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 [10258]. 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 2022.2	94.521	9696	562
Mathematica 13.2	93.264	9567	691

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 2022.2	0.180	271.14	30.743	2781365
Mathematica 13.2	4.046	829.60	691.715	8510026

The problem which Mathematica produced largest leaf size of \(2733033\) is 9606.

The problem which Maple produced largest leaf size of \(545927\) is 9648.

The problem which Mathematica used most CPU time of \(178.017\) seconds is 3759.

The problem which Maple used most CPU time of \(118.453\) seconds is 3752.

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]	467	99.14% [885, 3741, 3758, 3767]	99.79% [6550]
[[_linear, class A]]	148	100.00%	98.65% [6547, 6548]
[_separable]	769	99.48% [944, 2513, 5511, 7911]	99.48% [408, 409, 5511, 5665]
[_Riccati]	308	55.19% [958, 1697, 1698, 1700, 1701, 1702, 2198, 2795, 2815, 2817, 2830, 3131, 3878, 6592, 7691, 9592, 9596, 9597, 9598, 9603, 9616, 9618, 9619, 9620, 9672, 9689, 9693, 9695, 9696, 9697, 9702, 9709, 9710, 9716, 9717, 9718, 9719, 9720, 9733, 9734, 9735, 9736, 9737, 9738, 9739, 9740, 9741, 9744, 9745, 9753, 9757, 9758, 9760, 9761, 9762, 9763, 9764, 9770, 9771, 9773, 9774, 9775, 9776, 9777, 9782, 9783, 9788, 9789, 9793, 9794, 9795, 9798, 9802, 9803, 9805, 9806, 9811, 9812, 9813, 9814, 9817, 9819, 9820, 9823, 9826, 9828, 9829, 9832, 9835, 9837, 9838, 9841, 9844, 9846, 9847, 9850, 9854, 9855, 9856, 9860, 9861, 9863, 9864, 9866, 9868, 9869, 9870, 9871, 9872, 9873, 9874, 9875, 9877, 9878, 9879, 9880, 9881, 9882, 9883, 9884, 9885, 9886, 9889, 9890, 9893, 9894, 9895, 9896, 9897, 9898, 9899, 9900, 9901, 9902, 9903, 9904, 9905, 9906]	71.75% [958, 1697, 1700, 1701, 1702, 2198, 2815, 2817, 2830, 3878, 6592, 7691, 9596, 9603, 9616, 9618, 9620, 9675, 9683, 9689, 9693, 9695, 9697, 9702, 9718, 9733, 9736, 9737, 9738, 9740, 9744, 9758, 9760, 9771, 9773, 9789, 9802, 9804, 9811, 9819, 9820, 9823, 9828, 9829, 9832, 9837, 9838, 9841, 9846, 9847, 9850, 9854, 9855, 9860, 9861, 9863, 9864, 9866, 9868, 9869, 9870, 9871, 9872, 9873, 9874, 9875, 9877, 9880, 9881, 9882, 9883, 9885, 9889, 9893, 9894, 9895, 9896, 9897, 9898, 9899, 9900, 9901, 9902, 9903, 9904, 9905, 9906]
[[_homogeneous, class G]]	62	91.94% [2723, 2727, 2888, 3532, 7963]	93.55% [3487, 3532, 7948, 7963]
[_linear]	466	99.79% [5416]	99.57% [4749, 5416]
[[_homogeneous, class A], _exact, _rational, [_Abel, 2nd type, class A]]	18	100.00%	100.00%
[[_homogeneous, class A], _rational, _Bernoulli]	63	100.00%	100.00%
[[_homogeneous, class A], _dAlembert]	118	99.15% [10198]	99.15% [6370]
[[_homogeneous, class A], _rational, [_Abel, 2nd type, class A]]	71	98.59% [5501]	100.00%
[[_homogeneous, class A], _rational, [_Abel, 2nd type, class B]]	46	100.00%	100.00%
[[_homogeneous, class A], _rational, _dAlembert]	174	98.85% [5008, 5509]	99.43% [5509]
[[_homogeneous, class C], _dAlembert]	60	86.67% [2491, 3561, 3570, 3752, 3770, 6349, 10204, 10226]	100.00%
[[_homogeneous, class C], _Riccati]	16	100.00%	100.00%
[[_homogeneous, class G], _rational, _Bernoulli]	48	100.00%	100.00%
[_Bernoulli]	87	97.70% [4607, 6377]	100.00%
[[_1st_order, _with_linear_symmetries], _Bernoulli]	3	100.00%	100.00%
[[_1st_order, _with_symmetry_[F(x),G(x)]]]	45	100.00%	100.00%
[y=_G(x,y’)]	112	63.39% [133, 485, 959, 961, 962, 964, 966, 968, 1703, 1706, 1707, 2854, 2859, 2876, 2955, 3503, 3708, 3753, 3779, 3791, 4443, 4487, 5796, 6310, 6500, 7655, 7660, 7663, 7701, 7950, 7975, 8040, 8041, 8083, 8086, 8087, 8090, 8111, 8442, 10205, 10210]	59.82% [133, 485, 959, 961, 962, 964, 966, 968, 1703, 1706, 1707, 2581, 2854, 2859, 2874, 2876, 2887, 2955, 3364, 3503, 3708, 3779, 3790, 4406, 4443, 4487, 5796, 6310, 6500, 7655, 7660, 7663, 7701, 7950, 7975, 8040, 8041, 8083, 8086, 8087, 8090, 8111, 8123, 8140, 10210]
[[_1st_order, _with_linear_symmetries]]	94	93.62% [2720, 2722, 3782, 3786, 6054, 10201]	98.94% [8117]
[[_homogeneous, class A], _exact, _rational, _dAlembert]	26	100.00%	100.00%
[_exact, _rational]	31	96.77% [119]	100.00%
[_exact]	62	96.77% [2628, 5444]	100.00%
[[_1st_order, _with_linear_symmetries], _exact, _rational]	3	100.00%	100.00%
