Chapter 1
Introduction and Summary of results

1.1 Introduction

This report shows the result of running Maple and Mathematica on my collection of differential equations. These were collected over time and stored in sqlite3 database. These were collected from a number of textbooks and other references such as Kamke and Murphy collections. All books used are listed here.

The current number of differential equations is [10997]. Both Maple and Mathematica are given a CPU time limit of 3 minutes to solve each ode else the problem is considered not solved and marked as failed.

When Mathematica returns DifferentialRoot as a solution to an ode then this is considered as not solved. Similarly, when Maple returns DESol or ODSESolStruc, then this is also considered as not solved.

If CAS solves the ODE within the timelimit, then it is counted as solved. No verification is done to check that the solution is correct or not.

To reduce the size of latex output, in Maple the command simplify is called on the solution with timeout of 3 minutes. If this times out, then the unsimplified original ode solution is used otherwise the simplified one is used.

Similarly for Mathematica, FullSimplify is called on the solution with timeout of 3 minutes. If this timesout, then Simplify is next called. If this also timesout, then the unsimplified solution is used else the simplified one is used. The time used for simplification is not counted in the CPU time used. The CPU time used only records the time used to solve the ode.

Tests are run under windows 10 with 128 GB RAM running on intel i9-12900K 3.20 GHz

1.2 Summary of results

1.2.1 Percentage solved and CPU performance

The following table summarizes perentage solved for each CAS

Table 1.1: Summary of final results

System	% solved	Number solved	Number failed
Maple 2023.1	94.689	10413	584
Mathematica 13.3.1	93.407	10272	725

The following table summarizes the run-time performance of each CAS system.

Table 1.2: Summary of run time performance of each CAS system

System	mean time (sec)	mean leaf size	total time (min)	total leaf size
Maple 2023.1	0.138	330.48	25.238	3634236
Mathematica 13.3.1	2.965	521.32	543.363	5732920

The problem which Mathematica produced largest leaf size of \(1763961\) is 8969.

The problem which Maple produced largest leaf size of \(949416\) is 11040.

The problem which Mathematica used most CPU time of \(174.413\) seconds is 5443.

The problem which Maple used most CPU time of \(134.110\) seconds is 6085.

1.2.2 Performance based on ODE type

The following gives the performance of each CAS based on the type of the ODE. The first subsection uses the types as classified by Maple ode advisor.The next subsection uses my own ode solver ODE classificaiton.

Performance using Maple’s ODE types classification

The following table gives count of the number of ODE’s for each ODE type, where the ODE type here is as classified by Maple’s odeadvisor, and the percentage of solved ODE’s of that type for each CAS. It also gives a direct link to the ODE’s that failed if any.

