, 0.30), (3.19, 0.28), (3.30, 0.25), (3.41, 0.23), (3.52, 0.22), (3.63, 0.20), (3.74, 0.19), (3.85, 0.17), (3.96, 0.16), (4.07, 0.15), (4.18, 0.14), (4.29, 0.12), (4.40, 0.12), (4.51, 0.11), (4.62, 0.10), (4.73, 0.09), (4.84, 0.08), (4.95, 0.08), (5.06, 0.07), (5.17, 0.07), (5.28, 0.06), (5.39, 0.06), (5.50, 0.05), (5.61, 0.05), (5.72, 0.04), (5.83, 0.04), (5.94, 0.04), (6.06, 0.04), (6.17, 0.03), (6.28, 0.03), (6.39, 0.03), (6.50, 0.03), (6.61, 0.02), (6.72, 0.02), (6.83, 0.02), (6.94, 0.02), (7.05, 0.02), (7.16, 0.02), (7.27, 0.01), (7.38, 0.01), (7.49, 0.01), (7.60, 0.01), (7.71, 0.01), (7.82, 0.01), (7.93, 0.01), (8.04, 0.01), (8.15, 0.01), (8.26, 0.01), (8.37, 0.01), (8.48, 0.01), (8.59, 0.01), (8.70, 0.01), (8.81, 0.00), (8.92, 0.00), (9.03, 0.00), (9.14, 0.00), (9.25, 0.00), (9.36, 0.00), (9.47, 0.00), (9.58, 0.00), (9.69, 0.00), (9.80, 0.00), (9.91, 0.00), (10.02, 0.00), (10.13, 0.00), (10.24, 0.00), (10.35, 0.00), (10.46, 0.00), (10.57, 0.00), (10.68, 0.00), (10.79, 0.00), (10.90, 0.00), (11.01, 0.00), (11.12, 0.00), (11.23, 0.00), (11.34, 0.00), (11.45, 0.00), (11.56, 0.00), (11.67, 0.00), (11.78, 0.00), (11.89, 0.00), (12.00, 0.00)\n\n请找出其满足的微分方程，形式为：dx/dt = f(x)。\n以dx/dt = <表达式>格式表示你的答案。并且使用[answer]标签包裹你的最终答案, 例如[answer]dx/dt = <表达式>[/answer].", "ground_truth": {"t": [0.0, 0.11009174311926606, 0.22018348623853212, 0.3302752293577982, 0.44036697247706424, 0.5504587155963303, 0.6605504587155964, 0.7706422018348624, 0.8807339449541285, 0.9908256880733946, 1.1009174311926606, 1.2110091743119267, 1.3211009174311927, 1.4311926605504588, 1.5412844036697249, 1.651376146788991, 1.761467889908257, 1.871559633027523, 1.981651376146789, 2.091743119266055, 2.2018348623853212, 2.3119266055045875, 2.4220183486238533, 2.532110091743119, 2.6422018348623855, 2.7522935779816518, 2.8623853211009176, 2.9724770642201834, 3.0825688073394497, 3.192660550458716, 3.302752293577982, 3.4128440366972477, 3.522935779816514, 3.6330275229357802, 3.743119266055046, 3.853211009174312, 3.963302752293578, 4.0733944954128445, 4.18348623853211, 4.293577981651376, 4.4036697247706424, 4.513761467889909, 4.623853211009175, 4.73394495412844, 4.844036697247707, 4.954128440366973, 5.064220183486238, 5.174311926605505, 5.284403669724771, 5.394495412844037, 5.5045871559633035, 5.614678899082569, 5.724770642201835, 5.8348623853211015, 5.944954128440367, 6.055045871559633, 6.165137614678899, 6.275229357798166, 6.385321100917432, 6.495412844036697, 6.605504587155964, 6.71559633027523, 6.825688073394495, 6.935779816513762, 7.045871559633028, 7.155963302752294, 7.2660550458715605, 7.376146788990826, 7.486238532110092, 7.596330275229358, 7.706422018348624, 7.81651376146789, 7.926605504587156, 8.036697247706423, 8.146788990825689, 8.256880733944955, 8.36697247706422, 8.477064220183486, 8.587155963302752, 8.697247706422019, 8.807339449541285, 8.917431192660551, 9.027522935779817, 9.137614678899084, 9.24770642201835, 9.357798165137615, 9.46788990825688, 9.577981651376147, 9.688073394495413, 9.79816513761468, 9.908256880733946, 10.018348623853212, 10.128440366972477, 10.238532110091743, 10.34862385321101, 10.458715596330276, 10.568807339449542, 10.678899082568808, 10.788990825688074, 10.89908256880734, 11.009174311926607, 11.119266055045872, 11.229357798165138, 11.339449541284404, 11.44954128440367, 11.559633027522937, 11.669724770642203, 11.77981651376147, 11.889908256880734, 12.0], "x": [2.7138814157537636, 2.507908756620988, 2.317568525821206, 2.141674355655851, 1.9791298115939266, 1.8289218742136373, 1.6901140203797436, 1.5618411540223325, 1.4433036768032979, 1.3337627191934878, 1.2325354807829607, 1.138991012541465, 1.0525461612317988, 0.9726620971607912, 0.898840955600698, 0.8306225283841164, 0.7675816068520053, 0.7093252420366963, 0.6554903007142939, 0.6057412146255193, 0.5597678855389261, 0.5172837477229429, 0.4780239851010477, 0.4417438766366466, 0.40821728599101637, 0.37723522734197107, 0.3486045850672932, 0.32214689251402895, 0.29769723299738127, 0.2751032054902669, 0.2542239729568649, 0.2349293921182179, 0.21709919133565975, 0.2006222322703468, 0.1853958081567112, 0.1713250076818617, 0.15832212543850865, 0.14630611470996735, 0.13520207062136114, 0.12494077769059572, 0.1154582752530248, 0.10669545528035076, 0.09859769845977306, 0.09111452880829288, 0.08419930189140395, 0.07780891243636788, 0.07190352797516235, 0.06644633878361725, 0.06140332850853224, 0.05674306227928665, 0.05243649161892037, 0.04845677264953399, 0.044779099163735736, 0.04138054542325438, 0.03823992847526912, 0.03533767178457788, 0.03265568419704683, 0.030177249277086888, 0.027886917180292126, 0.02577041232792311, 0.023814541862776515, 0.022007113586942285, 0.020336862190592993, 0.018793375954391733, 0.01736703426496542, 0.016048946365362998, 0.014830895691468836, 0.013705290417170413, 0.012665113905395877, 0.011703882611448092, 0.010815605047764246, 0.009994743994246784, 0.009236183184126348, 0.008535194004556256, 0.007887407039815806, 0.007288784598858305, 0.006735595068169391, 0.0062243905139961475, 0.005751984300573021, 0.005315431784959695, 0.0049120119293195865, 0.004539209918787716, 0.004194702139574691, 0.003876341110696352, 0.0035821423791286664, 0.0033102722113061258, 0.003059035829364804, 0.0028268673094009487, 0.002612319441110953, 0.0024140548822248155, 0.0022308378419822255, 0.0020615262207293503, 0.0019050648348102402, 0.0017604783558469647, 0.001626865149798347, 0.0015033925783002815, 0.001389291054145885, 0.0012838493226303043, 0.00118640997707899, 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