[[_homogeneous, class A], _exact, _rational, [_Abel, 2nd type, class B]]	2	100.00%	100.00%
[[_homogeneous, class G], _exact, _rational]	3	66.67% [146]	100.00%
[[_2nd_order, _missing_x]]	410	96.59% [6655, 9190, 9191, 9194, 9195, 9197, 9215, 9216, 9218, 9223, 9241, 9287, 9289, 9415]	96.34% [6655, 9190, 9191, 9194, 9195, 9197, 9215, 9216, 9218, 9223, 9241, 9287, 9288, 9289, 9415]
[[_Emden, _Fowler], [_2nd_order, _linear, _with_symmetry_[0,F(x)]]]	58	100.00%	100.00%
[[_Emden, _Fowler]]	233	99.57% [5591]	96.57% [2032, 4210, 4709, 4803, 4835, 4836, 5831, 5864]
[[_2nd_order, _exact, _linear, _homogeneous]]	176	100.00%	98.30% [4837, 5707, 5865]
[[_2nd_order, _missing_y]]	80	92.50% [6070, 6103, 6105, 6459, 9406, 10317]	97.50% [5690, 6552]
[[_2nd_order, _with_linear_symmetries]]	2134	95.97% [1105, 1138, 4502, 4741, 4742, 4743, 5060, 5065, 5590, 5828, 6343, 6425, 6426, 6429, 6430, 6434, 6436, 6535, 6798, 6800, 7186, 7220, 7222, 8599, 8606, 8608, 8610, 8611, 8612, 8618, 8652, 8653, 8655, 8657, 8661, 8662, 8663, 8679, 8706, 8737, 8785, 8792, 8796, 8816, 8858, 8885, 8941, 8987, 8998, 9018, 9019, 9020, 9022, 9184, 9227, 9237, 9238, 9239, 9242, 9244, 9245, 9246, 9251, 9252, 9256, 9257, 9259, 9263, 9298, 9321, 9341, 9356, 9358, 9359, 9390, 9397, 9398, 9399, 9410, 9411, 10089, 10090, 10098, 10296, 10297, 10315]	96.81% [1794, 1797, 1805, 2411, 4193, 4206, 4495, 4502, 4768, 4773, 4811, 5065, 5289, 5688, 5696, 5828, 5839, 6426, 6434, 6436, 6535, 8599, 8606, 8608, 8610, 8611, 8618, 8652, 8653, 8655, 8657, 8661, 8737, 8785, 8792, 8796, 8816, 8858, 8987, 9018, 9019, 9020, 9022, 9184, 9227, 9237, 9238, 9239, 9242, 9244, 9245, 9246, 9251, 9252, 9256, 9259, 9261, 9263, 9298, 9321, 9341, 9356, 9390, 9399, 9410, 9411, 9413, 10315]
[[_2nd_order, _linear, _nonhomogeneous]]	560	99.29% [1162, 1186, 6706, 8656]	96.96% [1162, 1186, 4214, 4215, 4747, 4748, 5760, 6471, 6472, 6473, 6477, 6478, 6480, 6488, 6553, 6554, 8656]
[[_2nd_order, _exact, _linear, _nonhomogeneous]]	36	100.00%	100.00%
system of linear ODEs	449	95.32% [5351, 5789, 5790, 9469, 9484, 9494, 9497, 9498, 9499, 9500, 9501, 9506, 9507, 9508, 9511, 9512, 9513, 9514, 9515, 9516, 9518]	95.32% [5351, 5789, 5790, 5963, 5966, 9469, 9484, 9494, 9497, 9498, 9499, 9500, 9501, 9506, 9507, 9508, 9511, 9513, 9514, 9516, 9518]
[_Gegenbauer]	63	100.00%	100.00%
[[_high_order, _missing_x]]	96	96.88% [9123, 9126, 9155]	100.00%
[[_3rd_order, _missing_x]]	83	100.00%	100.00%
[[_3rd_order, _missing_y]]	35	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)]]]	54	92.59% [8654, 8902, 9023, 10097]	98.15% [5706]
[_Lienard]	47	100.00%	100.00%
[[_homogeneous, class A], _rational, _Riccati]	27	100.00%	100.00%
[x=_G(y,y’)]	12	66.67% [550, 2204, 5430, 8152]	66.67% [550, 2204, 5430, 8152]
[[_Abel, 2nd type, class B]]	15	26.67% [553, 1046, 7830, 9924, 9927, 9947, 9948, 9949, 9969, 9982, 9987]	40.00% [553, 1046, 7830, 9927, 9947, 9948, 9949, 9969, 9982]
[_exact, _rational, [_1st_order, _with_symmetry_[F(x),G(x)]], [_Abel, 2nd type, class A]]	6	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]	99	85.86% [1039, 1075, 2609, 2683, 2684, 3638, 3807, 5358, 8060, 8062, 8069, 8465, 8474, 10184]	77.78% [1039, 1075, 2609, 2683, 2684, 3418, 3638, 3690, 3691, 3807, 5358, 8032, 8060, 8062, 8065, 8288, 8465, 8474, 8492, 8500, 10184, 10216]
[_rational, [_Abel, 2nd type, class B]]	133	27.07% [1069, 2481, 2583, 3268, 3275, 5432, 6563, 7814, 7817, 7833, 7845, 9910, 9911, 9918, 9919, 9921, 9923, 9926, 9928, 9930, 9931, 9933, 9934, 9935, 9936, 9937, 9940, 9941, 9942, 9944, 9945, 9946, 9953, 9954, 9955, 9956, 9957, 9958, 9961, 9962, 9963, 9964, 9965, 9966, 9967, 9968, 9970, 9971, 9972, 9973, 9974, 9975, 9976, 9988, 10005, 10006, 10009, 10012, 10013, 10014, 10015, 10016, 10017, 10018, 10019, 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, 10080, 10081]	51.88% [2481, 2583, 3268, 3275, 5432, 6563, 7814, 7817, 7833, 7845, 9918, 9921, 9926, 9933, 9934, 9935, 9937, 9944, 9945, 9954, 9956, 9957, 9961, 9962, 9965, 9966, 9967, 9968, 9970, 9972, 9973, 9974, 9975, 9976, 10005, 10006, 10012, 10014, 10015, 10016, 10017, 10018, 10021, 10023, 10024, 10026, 10027, 10028, 10029, 10031, 10032, 10034, 10035, 10036, 10038, 10039, 10040, 10041, 10042, 10043, 10044, 10048, 10049, 10080]