Table 1.3: Percentage solved per Maple ODE type

Type of ODE	Count	Mathematica	Maple
[_quadrature]	520	99.04% [885, 3757, 3766, 10779, 10781]	99.62% [6549, 10646]
[[_linear, ‘class A‘]]	177	100.00%	98.31% [6546, 6547, 10500]
[_separable]	832	99.28% [944, 2513, 5510, 7910, 10363, 10397]	99.40% [408, 409, 5510, 5664, 10397]
[_Riccati]	308	53.90% [958, 1697, 1698, 1700, 1701, 1702, 2198, 2795, 2815, 2817, 2830, 3130, 3877, 6591, 7690, 9588, 9592, 9593, 9594, 9599, 9612, 9614, 9615, 9616, 9668, 9685, 9689, 9691, 9692, 9693, 9694, 9697, 9698, 9705, 9706, 9712, 9713, 9714, 9715, 9716, 9729, 9731, 9732, 9733, 9734, 9735, 9736, 9737, 9740, 9741, 9749, 9753, 9754, 9756, 9757, 9758, 9759, 9760, 9766, 9767, 9769, 9770, 9771, 9772, 9773, 9778, 9779, 9784, 9785, 9789, 9790, 9791, 9794, 9798, 9799, 9801, 9802, 9803, 9807, 9808, 9809, 9810, 9813, 9815, 9816, 9819, 9822, 9824, 9825, 9828, 9831, 9833, 9834, 9837, 9840, 9842, 9843, 9846, 9850, 9851, 9852, 9854, 9856, 9857, 9859, 9860, 9862, 9863, 9864, 9865, 9866, 9867, 9868, 9869, 9870, 9871, 9873, 9874, 9875, 9876, 9877, 9878, 9879, 9880, 9881, 9882, 9885, 9886, 9889, 9890, 9891, 9892, 9893, 9894, 9895, 9896, 9897, 9898, 9899, 9900, 9901, 9902]	71.43% [958, 1697, 1700, 1701, 1702, 2198, 2815, 2817, 2830, 3877, 6591, 7690, 9592, 9599, 9612, 9614, 9616, 9671, 9679, 9685, 9689, 9691, 9693, 9698, 9714, 9722, 9729, 9732, 9733, 9734, 9736, 9740, 9754, 9756, 9767, 9769, 9785, 9798, 9800, 9807, 9815, 9816, 9819, 9824, 9825, 9828, 9833, 9834, 9837, 9842, 9843, 9846, 9850, 9851, 9856, 9857, 9859, 9860, 9862, 9864, 9865, 9866, 9867, 9868, 9869, 9870, 9871, 9873, 9876, 9877, 9878, 9879, 9881, 9885, 9889, 9890, 9891, 9892, 9893, 9894, 9895, 9896, 9897, 9898, 9899, 9900, 9901, 9902]
[[_homogeneous, ‘class G‘]]	61	95.08% [2723, 2727, 10800]	93.44% [3486, 3531, 7947, 7962]
[_linear]	488	99.59% [5415, 10647]	99.59% [4748, 5415]
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	21	100.00%	100.00%
[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	71	100.00%	100.00%
[[_homogeneous, ‘class A‘], _dAlembert]	125	99.20% [10194]	100.00%
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	72	98.61% [5500]	100.00%
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	48	100.00%	100.00%
[[_homogeneous, ‘class A‘], _rational, _dAlembert]	175	98.86% [5007, 5508]	99.43% [5508]
[[_homogeneous, ‘class C‘], _dAlembert]	62	91.94% [2491, 3751, 3769, 6348, 10222]	100.00%
[[_homogeneous, ‘class C‘], _Riccati]	18	100.00%	100.00%
[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	52	100.00%	100.00%
[_Bernoulli]	89	97.75% [4606, 6376]	100.00%
[[_1st_order, _with_linear_symmetries], _Bernoulli]	4	100.00%	100.00%
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	46	100.00%	100.00%
[‘y=_G(x,y’)‘]	119	63.03% [133, 485, 959, 961, 962, 964, 966, 968, 1703, 1706, 1707, 2854, 2859, 2875, 2954, 3502, 3707, 3752, 3778, 3790, 4442, 4486, 5795, 6309, 6499, 7654, 7659, 7662, 7700, 7949, 7974, 8038, 8039, 8081, 8084, 8088, 8109, 8440, 10201, 10206, 10386, 10866, 10872, 10891]	57.98% [133, 485, 959, 961, 962, 964, 966, 968, 1703, 1706, 1707, 2581, 2854, 2859, 2873, 2875, 2886, 2954, 3363, 3502, 3707, 3778, 3789, 4405, 4442, 4486, 5795, 6309, 6499, 7654, 7659, 7662, 7700, 7949, 7974, 8030, 8038, 8039, 8081, 8084, 8088, 8091, 8109, 8121, 10206, 10386, 10866, 10870, 10872, 10891]
[[_1st_order, _with_linear_symmetries]]	94	92.55% [2720, 2722, 3781, 3785, 6043, 6053, 10197]	98.94% [8115]
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	28	100.00%	100.00%
[_exact, _rational]	33	96.97% [119]	96.97% [10588]
[_exact]	65	98.46% [2628]	100.00%
[[_1st_order, _with_linear_symmetries], _exact, _rational]	3	100.00%	100.00%
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	3	100.00%	100.00%
[[_homogeneous, ‘class G‘], _exact, _rational]	4	50.00% [146, 10592]	100.00%
[[_2nd_order, _missing_x]]	486	96.50% [6654, 9186, 9187, 9190, 9191, 9193, 9211, 9212, 9214, 9219, 9237, 9283, 9285, 9408, 9411, 10571, 10572]	96.50% [6654, 9186, 9187, 9190, 9191, 9193, 9211, 9212, 9214, 9219, 9237, 9283, 9284, 9285, 9411, 10571, 10572]
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	62	100.00%	100.00%
[[_Emden, _Fowler]]	250	99.60% [5590]	96.40% [2032, 4209, 4708, 4802, 4834, 4835, 5830, 5863, 11058]
[[_2nd_order, _exact, _linear, _homogeneous]]	190	99.47% [10910]	97.89% [4836, 5706, 5864, 11059]
[[_2nd_order, _missing_y]]	95	94.74% [6102, 6104, 6458, 9402, 10313]	97.89% [5689, 6551]
[[_2nd_order, _with_linear_symmetries]]	2196	95.81% [1105, 1138, 4501, 4740, 4741, 4742, 5059, 5064, 5589, 5827, 6342, 6424, 6425, 6428, 6429, 6433, 6435, 6534, 6797, 6799, 7185, 7219, 7221, 8597, 8604, 8606, 8608, 8609, 8610, 8616, 8650, 8651, 8653, 8655, 8659, 8660, 8661, 8677, 8704, 8735, 8783, 8790, 8794, 8814, 8856, 8883, 8939, 8985, 8996, 9016, 9017, 9018, 9020, 9180, 9223, 9233, 9234, 9235, 9238, 9240, 9241, 9242, 9247, 9248, 9252, 9253, 9255, 9259, 9294, 9317, 9337, 9352, 9354, 9355, 9386, 9393, 9394, 9395, 9406, 9407, 10085, 10086, 10094, 10292, 10293, 10311, 10702, 10901, 10902, 10904, 10916, 11064]	96.77% [1794, 1797, 1805, 2411, 4192, 4205, 4494, 4501, 4767, 4772, 4810, 5064, 5288, 5687, 5695, 5827, 5838, 6425, 6433, 6435, 6534, 8597, 8604, 8606, 8608, 8609, 8616, 8650, 8651, 8653, 8655, 8659, 8735, 8783, 8790, 8794, 8814, 8856, 8985, 9016, 9017, 9018, 9020, 9180, 9223, 9233, 9234, 9235, 9238, 9240, 9241, 9242, 9247, 9248, 9252, 9255, 9257, 9259, 9294, 9317, 9337, 9352, 9395, 9406, 9407, 9409, 10311, 10702, 10904, 10916, 11064]
[[_2nd_order, _linear, _nonhomogeneous]]	656	98.48% [1162, 1186, 6705, 8654, 10457, 10900, 10903, 10933, 11004, 11006]	96.65% [1162, 1186, 4213, 4214, 4746, 4747, 5759, 6470, 6471, 6472, 6476, 6477, 6479, 6487, 6552, 6553, 8654, 10900, 10903, 10933, 11004, 11006]
[[_2nd_order, _exact, _linear, _nonhomogeneous]]	44	100.00%	100.00%
system of linear ODEs	547	96.16% [5350, 5788, 5789, 9465, 9480, 9490, 9493, 9494, 9495, 9496, 9497, 9502, 9503, 9504, 9507, 9508, 9509, 9510, 9511, 9512, 9514]	96.53% [5350, 5788, 5789, 5965, 9465, 9480, 9490, 9493, 9494, 9495, 9496, 9497, 9502, 9503, 9507, 9509, 9510, 9512, 9514]
[_Gegenbauer]	65	100.00%	100.00%
[[_high_order, _missing_x]]	100	97.00% [9119, 9122, 9151]	100.00%
[[_3rd_order, _missing_x]]	101	100.00%	100.00%
[[_3rd_order, _missing_y]]	38	100.00%	100.00%
[[_3rd_order, _exact, _linear, _homogeneous]]	12	100.00%	100.00%
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	55	92.73% [8652, 8900, 9021, 10093]	98.18% [5705]
[_Lienard]	48	100.00%	100.00%
[[_homogeneous, ‘class A‘], _rational, _Riccati]	28	100.00%	100.00%
[‘x=_G(y,y’)‘]	12	66.67% [550, 2204, 5429, 8150]	66.67% [550, 2204, 5429, 8150]
[[_Abel, ‘2nd type‘, ‘class B‘]]	15	26.67% [553, 1046, 7829, 9920, 9923, 9943, 9944, 9945, 9965, 9978, 9983]	40.00% [553, 1046, 7829, 9923, 9943, 9944, 9945, 9965, 9978]
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]]	8	100.00%	100.00%
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	21	100.00%	100.00%
[[_homogeneous, ‘class D‘], _rational]	2	100.00%	100.00%
[[_1st_order, _with_exponential_symmetries]]	5	100.00%	100.00%
[_rational]	100	85.00% [1039, 1075, 2609, 2683, 2684, 3637, 3806, 5357, 8058, 8060, 8067, 8463, 8472, 10180, 10586]	79.00% [1039, 1075, 2609, 2683, 2684, 3417, 3637, 3689, 3690, 3806, 5357, 8058, 8060, 8286, 8463, 8472, 8490, 8498, 10180, 10212, 10586]
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	133	27.07% [1069, 2481, 2583, 3267, 3274, 5431, 6562, 7813, 7816, 7832, 7844, 9906, 9907, 9914, 9915, 9917, 9919, 9922, 9924, 9926, 9927, 9929, 9930, 9931, 9932, 9933, 9936, 9937, 9938, 9940, 9941, 9942, 9949, 9950, 9951, 9952, 9953, 9954, 9957, 9958, 9959, 9960, 9961, 9962, 9963, 9964, 9966, 9967, 9968, 9969, 9970, 9971, 9972, 9984, 10001, 10002, 10005, 10008, 10009, 10010, 10011, 10012, 10013, 10014, 10015, 10017, 10018, 10019, 10020, 10021, 10022, 10023, 10024, 10025, 10026, 10027, 10028, 10029, 10030, 10031, 10032, 10033, 10034, 10035, 10036, 10037, 10038, 10039, 10040, 10041, 10042, 10043, 10044, 10045, 10046, 10076, 10077]	51.88% [2481, 2583, 3267, 3274, 5431, 6562, 7813, 7816, 7832, 7844, 9914, 9917, 9922, 9929, 9930, 9931, 9933, 9940, 9941, 9950, 9952, 9953, 9957, 9958, 9961, 9962, 9963, 9964, 9966, 9968, 9969, 9970, 9971, 9972, 10001, 10002, 10008, 10010, 10011, 10012, 10013, 10014, 10017, 10019, 10020, 10022, 10023, 10024, 10025, 10027, 10028, 10030, 10031, 10032, 10034, 10035, 10036, 10037, 10038, 10039, 10040, 10044, 10045, 10076]