[_rational, [_1st_order, _with_symmetry_[F(x),G(x)]], [_Abel, 2nd type, class A]]	4	100.00%	100.00%
[NONE]	80	40.00% [710, 1041, 6357, 6461, 7637, 7668, 7782, 7947, 8155, 8156, 8415, 8417, 9174, 9177, 9178, 9182, 9185, 9187, 9188, 9196, 9198, 9202, 9203, 9204, 9207, 9213, 9221, 9222, 9224, 9228, 9254, 9264, 9272, 9281, 9283, 9308, 9311, 9313, 9314, 9317, 9318, 9330, 9336, 9368, 9380, 9381, 9394, 9430]	36.25% [710, 5485, 6357, 6461, 7637, 7668, 7782, 7947, 8155, 8156, 8415, 8417, 9174, 9177, 9178, 9185, 9187, 9188, 9196, 9198, 9202, 9203, 9204, 9207, 9213, 9221, 9222, 9224, 9228, 9254, 9264, 9272, 9277, 9281, 9283, 9284, 9285, 9300, 9308, 9311, 9313, 9314, 9317, 9318, 9330, 9336, 9368, 9380, 9381, 9394, 9430]
[_rational, [_1st_order, _with_symmetry_[F(x)*G(y),0]]]	21	100.00%	100.00%
[[_homogeneous, class G], _rational, [_Abel, 2nd type, class B]]	40	100.00%	100.00%
[_Gegenbauer, [_2nd_order, _linear, _with_symmetry_[0,F(x)]]]	12	100.00%	100.00%
[[_high_order, _with_linear_symmetries]]	39	82.05% [813, 9119, 9120, 9121, 9122, 9151, 9169]	82.05% [813, 9119, 9120, 9121, 9122, 9161, 9169]
[[_3rd_order, _with_linear_symmetries]]	103	83.50% [5064, 9036, 9037, 9038, 9039, 9040, 9041, 9042, 9052, 9053, 9055, 9063, 9068, 9079, 9094, 9095, 9110]	84.47% [5064, 9036, 9037, 9038, 9039, 9040, 9041, 9042, 9052, 9053, 9055, 9063, 9068, 9089, 9094, 9110]
[[_high_order, _linear, _nonhomogeneous]]	53	96.23% [9131, 9160]	98.11% [9160]
[[_1st_order, _with_linear_symmetries], _Clairaut]	44	100.00%	100.00%
[[_1st_order, _with_symmetry_[F(x),G(y)]]]	49	100.00%	100.00%
[[_1st_order, _with_symmetry_[F(x),G(x)*y+H(x)]]]	71	100.00%	100.00%
[[_homogeneous, class C], _rational, _Riccati]	5	100.00%	100.00%
[[_Abel, 2nd type, class A]]	34	14.71% [3168, 3220, 4446, 7786, 7799, 9914, 9915, 9979, 9980, 9981, 9990, 9991, 9992, 9993, 9994, 10008, 10054, 10061, 10062, 10064, 10065, 10067, 10068, 10069, 10070, 10071, 10072, 10073, 10074]	35.29% [3168, 3220, 4446, 7786, 7799, 9979, 9980, 9981, 9990, 9991, 9992, 9993, 9994, 10008, 10054, 10062, 10065, 10069, 10070, 10072, 10073, 10074]
[_rational, _Bernoulli]	39	100.00%	100.00%
[[_homogeneous, class A]]	7	100.00%	100.00%
[[_homogeneous, class C], _rational, [_Abel, 2nd type, class A]]	106	98.11% [3943, 10076]	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]]	14	100.00%	100.00%
[_exact, [_Abel, 2nd type, class B]]	2	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]]	2	100.00%	100.00%
[_exact, _Bernoulli]	6	100.00%	100.00%
[[_homogeneous, class A], _exact, _rational, _Bernoulli]	4	100.00%	100.00%
[_rational, [_Abel, 2nd type, class C]]	12	83.33% [4409, 4454]	83.33% [4409, 4454]
[[_homogeneous, class G], _rational]	74	100.00%	97.30% [3655, 6067]
[[_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% [9610, 9641, 9649, 9658, 9662, 9663]	97.03% [9658, 9662, 9663]
[[_3rd_order, _linear, _nonhomogeneous]]	53	100.00%	100.00%
[[_high_order, _missing_y]]	18	94.44% [9165]	94.44% [9165]
[[_3rd_order, _exact, _linear, _nonhomogeneous]]	6	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]]	1	100.00%	100.00%
[[_1st_order, _with_linear_symmetries], [_Abel, 2nd type, class A]]	2	100.00%	100.00%
[[_Riccati, _special]]	14	100.00%	100.00%
[_Abel]	25	76.00% [1704, 2843, 7628, 7629, 7630, 7631]	76.00% [1704, 2843, 7628, 7629, 7630, 7631]
[_Laguerre]	34	100.00%	100.00%
[_Laguerre, [_2nd_order, _linear, _with_symmetry_[0,F(x)]]]	4	100.00%	100.00%
[_Bessel]	15	100.00%	100.00%
[_rational, _Abel]	21	95.24% [1897]	100.00%
[_exact, _rational, [_1st_order, _with_symmetry_[F(x)*G(y),0]]]	9	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% [9355]	100.00%
[[_3rd_order, _exact, _nonlinear]]	2	50.00% [9420]	50.00% [9420]
[_Jacobi]	30	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]]	33	100.00%	96.97% [6551]
[[_3rd_order, _quadrature]]	3	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]	8	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	92.86% [10212]	100.00%
[[_homogeneous, class D]]	8	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]	22	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]]	37	27.03% [3165, 7783, 7785, 9912, 9916, 9943, 9959, 9977, 9978, 9995, 9997, 9998, 10002, 10004, 10007, 10020, 10051, 10052, 10053, 10055, 10056, 10057, 10058, 10059, 10060, 10077, 10079]	45.95% [3165, 7783, 7785, 9912, 9916, 9977, 9978, 9998, 10004, 10007, 10020, 10051, 10052, 10055, 10056, 10057, 10058, 10059, 10077, 10079]
[[_homogeneous, class G], _dAlembert]	6	100.00%	100.00%
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli]	3	100.00%	100.00%
[[_homogeneous, class D], _rational, _Bernoulli]	24	100.00%	100.00%
[[_1st_order, _with_linear_symmetries], _dAlembert]	47	76.60% [3743, 3744, 3745, 3766, 3797, 6058, 6060, 6062, 6121, 6125, 6501]	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, 3134, 7636]	0.00% [2846, 3134, 7636]
[_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% [3335, 7849]	71.43% [3335, 7849]
[[_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%	88.24% [3642, 8028]
unknown	5	60.00% [7920, 9385]	0.00% [3472, 7920, 7932, 9385, 9414]
[_dAlembert]	17	100.00%	100.00%
[_rational, _dAlembert]	11	90.91% [8010]	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%
[[_homogeneous, class G], _rational, _dAlembert]	6	100.00%	100.00%
[_rational, [_1st_order, _with_symmetry_[F(x),G(y)]]]	14	100.00%	92.86% [3702]
[[_homogeneous, class G], _Clairaut]	2	100.00%	100.00%
[_Clairaut]	7	100.00%	85.71% [3845]
[[_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]]	8	50.00% [4160, 4331, 4332, 4333]	100.00%
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	55	94.55% [5347, 6086, 6087]	96.36% [6086, 6087]
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	24	95.83% [4158]	95.83% [9387]
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	4	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]]	16	93.75% [6464]	100.00%
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_xy]]	2	0.00% [4159, 5493]	100.00%
[_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	7	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]	12	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% [8313, 8369, 8370]
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]	3	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]]	11	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]]	2	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]]	3	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]]	10	10.00% [6354, 6355, 9180, 9243, 9265, 9269, 9271, 9274, 9275]	20.00% [6354, 9180, 9243, 9265, 9269, 9271, 9274, 9275]
[[_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]]	2	50.00% [9205]	50.00% [9205]
[_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% [8595]	0.00% [8595]
[_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]]	5	100.00%	100.00%
[[_high_order, _fully, _exact, _linear]]	1	100.00%	100.00%
[[_Painleve, 1st]]	1	0.00% [9172]	0.00% [9172]
[[_Painleve, 2nd]]	1	0.00% [9175]	0.00% [9175]
[[_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	1	0.00% [9206]	0.00% [9206]
[[_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]]	1	100.00%	100.00%
[[_2nd_order, _reducible, _mu_xy]]	3	66.67% [9367]	66.67% [9367]
[[_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]	1	0.00% [9292]	0.00% [9292]
[[_Painleve, 4th]]	1	0.00% [9316]	0.00% [9316]
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_xy]]	1	100.00%	100.00%
[[_Painleve, 3rd]]	1	0.00% [9340]	0.00% [9340]
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1]]	1	100.00%	100.00%
[[_Painleve, 5th]]	1	0.00% [9376]	0.00% [9376]
[[_Painleve, 6th]]	1	0.00% [9386]	0.00% [9386]
[[_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% [9395]	0.00% [9395]
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_poly_yn]]	1	0.00% [9400]	0.00% [9400]
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1]]	1	0.00% [9404]	0.00% [9404]
[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]]	6	33.33% [9417, 9418, 9419, 9434]	33.33% [9417, 9418, 9419, 9434]
[[_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% [9429]	50.00% [9429]
[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries], [_high_order, _reducible, _mu_poly_yn]]	1	100.00%	100.00%
	62	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%