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]]	4	100.00%	100.00%
[NONE]	80	36.25% [710, 1041, 6356, 6460, 7636, 7667, 7781, 7946, 8153, 8154, 8413, 8415, 9170, 9173, 9174, 9178, 9181, 9183, 9184, 9192, 9194, 9198, 9199, 9200, 9203, 9209, 9217, 9218, 9220, 9224, 9250, 9260, 9268, 9277, 9279, 9304, 9307, 9309, 9310, 9313, 9314, 9326, 9332, 9364, 9376, 9377, 9390, 9426, 10890, 10893, 10895]	32.50% [710, 5484, 6356, 6460, 7636, 7667, 7781, 7946, 8153, 8154, 8413, 8415, 9170, 9173, 9174, 9181, 9183, 9184, 9192, 9194, 9198, 9199, 9200, 9203, 9209, 9217, 9218, 9220, 9224, 9250, 9260, 9268, 9273, 9277, 9279, 9280, 9281, 9296, 9304, 9307, 9309, 9310, 9313, 9314, 9326, 9332, 9364, 9376, 9377, 9390, 9426, 10890, 10893, 10895]
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	22	100.00%	100.00%
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	41	100.00%	100.00%
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	12	100.00%	100.00%
[[_high_order, _with_linear_symmetries]]	42	83.33% [813, 9115, 9116, 9117, 9118, 9147, 9165]	83.33% [813, 9115, 9116, 9117, 9118, 9157, 9165]
[[_3rd_order, _with_linear_symmetries]]	108	84.26% [5063, 9034, 9035, 9036, 9037, 9038, 9039, 9040, 9050, 9051, 9053, 9061, 9066, 9077, 9090, 9091, 9106]	85.19% [5063, 9034, 9035, 9036, 9037, 9038, 9039, 9040, 9050, 9051, 9053, 9061, 9066, 9085, 9090, 9106]
[[_high_order, _linear, _nonhomogeneous]]	59	96.61% [9127, 9156]	98.31% [9156]
[[_1st_order, _with_linear_symmetries], _Clairaut]	47	97.87% [10208]	100.00%
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	48	100.00%	100.00%
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	72	100.00%	100.00%
[[_homogeneous, ‘class C‘], _rational, _Riccati]	5	100.00%	100.00%
[[_Abel, ‘2nd type‘, ‘class A‘]]	34	14.71% [3167, 3219, 4445, 7785, 7798, 9910, 9911, 9975, 9976, 9977, 9986, 9987, 9988, 9989, 9990, 10004, 10050, 10057, 10058, 10060, 10061, 10063, 10064, 10065, 10066, 10067, 10068, 10069, 10070]	35.29% [3167, 3219, 4445, 7785, 7798, 9975, 9976, 9977, 9986, 9987, 9988, 9989, 9990, 10004, 10050, 10058, 10061, 10065, 10066, 10068, 10069, 10070]
[_rational, _Bernoulli]	39	100.00%	100.00%
[[_homogeneous, ‘class A‘]]	7	100.00%	100.00%
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	112	98.21% [3942, 10072]	100.00%
[[_homogeneous, ‘class G‘], _rational, _Riccati]	19	100.00%	100.00%
[[_1st_order, _with_linear_symmetries], _Riccati]	10	100.00%	100.00%
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], _Riccati]	1	100.00%	100.00%
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], [_Abel, ‘2nd type‘, ‘class A‘]]	1	100.00%	100.00%
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	15	100.00%	100.00%
[_exact, [_Abel, ‘2nd type‘, ‘class B‘]]	4	100.00%	100.00%
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	6	100.00%	100.00%
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]]	3	100.00%	100.00%
[_exact, _Bernoulli]	6	100.00%	100.00%
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli]	5	100.00%	100.00%
[_rational, [_Abel, ‘2nd type‘, ‘class C‘]]	12	83.33% [4408, 4453]	83.33% [4408, 4453]
[[_homogeneous, ‘class G‘], _rational]	77	100.00%	97.40% [3654, 6066]
[[_homogeneous, ‘class D‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	2	100.00%	100.00%
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]	14	100.00%	100.00%
[_rational, _Riccati]	101	94.06% [9606, 9637, 9645, 9654, 9658, 9659]	97.03% [9654, 9658, 9659]
[[_3rd_order, _linear, _nonhomogeneous]]	58	98.28% [10879]	100.00%
[[_high_order, _missing_y]]	21	95.24% [9161]	95.24% [9161]
[[_3rd_order, _exact, _linear, _nonhomogeneous]]	5	100.00%	100.00%
[[_high_order, _exact, _linear, _nonhomogeneous]]	5	100.00%	100.00%
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	20	100.00%	100.00%
[_exact, [_Abel, ‘2nd type‘, ‘class A‘]]	2	100.00%	100.00%
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class A‘]]	2	100.00%	100.00%
[[_Riccati, _special]]	18	100.00%	100.00%
[_Abel]	26	73.08% [1704, 2843, 7627, 7628, 7629, 7630, 10786]	73.08% [1704, 2843, 7627, 7628, 7629, 7630, 10786]
[_Laguerre]	34	100.00%	100.00%
[_Laguerre, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	4	100.00%	100.00%
[_Bessel]	17	100.00%	100.00%
[_rational, _Abel]	21	95.24% [1897]	100.00%
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	10	100.00%	100.00%
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]]	1	100.00%	100.00%
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]	4	100.00%	100.00%
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	6	100.00%	100.00%
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]]	3	100.00%	100.00%
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]]	11	90.91% [9351]	100.00%
[[_3rd_order, _exact, _nonlinear]]	2	50.00% [9416]	50.00% [9416]
[_Jacobi]	31	100.00%	100.00%
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]]	5	100.00%	100.00%
[[_2nd_order, _quadrature]]	35	97.14% [10850]	97.14% [6550]
[[_3rd_order, _quadrature]]	4	100.00%	100.00%
[[_homogeneous, ‘class D‘], _Bernoulli]	3	100.00%	100.00%
[[_homogeneous, ‘class G‘], _exact]	1	100.00%	100.00%
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	5	100.00%	100.00%
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli]	9	100.00%	100.00%
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	1	100.00%	100.00%
[[_homogeneous, ‘class A‘], _exact, _rational, _Riccati]	1	100.00%	100.00%
[_erf]	4	100.00%	100.00%
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut]	14	100.00%	100.00%
[[_homogeneous, ‘class D‘]]	13	100.00%	100.00%
[_exact, _rational, _Riccati]	3	100.00%	100.00%
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]]	5	100.00%	100.00%
[[_1st_order, _with_linear_symmetries], _rational]	23	100.00%	100.00%
[[_homogeneous, ‘class D‘], _rational, _Riccati]	19	100.00%	100.00%
[[_1st_order, _with_linear_symmetries], _exact]	2	100.00%	100.00%
[[_homogeneous, ‘class C‘], _exact, _dAlembert]	3	100.00%	100.00%
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class A‘]]	1	100.00%	100.00%
[[_homogeneous, ‘class D‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	2	100.00%	100.00%
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]]	39	28.21% [3164, 7782, 7784, 9908, 9912, 9939, 9955, 9973, 9974, 9991, 9993, 9994, 9998, 10000, 10003, 10016, 10047, 10048, 10049, 10051, 10052, 10053, 10054, 10055, 10056, 10073, 10075, 10581]	46.15% [3164, 7782, 7784, 9908, 9912, 9973, 9974, 9994, 10000, 10003, 10016, 10047, 10048, 10051, 10052, 10053, 10054, 10055, 10073, 10075, 10581]
[[_homogeneous, ‘class G‘], _dAlembert]	4	100.00%	100.00%
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli]	4	100.00%	100.00%
[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	25	100.00%	100.00%
[[_1st_order, _with_linear_symmetries], _dAlembert]	49	79.59% [3742, 3743, 3744, 3765, 3796, 6057, 6059, 6120, 6124, 6500]	100.00%
[[_homogeneous, ‘class G‘], _Abel]	4	100.00%	100.00%
[[_homogeneous, ‘class G‘], _Chini]	4	100.00%	100.00%
[_Chini]	3	0.00% [2846, 3133, 7635]	0.00% [2846, 3133, 7635]
[_rational, [_Riccati, _special]]	9	100.00%	100.00%
[[_1st_order, _with_linear_symmetries], _rational, _Riccati]	2	100.00%	100.00%
[[_homogeneous, ‘class D‘], _Riccati]	20	100.00%	100.00%
[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]]	4	100.00%	100.00%
[[_homogeneous, ‘class G‘], _Riccati]	4	100.00%	100.00%
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]]	5	100.00%	100.00%
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	3	100.00%	100.00%
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]	1	100.00%	100.00%
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]	4	100.00%	100.00%
[_exact, _rational, _Bernoulli]	1	100.00%	100.00%
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘]]	5	100.00%	100.00%
[[_Abel, ‘2nd type‘, ‘class C‘]]	7	71.43% [3334, 7848]	71.43% [3334, 7848]
[[_homogeneous, ‘class C‘], _rational]	7	100.00%	100.00%
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	2	100.00%	100.00%
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	17	100.00%	100.00%
unknown	6	50.00% [7919, 9381, 9730]	0.00% [3471, 7919, 7931, 9381, 9410, 9730]