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 1.4: Percentage solved per own ODE type

Type of ODE	Count	Mathematica	Maple
quadrature	178	100.00%	100.00%
linear	761	99.74% [5416, 5511]	99.74% [5416, 5511]
separable	681	98.97% [885, 944, 2513, 3741, 3758, 3767, 7911]	100.00%
homogeneous	481	99.17% [5008, 5501, 5509, 10198]	99.79% [5509]
homogeneousTypeC	24	100.00%	100.00%
exact	202	98.02% [119, 146, 2628, 5444]	99.01% [3472, 7932]
exactWithIntegrationFactor	268	99.63% [7920]	98.51% [2581, 3642, 7920, 8028]
exactByInspection	32	100.00%	96.88% [3418]
bernoulli	339	99.41% [4607, 6377]	100.00%
riccati	525	72.95% [958, 1697, 1698, 1700, 1701, 1702, 2198, 2795, 2815, 2817, 2830, 3131, 3878, 6592, 7691, 9592, 9596, 9597, 9598, 9603, 9610, 9616, 9618, 9619, 9620, 9641, 9649, 9658, 9662, 9663, 9672, 9689, 9693, 9695, 9696, 9697, 9702, 9709, 9710, 9716, 9717, 9718, 9719, 9720, 9733, 9734, 9735, 9736, 9737, 9738, 9739, 9740, 9741, 9744, 9745, 9753, 9757, 9760, 9761, 9762, 9763, 9764, 9770, 9773, 9774, 9775, 9776, 9777, 9782, 9783, 9788, 9789, 9793, 9794, 9795, 9798, 9802, 9803, 9805, 9806, 9811, 9812, 9813, 9814, 9817, 9819, 9820, 9823, 9826, 9828, 9829, 9832, 9835, 9837, 9838, 9841, 9844, 9846, 9847, 9850, 9854, 9855, 9856, 9860, 9861, 9863, 9864, 9866, 9868, 9869, 9870, 9871, 9872, 9873, 9874, 9875, 9877, 9878, 9879, 9880, 9881, 9882, 9883, 9884, 9885, 9886, 9889, 9890, 9893, 9894, 9895, 9896, 9897, 9898, 9899, 9900, 9901, 9902, 9903, 9904, 9905, 9906]	83.24% [958, 1697, 1700, 1701, 1702, 2198, 2815, 2817, 2830, 3878, 6592, 7691, 9596, 9603, 9616, 9618, 9620, 9658, 9662, 9663, 9675, 9683, 9689, 9693, 9695, 9697, 9702, 9718, 9733, 9736, 9737, 9738, 9740, 9744, 9760, 9773, 9789, 9802, 9804, 9811, 9819, 9820, 9823, 9828, 9829, 9832, 9837, 9838, 9841, 9846, 9847, 9850, 9854, 9855, 9860, 9861, 9863, 9864, 9866, 9868, 9869, 9870, 9871, 9872, 9873, 9874, 9875, 9877, 9880, 9881, 9882, 9883, 9885, 9889, 9893, 9894, 9895, 9896, 9897, 9898, 9899, 9900, 9901, 9902, 9903, 9904, 9905, 9906]
clairaut	79	98.73% [10212]	98.73% [3845]
dAlembert	151	86.75% [2491, 3561, 3570, 3743, 3744, 3745, 3752, 3766, 3770, 3797, 6058, 6060, 6062, 6121, 6125, 6349, 6501, 8010, 10204, 10226]	99.34% [6370]
isobaric	166	93.37% [2720, 2722, 2723, 2727, 2888, 3532, 3782, 3786, 6054, 7963, 10201]	95.78% [3487, 3532, 3655, 6067, 7948, 7963, 8117]
first order special form ID 1	5	100.00%	100.00%
polynomial	97	97.94% [3943, 10076]	100.00%
abelFirstKind	6	100.00%	100.00%
differentialType	67	100.00%	100.00%
first order ode series method. Ordinary point	42	100.00%	92.86% [6547, 6548, 6550]
first order ode series method. Regular singular point	9	100.00%	88.89% [4749]
first order ode series method. Irregular singular point	3	100.00%	0.00% [408, 409, 5665]
first_order_laplace	42	100.00%	100.00%
system of linear ODEs	403	99.26% [5351, 5790, 9484]	98.76% [5351, 5790, 5963, 5966, 9484]
second_order_laplace	159	100.00%	99.37% [5760]
reduction_of_order	90	96.67% [1138, 5590, 5591]	100.00%
second_order_ode_quadrature	21	100.00%	100.00%
second_order_linear_constant_coeff	703	100.00%	100.00%
second_order_airy	23	100.00%	100.00%
second_order_euler_ode	166	100.00%	100.00%
second_order_change_of_variable_on_x_q1_constant_method	1	100.00%	100.00%
second_order_change_of_variable_on_y_general_n	58	96.55% [8902, 8998]	100.00%
second_order_integrable_as_is	69	86.96% [4159, 4160, 4331, 4332, 4333, 5493, 9205, 9395, 9400]	95.65% [9205, 9395, 9400]
second_order_ode_can_be_made_integrable	21	85.71% [5347, 6086, 6087]	90.48% [6086, 6087]
second_order_ode_solved_by_an_integrating_factor	18	100.00%	100.00%
second_order_change_of_variable_on_x_p1_zero_method	70	97.14% [8654, 9023]	100.00%
second_order_ode_lagrange_adjoint_equation_method	18	100.00%	100.00%
second_order_nonlinear_solved_by_mainardi_lioville_method	10	100.00%	100.00%
second_order_change_of_variable_on_y_n_one_case	40	97.50% [8706]	100.00%
second_order_bessel_ode	116	100.00%	100.00%
second_order_ode_missing_x	146	91.78% [4158, 9190, 9191, 9195, 9197, 9215, 9216, 9218, 9241, 9287, 9289, 9415]	91.10% [9190, 9191, 9195, 9197, 9215, 9216, 9218, 9241, 9287, 9288, 9289, 9387, 9415]
second_order_ode_missing_y	49	85.71% [6070, 6103, 6105, 6459, 6464, 9406, 10317]	100.00%
second order series method. Ordinary point	456	100.00%	100.00%
second order series method. Regular singular point. Difference not integer	188	100.00%	100.00%
second order series method. Regular singular point. Repeated root	167	100.00%	100.00%
second order series method. Regular singular point. Difference is integer	260	100.00%	100.00%
second order series method. Irregular singular point	29	93.10% [4502, 5828]	0.00% [1794, 1797, 1805, 2032, 2411, 4193, 4206, 4210, 4495, 4502, 4709, 4768, 4773, 4803, 4811, 4835, 4836, 4837, 5289, 5688, 5690, 5696, 5706, 5707, 5828, 5831, 5839, 5864, 5865]
second order series method. Regular singular point. Complex roots	24	87.50% [4741, 4742, 4743]	100.00%
second_order_ode_high_degree	1	100.00%	100.00%
Higher order linear constant coefficients ODE	322	99.07% [9123, 9126, 9155]	100.00%
Higher order ODE, non constant coefficients of type Euler	45	100.00%	100.00%
higher_order_laplace	9	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

(691) [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, 2876, 2888, 2955, 3131, 3134, 3165, 3168, 3220, 3268, 3275, 3335, 3503, 3532, 3561, 3570, 3638, 3708, 3741, 3743, 3744, 3745, 3752, 3753, 3758, 3766, 3767, 3770, 3779, 3782, 3786, 3791, 3797, 3807, 3878, 3943, 4158, 4159, 4160, 4331, 4332, 4333, 4409, 4443, 4446, 4454, 4487, 4502, 4607, 4741, 4742, 4743, 5008, 5060, 5064, 5065, 5347, 5351, 5358, 5416, 5430, 5432, 5444, 5493, 5501, 5509, 5511, 5590, 5591, 5789, 5790, 5796, 5828, 6054, 6058, 6060, 6062, 6070, 6086, 6087, 6103, 6105, 6121, 6125, 6310, 6343, 6349, 6354, 6355, 6357, 6377, 6425, 6426, 6429, 6430, 6434, 6436, 6459, 6461, 6464, 6500, 6501, 6535, 6563, 6592, 6655, 6706, 6798, 6800, 7186, 7220, 7222, 7628, 7629, 7630, 7631, 7636, 7637, 7655, 7660, 7663, 7668, 7691, 7701, 7782, 7783, 7785, 7786, 7799, 7814, 7817, 7830, 7833, 7845, 7849, 7911, 7920, 7947, 7950, 7963, 7975, 8010, 8040, 8041, 8060, 8062, 8069, 8083, 8086, 8087, 8090, 8111, 8152, 8155, 8156, 8415, 8417, 8442, 8465, 8474, 8595, 8599, 8606, 8608, 8610, 8611, 8612, 8618, 8652, 8653, 8654, 8655, 8656, 8657, 8661, 8662, 8663, 8679, 8706, 8737, 8785, 8792, 8796, 8816, 8858, 8885, 8902, 8941, 8987, 8998, 9018, 9019, 9020, 9022, 9023, 9036, 9037, 9038, 9039, 9040, 9041, 9042, 9052, 9053, 9055, 9063, 9068, 9079, 9094, 9095, 9110, 9119, 9120, 9121, 9122, 9123, 9126, 9131, 9151, 9155, 9160, 9165, 9169, 9172, 9174, 9175, 9177, 9178, 9180, 9182, 9184, 9185, 9187, 9188, 9190, 9191, 9194, 9195, 9196, 9197, 9198, 9202, 9203, 9204, 9205, 9206, 9207, 9213, 9215, 9216, 9218, 9221, 9222, 9223, 9224, 9227, 9228, 9237, 9238, 9239, 9241, 9242, 9243, 9244, 9245, 9246, 9251, 9252, 9254, 9256, 9257, 9259, 9263, 9264, 9265, 9269, 9271, 9272, 9274, 9275, 9281, 9283, 9287, 9289, 9292, 9298, 9308, 9311, 9313, 9314, 9316, 9317, 9318, 9321, 9330, 9336, 9340, 9341, 9355, 9356, 9358, 9359, 9367, 9368, 9376, 9380, 9381, 9385, 9386, 9390, 9394, 9395, 9397, 9398, 9399, 9400, 9404, 9406, 9410, 9411, 9415, 9417, 9418, 9419, 9420, 9429, 9430, 9434, 9469, 9484, 9494, 9497, 9498, 9499, 9500, 9501, 9506, 9507, 9508, 9511, 9512, 9513, 9514, 9515, 9516, 9518, 9592, 9596, 9597, 9598, 9603, 9610, 9616, 9618, 9619, 9620, 9641, 9649, 9658, 9662, 9663, 9672, 9689, 9693, 9695, 9696, 9697, 9702, 9709, 9710, 9716, 9717, 9718, 9719, 9720, 9733, 9734, 9735, 9736, 9737, 9738, 9739, 9740, 9741, 9744, 9745, 9753, 9757, 9758, 9760, 9761, 9762, 9763, 9764, 9770, 9771, 9773, 9774, 9775, 9776, 9777, 9782, 9783, 9788, 9789, 9793, 9794, 9795, 9798, 9802, 9803, 9805, 9806, 9811, 9812, 9813, 9814, 9817, 9819, 9820, 9823, 9826, 9828, 9829, 9832, 9835, 9837, 9838, 9841, 9844, 9846, 9847, 9850, 9854, 9855, 9856, 9860, 9861, 9863, 9864, 9866, 9868, 9869, 9870, 9871, 9872, 9873, 9874, 9875, 9877, 9878, 9879, 9880, 9881, 9882, 9883, 9884, 9885, 9886, 9889, 9890, 9893, 9894, 9895, 9896, 9897, 9898, 9899, 9900, 9901, 9902, 9903, 9904, 9905, 9906, 9910, 9911, 9912, 9914, 9915, 9916, 9918, 9919, 9921, 9923, 9924, 9926, 9927, 9928, 9930, 9931, 9933, 9934, 9935, 9936, 9937, 9940, 9941, 9942, 9943, 9944, 9945, 9946, 9947, 9948, 9949, 9953, 9954, 9955, 9956, 9957, 9958, 9959, 9961, 9962, 9963, 9964, 9965, 9966, 9967, 9968, 9969, 9970, 9971, 9972, 9973, 9974, 9975, 9976, 9977, 9978, 9979, 9980, 9981, 9982, 9987, 9988, 9990, 9991, 9992, 9993, 9994, 9995, 9997, 9998, 10002, 10004, 10005, 10006, 10007, 10008, 10009, 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, 10059, 10060, 10061, 10062, 10064, 10065, 10067, 10068, 10069, 10070, 10071, 10072, 10073, 10074, 10076, 10077, 10079, 10080, 10081, 10089, 10090, 10097, 10098, 10184, 10198, 10201, 10204, 10205, 10210, 10212, 10226, 10296, 10297, 10315, 10317]