[_dAlembert]	17	100.00%	100.00%
[_rational, _dAlembert]	11	90.91% [8009]	100.00%
[[_homogeneous, ‘class G‘], _rational, _dAlembert]	8	100.00%	100.00%
[[_homogeneous, ‘class G‘], _rational, _Clairaut]	5	100.00%	100.00%
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert]	10	100.00%	100.00%
[[_homogeneous, ‘class C‘], _rational, _dAlembert]	10	100.00%	100.00%
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	14	100.00%	100.00%
[[_homogeneous, ‘class G‘], _Clairaut]	2	100.00%	100.00%
[_Clairaut]	7	100.00%	85.71% [3834]
[[_homogeneous, ‘class A‘], _exact, _dAlembert]	2	100.00%	100.00%
[[_homogeneous, ‘class D‘], _exact, _rational, _Bernoulli]	1	100.00%	100.00%
[[_homogeneous, ‘class D‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	3	100.00%	100.00%
[[_high_order, _quadrature]]	6	100.00%	100.00%
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	9	55.56% [4159, 4330, 4331, 4332]	100.00%
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	60	95.00% [5346, 6085, 6086]	100.00%
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	26	96.15% [4157]	96.15% [9383]
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	5	100.00%	100.00%
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]]	6	100.00%	100.00%
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]	17	94.12% [6463]	100.00%
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_xy]]	2	0.00% [4158, 5492]	100.00%
[_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	9	100.00%	100.00%
[[_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	3	100.00%	100.00%
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	3	100.00%	100.00%
[[_homogeneous, ‘class G‘], _rational, _Abel]	2	100.00%	100.00%
[[_elliptic, _class_I]]	2	100.00%	100.00%
[[_elliptic, _class_II]]	2	100.00%	100.00%
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear]]	1	100.00%	100.00%
[_Hermite]	15	100.00%	100.00%
[[_1st_order, _with_linear_symmetries], _Chini]	2	100.00%	100.00%
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	2	100.00%	100.00%
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_exponential_symmetries], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]]	1	100.00%	100.00%
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]	3	100.00%	100.00%
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]	36	100.00%	91.67% [8311, 8367, 8368]
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]	4	100.00%	100.00%
[[_2nd_order, _missing_x], [_2nd_order, _with_potential_symmetries], [_2nd_order, _reducible, _mu_xy]]	3	100.00%	100.00%
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]	14	100.00%	100.00%
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_poly_yn]]	1	100.00%	100.00%
[[_2nd_order, _missing_y], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_poly_yn]]	1	100.00%	100.00%
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]]	3	100.00%	100.00%
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	3	100.00%	100.00%
[[_2nd_order, _missing_y], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_poly_yn]]	1	100.00%	100.00%
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	4	100.00%	100.00%
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_y_y1]]	2	100.00%	100.00%
[[_2nd_order, _missing_y], _Liouville, [_2nd_order, _reducible, _mu_xy]]	2	100.00%	100.00%
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_xy]]	2	100.00%	100.00%
[[_Bessel, _modified]]	1	100.00%	100.00%
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]]	11	9.09% [6353, 6354, 9176, 9239, 9261, 9265, 9267, 9270, 9271, 10908]	27.27% [6353, 9176, 9239, 9261, 9265, 9267, 9270, 9271]
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]	3	100.00%	100.00%
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]	3	33.33% [9201, 10921]	33.33% [9201, 10921]
[_Liouville, [_2nd_order, _reducible, _mu_xy]]	3	100.00%	100.00%
[_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	8	100.00%	100.00%
[_Chini, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	2	100.00%	100.00%
[[_1st_order, _with_exponential_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	1	100.00%	100.00%
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	1	100.00%	100.00%
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	1	100.00%	100.00%
[[_homogeneous, ‘class G‘], [_Abel, ‘2nd type‘, ‘class C‘]]	1	100.00%	100.00%
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class C‘]]	7	100.00%	100.00%
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class C‘]]	8	100.00%	100.00%
[[_Abel, ‘2nd type‘, ‘class C‘], [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	4	100.00%	100.00%
[[_1st_order, _with_linear_symmetries], _Abel]	13	100.00%	100.00%
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	7	100.00%	100.00%
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], [_Abel, ‘2nd type‘, ‘class C‘]]	2	100.00%	100.00%
[[_homogeneous, ‘class D‘], _rational, _Abel]	3	100.00%	100.00%
[[_homogeneous, ‘class C‘], _rational, _Abel]	3	100.00%	100.00%
[_rational, [_Abel, ‘2nd type‘, ‘class C‘], [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	3	100.00%	100.00%
[[_homogeneous, ‘class D‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘]]	1	100.00%	100.00%
[[_homogeneous, ‘class C‘], _Abel]	3	100.00%	100.00%
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class C‘]]	6	100.00%	100.00%
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel]	5	100.00%	100.00%
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel]	10	100.00%	100.00%
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class C‘]]	2	100.00%	100.00%
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], _Abel]	2	100.00%	100.00%
[[_1st_order, _with_linear_symmetries], _rational, _Abel]	1	100.00%	100.00%
[_Titchmarsh]	1	0.00% [8593]	0.00% [8593]
[_ellipsoidal]	2	100.00%	100.00%
[_Jacobi, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	1	100.00%	100.00%
[_Halm]	2	100.00%	100.00%
[[_3rd_order, _fully, _exact, _linear]]	6	100.00%	100.00%
[[_high_order, _fully, _exact, _linear]]	1	100.00%	100.00%
[[_Painleve, ‘1st‘]]	1	0.00% [9168]	0.00% [9168]
[[_Painleve, ‘2nd‘]]	1	0.00% [9171]	0.00% [9171]
[[_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	1	0.00% [9202]	0.00% [9202]
[[_2nd_order, _with_potential_symmetries]]	2	100.00%	100.00%
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]]	6	100.00%	100.00%
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]]	2	100.00%	100.00%
[[_2nd_order, _reducible, _mu_xy]]	3	66.67% [9363]	66.67% [9363]
[[_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]	1	0.00% [9288]	0.00% [9288]
[[_Painleve, ‘4th‘]]	1	0.00% [9312]	0.00% [9312]
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_xy]]	3	100.00%	100.00%
[[_Painleve, ‘3rd‘]]	1	0.00% [9336]	0.00% [9336]
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1]]	1	100.00%	100.00%
[[_Painleve, ‘5th‘]]	1	0.00% [9372]	0.00% [9372]
[[_Painleve, ‘6th‘]]	1	0.00% [9382]	0.00% [9382]
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_poly_yn]]	1	0.00% [9391]	0.00% [9391]
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_poly_yn]]	1	0.00% [9396]	0.00% [9396]
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1]]	1	0.00% [9400]	0.00% [9400]
[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]]	6	33.33% [9413, 9414, 9415, 9430]	33.33% [9413, 9414, 9415, 9430]
[[_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]	1	100.00%	100.00%
[[_3rd_order, _missing_x], [_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]]	1	100.00%	100.00%
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]]	2	100.00%	100.00%
[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries]]	2	50.00% [9425]	50.00% [9425]
[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries], [_high_order, _reducible, _mu_poly_yn]]	2	100.00%	100.00%
	71	100.00%	100.00%
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class B‘]]	1	100.00%	100.00%
[[_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries]]	1	100.00%	100.00%
[[_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]]	1	100.00%	100.00%
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]]	1	100.00%	100.00%
[[_high_order, _missing_x], [_high_order, _with_linear_symmetries]]	2	0.00% [10878, 10892]	0.00% [10878, 10892]
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]	2	100.00%	100.00%

Performance using own ODE types classification

The types of the ODE’s are described in my ode solver page at ode types.

The following table gives count of the number of ODE’s for each ODE type, where the ODE type here is as classified by my own ode solver, and the percentage of solved ODE’s of that type for each CAS. It also gives a direct link to the ODE’s that failed if any.

Table 1.5: Percentage solved per own ODE type

Type of ODE	Count	Mathematica	Maple
quadrature	160	97.50% [3757, 3766, 10779, 10781]	100.00%
linear	65	98.46% [5415]	98.46% [5415]
separable	96	100.00%	100.00%
homogeneous	70	98.57% [5007]	100.00%
homogeneousTypeD2	23	100.00%	100.00%
exact	222	98.65% [119, 146, 2628]	98.65% [3471, 7931, 10588]
exactWithIntegrationFactor	112	99.11% [7919]	98.21% [2581, 7919]
exactByInspection	18	100.00%	94.44% [3417]
bernoulli	25	100.00%	100.00%
riccati	455	67.25% [958, 1697, 1698, 1700, 1701, 1702, 2198, 2795, 2815, 2817, 2830, 3130, 3877, 6591, 7690, 9588, 9592, 9593, 9594, 9599, 9606, 9612, 9614, 9615, 9616, 9637, 9645, 9654, 9658, 9659, 9668, 9685, 9689, 9691, 9692, 9693, 9694, 9697, 9698, 9705, 9706, 9712, 9713, 9714, 9715, 9716, 9729, 9730, 9731, 9732, 9733, 9734, 9735, 9736, 9737, 9740, 9741, 9749, 9753, 9754, 9756, 9757, 9758, 9759, 9760, 9766, 9767, 9769, 9770, 9771, 9772, 9773, 9778, 9779, 9784, 9785, 9789, 9790, 9791, 9794, 9798, 9799, 9801, 9802, 9803, 9807, 9808, 9809, 9810, 9813, 9815, 9816, 9819, 9822, 9824, 9825, 9828, 9831, 9833, 9834, 9837, 9840, 9842, 9843, 9846, 9850, 9851, 9852, 9854, 9856, 9857, 9859, 9860, 9862, 9863, 9864, 9865, 9866, 9867, 9868, 9869, 9870, 9871, 9873, 9874, 9875, 9876, 9877, 9878, 9879, 9880, 9881, 9882, 9885, 9886, 9889, 9890, 9891, 9892, 9893, 9894, 9895, 9896, 9897, 9898, 9899, 9900, 9901, 9902]	79.34% [958, 1697, 1700, 1701, 1702, 2198, 2815, 2817, 2830, 3877, 6591, 7690, 8311, 8368, 9592, 9599, 9612, 9614, 9616, 9654, 9658, 9659, 9671, 9679, 9685, 9689, 9691, 9693, 9698, 9714, 9722, 9729, 9730, 9732, 9733, 9734, 9736, 9740, 9754, 9756, 9767, 9769, 9785, 9798, 9800, 9807, 9815, 9816, 9819, 9824, 9825, 9828, 9833, 9834, 9837, 9842, 9843, 9846, 9850, 9851, 9856, 9857, 9859, 9860, 9862, 9864, 9865, 9866, 9867, 9868, 9869, 9870, 9871, 9873, 9876, 9877, 9878, 9879, 9881, 9885, 9889, 9890, 9891, 9892, 9893, 9894, 9895, 9896, 9897, 9898, 9899, 9900, 9901, 9902]
clairaut	57	98.25% [10208]	98.25% [3834]
dAlembert	70	92.86% [2491, 3751, 3769, 8009, 10222]	100.00%
isobaric	144	91.67% [2720, 2722, 2723, 2727, 3781, 3785, 6043, 6053, 8463, 8472, 10197, 10800]	93.75% [3486, 3531, 3654, 6066, 7947, 7962, 8115, 8463, 8472]
polynomial	16	100.00%	100.00%
abelFirstKind	54	87.04% [1704, 1897, 2843, 7627, 7628, 7630, 10786]	88.89% [1704, 2843, 7627, 7628, 7630, 10786]
first order ode series method. Taylor series method	2	100.00%	100.00%
first order ode series method. Regular singular point	8	100.00%	100.00%
first order ode series method. Irregular singular point	3	100.00%	0.00% [408, 409, 5664]
first_order_laplace	54	100.00%	98.15% [10500]
first_order_ode_lie_symmetry_calculated	155	100.00%	99.35% [8490]
system of linear ODEs	499	99.40% [5350, 5789, 9480]	99.20% [5350, 5789, 5965, 9480]
second_order_laplace	224	100.00%	99.55% [5759]
reduction_of_order	105	96.19% [1138, 5589, 5590, 10702]	99.05% [10702]
second_order_linear_constant_coeff	1	100.00%	0.00% [6552]
second_order_airy	15	100.00%	100.00%
second_order_change_of_variable_on_x_q1_constant_method	1	0.00% [8652]	100.00%
second_order_change_of_variable_on_y_general_n	9	88.89% [8996]	100.00%
second_order_integrable_as_is	10	80.00% [9396, 10921]	80.00% [9396, 10921]
second_order_change_of_variable_on_x_p1_zero_method	3	100.00%	100.00%
second_order_ode_lagrange_adjoint_equation_method	3	100.00%	100.00%
second_order_nonlinear_solved_by_mainardi_lioville_method	14	100.00%	100.00%
second_order_change_of_variable_on_y_n_one_case	17	100.00%	100.00%
second_order_bessel_ode	68	100.00%	100.00%
second_order_bessel_ode_form_A	3	100.00%	100.00%
second_order_ode_missing_x	123	89.43% [4157, 9186, 9187, 9191, 9193, 9211, 9212, 9214, 9237, 9283, 9285, 9408, 9411]	89.43% [9186, 9187, 9191, 9193, 9211, 9212, 9214, 9237, 9283, 9284, 9285, 9383, 9411]
second_order_ode_missing_y	41	85.37% [6102, 6104, 6458, 6463, 9402, 10313]	100.00%
second order series method. Regular singular point. Difference not integer	210	100.00%	97.14% [6470, 6471, 6472, 6476, 6477, 6479]
second order series method. Regular singular point. Repeated root	172	100.00%	99.42% [6487]
second order series method. Regular singular point. Difference is integer	266	100.00%	99.62% [4747]
second order series method. Irregular singular point	34	94.12% [4501, 5827]	0.00% [1794, 1797, 1805, 2032, 2411, 4192, 4205, 4209, 4213, 4214, 4494, 4501, 4708, 4746, 4767, 4772, 4802, 4810, 4834, 4835, 4836, 5288, 5687, 5689, 5695, 5705, 5706, 5827, 5830, 5838, 5863, 5864, 11058, 11059]
second order series method. Regular singular point. Complex roots	24	87.50% [4740, 4741, 4742]	100.00%
second_order_ode_high_degree	1	100.00%	100.00%
higher_order_linear_constant_coefficients_ODE	352	99.15% [9119, 9122, 9151]	100.00%
higher_order_ODE_non_constant_coefficients_of_type_Euler	46	100.00%	100.00%
higher_order_laplace	23	100.00%	100.00%