Not solved by Maple

(562) [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, 2874, 2876, 2887, 2955, 3134, 3165, 3168, 3220, 3268, 3275, 3335, 3364, 3418, 3472, 3487, 3503, 3532, 3638, 3642, 3655, 3690, 3691, 3702, 3708, 3779, 3790, 3807, 3845, 3878, 4193, 4206, 4210, 4214, 4215, 4406, 4409, 4443, 4446, 4454, 4487, 4495, 4502, 4709, 4747, 4748, 4749, 4768, 4773, 4803, 4811, 4835, 4836, 4837, 5064, 5065, 5289, 5351, 5358, 5416, 5430, 5432, 5485, 5509, 5511, 5665, 5688, 5690, 5696, 5706, 5707, 5760, 5789, 5790, 5796, 5828, 5831, 5839, 5864, 5865, 5963, 5966, 6067, 6086, 6087, 6310, 6354, 6357, 6370, 6426, 6434, 6436, 6461, 6471, 6472, 6473, 6477, 6478, 6480, 6488, 6500, 6535, 6547, 6548, 6550, 6551, 6552, 6553, 6554, 6563, 6592, 6655, 7628, 7629, 7630, 7631, 7636, 7637, 7655, 7660, 7663, 7668, 7691, 7701, 7782, 7783, 7785, 7786, 7799, 7814, 7817, 7830, 7833, 7845, 7849, 7920, 7932, 7947, 7948, 7950, 7963, 7975, 8028, 8032, 8040, 8041, 8060, 8062, 8065, 8083, 8086, 8087, 8090, 8111, 8117, 8123, 8140, 8152, 8155, 8156, 8288, 8313, 8369, 8370, 8415, 8417, 8465, 8474, 8492, 8500, 8595, 8599, 8606, 8608, 8610, 8611, 8618, 8652, 8653, 8655, 8656, 8657, 8661, 8737, 8785, 8792, 8796, 8816, 8858, 8987, 9018, 9019, 9020, 9022, 9036, 9037, 9038, 9039, 9040, 9041, 9042, 9052, 9053, 9055, 9063, 9068, 9089, 9094, 9110, 9119, 9120, 9121, 9122, 9160, 9161, 9165, 9169, 9172, 9174, 9175, 9177, 9178, 9180, 9184, 9185, 9187, 9188, 9190, 9191, 9194, 9195, 9196, 9197, 9198, 9202, 9203, 9204, 9205, 9206, 9207, 9213, 9215, 9216, 9218, 9221, 9222, 9223, 9224, 9227, 9228, 9237, 9238, 9239, 9241, 9242, 9243, 9244, 9245, 9246, 9251, 9252, 9254, 9256, 9259, 9261, 9263, 9264, 9265, 9269, 9271, 9272, 9274, 9275, 9277, 9281, 9283, 9284, 9285, 9287, 9288, 9289, 9292, 9298, 9300, 9308, 9311, 9313, 9314, 9316, 9317, 9318, 9321, 9330, 9336, 9340, 9341, 9356, 9367, 9368, 9376, 9380, 9381, 9385, 9386, 9387, 9390, 9394, 9395, 9399, 9400, 9404, 9410, 9411, 9413, 9414, 9415, 9417, 9418, 9419, 9420, 9429, 9430, 9434, 9469, 9484, 9494, 9497, 9498, 9499, 9500, 9501, 9506, 9507, 9508, 9511, 9513, 9514, 9516, 9518, 9596, 9603, 9616, 9618, 9620, 9658, 9662, 9663, 9675, 9683, 9689, 9693, 9695, 9697, 9702, 9718, 9733, 9736, 9737, 9738, 9740, 9744, 9758, 9760, 9771, 9773, 9789, 9802, 9804, 9811, 9819, 9820, 9823, 9828, 9829, 9832, 9837, 9838, 9841, 9846, 9847, 9850, 9854, 9855, 9860, 9861, 9863, 9864, 9866, 9868, 9869, 9870, 9871, 9872, 9873, 9874, 9875, 9877, 9880, 9881, 9882, 9883, 9885, 9889, 9893, 9894, 9895, 9896, 9897, 9898, 9899, 9900, 9901, 9902, 9903, 9904, 9905, 9906, 9912, 9916, 9918, 9921, 9926, 9927, 9933, 9934, 9935, 9937, 9944, 9945, 9947, 9948, 9949, 9954, 9956, 9957, 9961, 9962, 9965, 9966, 9967, 9968, 9969, 9970, 9972, 9973, 9974, 9975, 9976, 9977, 9978, 9979, 9980, 9981, 9982, 9990, 9991, 9992, 9993, 9994, 9998, 10004, 10005, 10006, 10007, 10008, 10012, 10014, 10015, 10016, 10017, 10018, 10020, 10021, 10023, 10024, 10026, 10027, 10028, 10029, 10031, 10032, 10034, 10035, 10036, 10038, 10039, 10040, 10041, 10042, 10043, 10044, 10048, 10049, 10051, 10052, 10054, 10055, 10056, 10057, 10058, 10059, 10062, 10065, 10069, 10070, 10072, 10073, 10074, 10077, 10079, 10080, 10184, 10210, 10216, 10315]