1.3 Links to problems based on solution result

These are direct links to the ode problems based on status of solving.

Not solved by Mathematica

(725) [119, 133, 146, 485, 550, 553, 710, 813, 885, 944, 958, 959, 961, 962, 964, 966, 968, 1039, 1041, 1046, 1069, 1075, 1105, 1138, 1162, 1186, 1697, 1698, 1700, 1701, 1702, 1703, 1704, 1706, 1707, 1897, 2198, 2204, 2481, 2491, 2513, 2583, 2609, 2628, 2683, 2684, 2720, 2722, 2723, 2727, 2795, 2815, 2817, 2830, 2843, 2846, 2854, 2859, 2875, 2954, 3130, 3133, 3164, 3167, 3219, 3267, 3274, 3334, 3502, 3637, 3707, 3742, 3743, 3744, 3751, 3752, 3757, 3765, 3766, 3769, 3778, 3781, 3785, 3790, 3796, 3806, 3877, 3942, 4157, 4158, 4159, 4330, 4331, 4332, 4408, 4442, 4445, 4453, 4486, 4501, 4606, 4740, 4741, 4742, 5007, 5059, 5063, 5064, 5346, 5350, 5357, 5415, 5429, 5431, 5492, 5500, 5508, 5510, 5589, 5590, 5788, 5789, 5795, 5827, 6043, 6053, 6057, 6059, 6085, 6086, 6102, 6104, 6120, 6124, 6309, 6342, 6348, 6353, 6354, 6356, 6376, 6424, 6425, 6428, 6429, 6433, 6435, 6458, 6460, 6463, 6499, 6500, 6534, 6562, 6591, 6654, 6705, 6797, 6799, 7185, 7219, 7221, 7627, 7628, 7629, 7630, 7635, 7636, 7654, 7659, 7662, 7667, 7690, 7700, 7781, 7782, 7784, 7785, 7798, 7813, 7816, 7829, 7832, 7844, 7848, 7910, 7919, 7946, 7949, 7974, 8009, 8038, 8039, 8058, 8060, 8067, 8081, 8084, 8088, 8109, 8150, 8153, 8154, 8413, 8415, 8440, 8463, 8472, 8593, 8597, 8604, 8606, 8608, 8609, 8610, 8616, 8650, 8651, 8652, 8653, 8654, 8655, 8659, 8660, 8661, 8677, 8704, 8735, 8783, 8790, 8794, 8814, 8856, 8883, 8900, 8939, 8985, 8996, 9016, 9017, 9018, 9020, 9021, 9034, 9035, 9036, 9037, 9038, 9039, 9040, 9050, 9051, 9053, 9061, 9066, 9077, 9090, 9091, 9106, 9115, 9116, 9117, 9118, 9119, 9122, 9127, 9147, 9151, 9156, 9161, 9165, 9168, 9170, 9171, 9173, 9174, 9176, 9178, 9180, 9181, 9183, 9184, 9186, 9187, 9190, 9191, 9192, 9193, 9194, 9198, 9199, 9200, 9201, 9202, 9203, 9209, 9211, 9212, 9214, 9217, 9218, 9219, 9220, 9223, 9224, 9233, 9234, 9235, 9237, 9238, 9239, 9240, 9241, 9242, 9247, 9248, 9250, 9252, 9253, 9255, 9259, 9260, 9261, 9265, 9267, 9268, 9270, 9271, 9277, 9279, 9283, 9285, 9288, 9294, 9304, 9307, 9309, 9310, 9312, 9313, 9314, 9317, 9326, 9332, 9336, 9337, 9351, 9352, 9354, 9355, 9363, 9364, 9372, 9376, 9377, 9381, 9382, 9386, 9390, 9391, 9393, 9394, 9395, 9396, 9400, 9402, 9406, 9407, 9408, 9411, 9413, 9414, 9415, 9416, 9425, 9426, 9430, 9465, 9480, 9490, 9493, 9494, 9495, 9496, 9497, 9502, 9503, 9504, 9507, 9508, 9509, 9510, 9511, 9512, 9514, 9588, 9592, 9593, 9594, 9599, 9606, 9612, 9614, 9615, 9616, 9637, 9645, 9654, 9658, 9659, 9668, 9685, 9689, 9691, 9692, 9693, 9694, 9697, 9698, 9705, 9706, 9712, 9713, 9714, 9715, 9716, 9729, 9730, 9731, 9732, 9733, 9734, 9735, 9736, 9737, 9740, 9741, 9749, 9753, 9754, 9756, 9757, 9758, 9759, 9760, 9766, 9767, 9769, 9770, 9771, 9772, 9773, 9778, 9779, 9784, 9785, 9789, 9790, 9791, 9794, 9798, 9799, 9801, 9802, 9803, 9807, 9808, 9809, 9810, 9813, 9815, 9816, 9819, 9822, 9824, 9825, 9828, 9831, 9833, 9834, 9837, 9840, 9842, 9843, 9846, 9850, 9851, 9852, 9854, 9856, 9857, 9859, 9860, 9862, 9863, 9864, 9865, 9866, 9867, 9868, 9869, 9870, 9871, 9873, 9874, 9875, 9876, 9877, 9878, 9879, 9880, 9881, 9882, 9885, 9886, 9889, 9890, 9891, 9892, 9893, 9894, 9895, 9896, 9897, 9898, 9899, 9900, 9901, 9902, 9906, 9907, 9908, 9910, 9911, 9912, 9914, 9915, 9917, 9919, 9920, 9922, 9923, 9924, 9926, 9927, 9929, 9930, 9931, 9932, 9933, 9936, 9937, 9938, 9939, 9940, 9941, 9942, 9943, 9944, 9945, 9949, 9950, 9951, 9952, 9953, 9954, 9955, 9957, 9958, 9959, 9960, 9961, 9962, 9963, 9964, 9965, 9966, 9967, 9968, 9969, 9970, 9971, 9972, 9973, 9974, 9975, 9976, 9977, 9978, 9983, 9984, 9986, 9987, 9988, 9989, 9990, 9991, 9993, 9994, 9998, 10000, 10001, 10002, 10003, 10004, 10005, 10008, 10009, 10010, 10011, 10012, 10013, 10014, 10015, 10016, 10017, 10018, 10019, 10020, 10021, 10022, 10023, 10024, 10025, 10026, 10027, 10028, 10029, 10030, 10031, 10032, 10033, 10034, 10035, 10036, 10037, 10038, 10039, 10040, 10041, 10042, 10043, 10044, 10045, 10046, 10047, 10048, 10049, 10050, 10051, 10052, 10053, 10054, 10055, 10056, 10057, 10058, 10060, 10061, 10063, 10064, 10065, 10066, 10067, 10068, 10069, 10070, 10072, 10073, 10075, 10076, 10077, 10085, 10086, 10093, 10094, 10180, 10194, 10197, 10201, 10206, 10208, 10222, 10292, 10293, 10311, 10313, 10363, 10386, 10397, 10457, 10571, 10572, 10581, 10586, 10592, 10647, 10702, 10779, 10781, 10786, 10800, 10850, 10866, 10872, 10878, 10879, 10890, 10891, 10892, 10893, 10895, 10900, 10901, 10902, 10903, 10904, 10908, 10910, 10916, 10921, 10933, 11004, 11006, 11064]

Not solved by Maple

(584) [133, 408, 409, 485, 550, 553, 710, 813, 958, 959, 961, 962, 964, 966, 968, 1039, 1046, 1075, 1162, 1186, 1697, 1700, 1701, 1702, 1703, 1704, 1706, 1707, 1794, 1797, 1805, 2032, 2198, 2204, 2411, 2481, 2581, 2583, 2609, 2683, 2684, 2815, 2817, 2830, 2843, 2846, 2854, 2859, 2873, 2875, 2886, 2954, 3133, 3164, 3167, 3219, 3267, 3274, 3334, 3363, 3417, 3471, 3486, 3502, 3531, 3637, 3654, 3689, 3690, 3707, 3778, 3789, 3806, 3834, 3877, 4192, 4205, 4209, 4213, 4214, 4405, 4408, 4442, 4445, 4453, 4486, 4494, 4501, 4708, 4746, 4747, 4748, 4767, 4772, 4802, 4810, 4834, 4835, 4836, 5063, 5064, 5288, 5350, 5357, 5415, 5429, 5431, 5484, 5508, 5510, 5664, 5687, 5689, 5695, 5705, 5706, 5759, 5788, 5789, 5795, 5827, 5830, 5838, 5863, 5864, 5965, 6066, 6309, 6353, 6356, 6425, 6433, 6435, 6460, 6470, 6471, 6472, 6476, 6477, 6479, 6487, 6499, 6534, 6546, 6547, 6549, 6550, 6551, 6552, 6553, 6562, 6591, 6654, 7627, 7628, 7629, 7630, 7635, 7636, 7654, 7659, 7662, 7667, 7690, 7700, 7781, 7782, 7784, 7785, 7798, 7813, 7816, 7829, 7832, 7844, 7848, 7919, 7931, 7946, 7947, 7949, 7962, 7974, 8030, 8038, 8039, 8058, 8060, 8081, 8084, 8088, 8091, 8109, 8115, 8121, 8150, 8153, 8154, 8286, 8311, 8367, 8368, 8413, 8415, 8463, 8472, 8490, 8498, 8593, 8597, 8604, 8606, 8608, 8609, 8616, 8650, 8651, 8653, 8654, 8655, 8659, 8735, 8783, 8790, 8794, 8814, 8856, 8985, 9016, 9017, 9018, 9020, 9034, 9035, 9036, 9037, 9038, 9039, 9040, 9050, 9051, 9053, 9061, 9066, 9085, 9090, 9106, 9115, 9116, 9117, 9118, 9156, 9157, 9161, 9165, 9168, 9170, 9171, 9173, 9174, 9176, 9180, 9181, 9183, 9184, 9186, 9187, 9190, 9191, 9192, 9193, 9194, 9198, 9199, 9200, 9201, 9202, 9203, 9209, 9211, 9212, 9214, 9217, 9218, 9219, 9220, 9223, 9224, 9233, 9234, 9235, 9237, 9238, 9239, 9240, 9241, 9242, 9247, 9248, 9250, 9252, 9255, 9257, 9259, 9260, 9261, 9265, 9267, 9268, 9270, 9271, 9273, 9277, 9279, 9280, 9281, 9283, 9284, 9285, 9288, 9294, 9296, 9304, 9307, 9309, 9310, 9312, 9313, 9314, 9317, 9326, 9332, 9336, 9337, 9352, 9363, 9364, 9372, 9376, 9377, 9381, 9382, 9383, 9390, 9391, 9395, 9396, 9400, 9406, 9407, 9409, 9410, 9411, 9413, 9414, 9415, 9416, 9425, 9426, 9430, 9465, 9480, 9490, 9493, 9494, 9495, 9496, 9497, 9502, 9503, 9507, 9509, 9510, 9512, 9514, 9592, 9599, 9612, 9614, 9616, 9654, 9658, 9659, 9671, 9679, 9685, 9689, 9691, 9693, 9698, 9714, 9722, 9729, 9730, 9732, 9733, 9734, 9736, 9740, 9754, 9756, 9767, 9769, 9785, 9798, 9800, 9807, 9815, 9816, 9819, 9824, 9825, 9828, 9833, 9834, 9837, 9842, 9843, 9846, 9850, 9851, 9856, 9857, 9859, 9860, 9862, 9864, 9865, 9866, 9867, 9868, 9869, 9870, 9871, 9873, 9876, 9877, 9878, 9879, 9881, 9885, 9889, 9890, 9891, 9892, 9893, 9894, 9895, 9896, 9897, 9898, 9899, 9900, 9901, 9902, 9908, 9912, 9914, 9917, 9922, 9923, 9929, 9930, 9931, 9933, 9940, 9941, 9943, 9944, 9945, 9950, 9952, 9953, 9957, 9958, 9961, 9962, 9963, 9964, 9965, 9966, 9968, 9969, 9970, 9971, 9972, 9973, 9974, 9975, 9976, 9977, 9978, 9986, 9987, 9988, 9989, 9990, 9994, 10000, 10001, 10002, 10003, 10004, 10008, 10010, 10011, 10012, 10013, 10014, 10016, 10017, 10019, 10020, 10022, 10023, 10024, 10025, 10027, 10028, 10030, 10031, 10032, 10034, 10035, 10036, 10037, 10038, 10039, 10040, 10044, 10045, 10047, 10048, 10050, 10051, 10052, 10053, 10054, 10055, 10058, 10061, 10065, 10066, 10068, 10069, 10070, 10073, 10075, 10076, 10180, 10206, 10212, 10311, 10386, 10397, 10500, 10571, 10572, 10581, 10586, 10588, 10646, 10702, 10786, 10866, 10870, 10872, 10878, 10890, 10891, 10892, 10893, 10895, 10900, 10903, 10904, 10916, 10921, 10933, 11004, 11006, 11058, 11059, 11064]

Solved by Maple but not by Mathematica

(243) [119, 146, 885, 944, 1041, 1069, 1105, 1138, 1698, 1897, 2491, 2513, 2628, 2720, 2722, 2723, 2727, 2795, 3130, 3742, 3743, 3744, 3751, 3752, 3757, 3765, 3766, 3769, 3781, 3785, 3790, 3796, 3942, 4157, 4158, 4159, 4330, 4331, 4332, 4606, 4740, 4741, 4742, 5007, 5059, 5346, 5492, 5500, 5589, 5590, 6043, 6053, 6057, 6059, 6085, 6086, 6102, 6104, 6120, 6124, 6342, 6348, 6354, 6376, 6424, 6428, 6429, 6458, 6463, 6500, 6705, 6797, 6799, 7185, 7219, 7221, 7910, 8009, 8067, 8440, 8610, 8652, 8660, 8661, 8677, 8704, 8883, 8900, 8939, 8996, 9021, 9077, 9091, 9119, 9122, 9127, 9147, 9151, 9178, 9253, 9351, 9354, 9355, 9386, 9393, 9394, 9402, 9408, 9504, 9508, 9511, 9588, 9593, 9594, 9606, 9615, 9637, 9645, 9668, 9692, 9694, 9697, 9705, 9706, 9712, 9713, 9715, 9716, 9731, 9735, 9737, 9741, 9749, 9753, 9757, 9758, 9759, 9760, 9766, 9770, 9771, 9772, 9773, 9778, 9779, 9784, 9789, 9790, 9791, 9794, 9799, 9801, 9802, 9803, 9808, 9809, 9810, 9813, 9822, 9831, 9840, 9852, 9854, 9863, 9874, 9875, 9880, 9882, 9886, 9906, 9907, 9910, 9911, 9915, 9919, 9920, 9924, 9926, 9927, 9932, 9936, 9937, 9938, 9939, 9942, 9949, 9951, 9954, 9955, 9959, 9960, 9967, 9983, 9984, 9991, 9993, 9998, 10005, 10009, 10015, 10018, 10021, 10026, 10029, 10033, 10041, 10042, 10043, 10046, 10049, 10056, 10057, 10060, 10063, 10064, 10067, 10072, 10077, 10085, 10086, 10093, 10094, 10194, 10197, 10201, 10208, 10222, 10292, 10293, 10313, 10363, 10457, 10592, 10647, 10779, 10781, 10800, 10850, 10879, 10901, 10902, 10908, 10910]

Solved by Mathematica but not by Maple

(102) [408, 409, 1794, 1797, 1805, 2032, 2411, 2581, 2873, 2886, 3363, 3417, 3471, 3486, 3531, 3654, 3689, 3690, 3789, 3834, 4192, 4205, 4209, 4213, 4214, 4405, 4494, 4708, 4746, 4747, 4748, 4767, 4772, 4802, 4810, 4834, 4835, 4836, 5288, 5484, 5664, 5687, 5689, 5695, 5705, 5706, 5759, 5830, 5838, 5863, 5864, 5965, 6066, 6470, 6471, 6472, 6476, 6477, 6479, 6487, 6546, 6547, 6549, 6550, 6551, 6552, 6553, 7931, 7947, 7962, 8030, 8091, 8115, 8121, 8286, 8311, 8367, 8368, 8490, 8498, 9085, 9157, 9257, 9273, 9280, 9281, 9284, 9296, 9383, 9409, 9410, 9671, 9679, 9722, 9800, 10212, 10500, 10588, 10646, 10870, 11058, 11059]

Both systems unable to solve

(482) [133, 485, 550, 553, 710, 813, 958, 959, 961, 962, 964, 966, 968, 1039, 1046, 1075, 1162, 1186, 1697, 1700, 1701, 1702, 1703, 1704, 1706, 1707, 2198, 2204, 2481, 2583, 2609, 2683, 2684, 2815, 2817, 2830, 2843, 2846, 2854, 2859, 2875, 2954, 3133, 3164, 3167, 3219, 3267, 3274, 3334, 3502, 3637, 3707, 3778, 3806, 3877, 4408, 4442, 4445, 4453, 4486, 4501, 5063, 5064, 5350, 5357, 5415, 5429, 5431, 5508, 5510, 5788, 5789, 5795, 5827, 6309, 6353, 6356, 6425, 6433, 6435, 6460, 6499, 6534, 6562, 6591, 6654, 7627, 7628, 7629, 7630, 7635, 7636, 7654, 7659, 7662, 7667, 7690, 7700, 7781, 7782, 7784, 7785, 7798, 7813, 7816, 7829, 7832, 7844, 7848, 7919, 7946, 7949, 7974, 8038, 8039, 8058, 8060, 8081, 8084, 8088, 8109, 8150, 8153, 8154, 8413, 8415, 8463, 8472, 8593, 8597, 8604, 8606, 8608, 8609, 8616, 8650, 8651, 8653, 8654, 8655, 8659, 8735, 8783, 8790, 8794, 8814, 8856, 8985, 9016, 9017, 9018, 9020, 9034, 9035, 9036, 9037, 9038, 9039, 9040, 9050, 9051, 9053, 9061, 9066, 9090, 9106, 9115, 9116, 9117, 9118, 9156, 9161, 9165, 9168, 9170, 9171, 9173, 9174, 9176, 9180, 9181, 9183, 9184, 9186, 9187, 9190, 9191, 9192, 9193, 9194, 9198, 9199, 9200, 9201, 9202, 9203, 9209, 9211, 9212, 9214, 9217, 9218, 9219, 9220, 9223, 9224, 9233, 9234, 9235, 9237, 9238, 9239, 9240, 9241, 9242, 9247, 9248, 9250, 9252, 9255, 9259, 9260, 9261, 9265, 9267, 9268, 9270, 9271, 9277, 9279, 9283, 9285, 9288, 9294, 9304, 9307, 9309, 9310, 9312, 9313, 9314, 9317, 9326, 9332, 9336, 9337, 9352, 9363, 9364, 9372, 9376, 9377, 9381, 9382, 9390, 9391, 9395, 9396, 9400, 9406, 9407, 9411, 9413, 9414, 9415, 9416, 9425, 9426, 9430, 9465, 9480, 9490, 9493, 9494, 9495, 9496, 9497, 9502, 9503, 9507, 9509, 9510, 9512, 9514, 9592, 9599, 9612, 9614, 9616, 9654, 9658, 9659, 9685, 9689, 9691, 9693, 9698, 9714, 9729, 9730, 9732, 9733, 9734, 9736, 9740, 9754, 9756, 9767, 9769, 9785, 9798, 9807, 9815, 9816, 9819, 9824, 9825, 9828, 9833, 9834, 9837, 9842, 9843, 9846, 9850, 9851, 9856, 9857, 9859, 9860, 9862, 9864, 9865, 9866, 9867, 9868, 9869, 9870, 9871, 9873, 9876, 9877, 9878, 9879, 9881, 9885, 9889, 9890, 9891, 9892, 9893, 9894, 9895, 9896, 9897, 9898, 9899, 9900, 9901, 9902, 9908, 9912, 9914, 9917, 9922, 9923, 9929, 9930, 9931, 9933, 9940, 9941, 9943, 9944, 9945, 9950, 9952, 9953, 9957, 9958, 9961, 9962, 9963, 9964, 9965, 9966, 9968, 9969, 9970, 9971, 9972, 9973, 9974, 9975, 9976, 9977, 9978, 9986, 9987, 9988, 9989, 9990, 9994, 10000, 10001, 10002, 10003, 10004, 10008, 10010, 10011, 10012, 10013, 10014, 10016, 10017, 10019, 10020, 10022, 10023, 10024, 10025, 10027, 10028, 10030, 10031, 10032, 10034, 10035, 10036, 10037, 10038, 10039, 10040, 10044, 10045, 10047, 10048, 10050, 10051, 10052, 10053, 10054, 10055, 10058, 10061, 10065, 10066, 10068, 10069, 10070, 10073, 10075, 10076, 10180, 10206, 10311, 10386, 10397, 10571, 10572, 10581, 10586, 10702, 10786, 10866, 10872, 10878, 10890, 10891, 10892, 10893, 10895, 10900, 10903, 10904, 10916, 10921, 10933, 11004, 11006, 11064]