Solved by Maple but not by Mathematica

(228) [119, 146, 885, 944, 1041, 1069, 1105, 1138, 1698, 1897, 2491, 2513, 2628, 2720, 2722, 2723, 2727, 2795, 2888, 3131, 3561, 3570, 3741, 3743, 3744, 3745, 3752, 3753, 3758, 3766, 3767, 3770, 3782, 3786, 3791, 3797, 3943, 4158, 4159, 4160, 4331, 4332, 4333, 4607, 4741, 4742, 4743, 5008, 5060, 5347, 5444, 5493, 5501, 5590, 5591, 6054, 6058, 6060, 6062, 6070, 6103, 6105, 6121, 6125, 6343, 6349, 6355, 6377, 6425, 6429, 6430, 6459, 6464, 6501, 6706, 6798, 6800, 7186, 7220, 7222, 7911, 8010, 8069, 8442, 8612, 8654, 8662, 8663, 8679, 8706, 8885, 8902, 8941, 8998, 9023, 9079, 9095, 9123, 9126, 9131, 9151, 9155, 9182, 9257, 9355, 9358, 9359, 9397, 9398, 9406, 9512, 9515, 9592, 9597, 9598, 9610, 9619, 9641, 9649, 9672, 9696, 9709, 9710, 9716, 9717, 9719, 9720, 9734, 9735, 9739, 9741, 9745, 9753, 9757, 9761, 9762, 9763, 9764, 9770, 9774, 9775, 9776, 9777, 9782, 9783, 9788, 9793, 9794, 9795, 9798, 9803, 9805, 9806, 9812, 9813, 9814, 9817, 9826, 9835, 9844, 9856, 9878, 9879, 9884, 9886, 9890, 9910, 9911, 9914, 9915, 9919, 9923, 9924, 9928, 9930, 9931, 9936, 9940, 9941, 9942, 9943, 9946, 9953, 9955, 9958, 9959, 9963, 9964, 9971, 9987, 9988, 9995, 9997, 10002, 10009, 10013, 10019, 10022, 10025, 10030, 10033, 10037, 10045, 10046, 10047, 10050, 10053, 10060, 10061, 10064, 10067, 10068, 10071, 10076, 10081, 10089, 10090, 10097, 10098, 10198, 10201, 10204, 10205, 10212, 10226, 10296, 10297, 10317]

Solved by Mathematica but not by Maple

(99) [408, 409, 1794, 1797, 1805, 2032, 2411, 2581, 2874, 2887, 3364, 3418, 3472, 3487, 3642, 3655, 3690, 3691, 3702, 3790, 3845, 4193, 4206, 4210, 4214, 4215, 4406, 4495, 4709, 4747, 4748, 4749, 4768, 4773, 4803, 4811, 4835, 4836, 4837, 5289, 5485, 5665, 5688, 5690, 5696, 5706, 5707, 5760, 5831, 5839, 5864, 5865, 5963, 5966, 6067, 6370, 6471, 6472, 6473, 6477, 6478, 6480, 6488, 6547, 6548, 6550, 6551, 6552, 6553, 6554, 7932, 7948, 8028, 8032, 8065, 8117, 8123, 8140, 8288, 8313, 8369, 8370, 8492, 8500, 9089, 9161, 9261, 9277, 9284, 9285, 9288, 9300, 9387, 9413, 9414, 9675, 9683, 9804, 10216]

Both systems unable to solve

(463) [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, 2876, 2955, 3134, 3165, 3168, 3220, 3268, 3275, 3335, 3503, 3532, 3638, 3708, 3779, 3807, 3878, 4409, 4443, 4446, 4454, 4487, 4502, 5064, 5065, 5351, 5358, 5416, 5430, 5432, 5509, 5511, 5789, 5790, 5796, 5828, 6086, 6087, 6310, 6354, 6357, 6426, 6434, 6436, 6461, 6500, 6535, 6563, 6592, 6655, 7628, 7629, 7630, 7631, 7636, 7637, 7655, 7660, 7663, 7668, 7691, 7701, 7782, 7783, 7785, 7786, 7799, 7814, 7817, 7830, 7833, 7845, 7849, 7920, 7947, 7950, 7963, 7975, 8040, 8041, 8060, 8062, 8083, 8086, 8087, 8090, 8111, 8152, 8155, 8156, 8415, 8417, 8465, 8474, 8595, 8599, 8606, 8608, 8610, 8611, 8618, 8652, 8653, 8655, 8656, 8657, 8661, 8737, 8785, 8792, 8796, 8816, 8858, 8987, 9018, 9019, 9020, 9022, 9036, 9037, 9038, 9039, 9040, 9041, 9042, 9052, 9053, 9055, 9063, 9068, 9094, 9110, 9119, 9120, 9121, 9122, 9160, 9165, 9169, 9172, 9174, 9175, 9177, 9178, 9180, 9184, 9185, 9187, 9188, 9190, 9191, 9194, 9195, 9196, 9197, 9198, 9202, 9203, 9204, 9205, 9206, 9207, 9213, 9215, 9216, 9218, 9221, 9222, 9223, 9224, 9227, 9228, 9237, 9238, 9239, 9241, 9242, 9243, 9244, 9245, 9246, 9251, 9252, 9254, 9256, 9259, 9263, 9264, 9265, 9269, 9271, 9272, 9274, 9275, 9281, 9283, 9287, 9289, 9292, 9298, 9308, 9311, 9313, 9314, 9316, 9317, 9318, 9321, 9330, 9336, 9340, 9341, 9356, 9367, 9368, 9376, 9380, 9381, 9385, 9386, 9390, 9394, 9395, 9399, 9400, 9404, 9410, 9411, 9415, 9417, 9418, 9419, 9420, 9429, 9430, 9434, 9469, 9484, 9494, 9497, 9498, 9499, 9500, 9501, 9506, 9507, 9508, 9511, 9513, 9514, 9516, 9518, 9596, 9603, 9616, 9618, 9620, 9658, 9662, 9663, 9689, 9693, 9695, 9697, 9702, 9718, 9733, 9736, 9737, 9738, 9740, 9744, 9758, 9760, 9771, 9773, 9789, 9802, 9811, 9819, 9820, 9823, 9828, 9829, 9832, 9837, 9838, 9841, 9846, 9847, 9850, 9854, 9855, 9860, 9861, 9863, 9864, 9866, 9868, 9869, 9870, 9871, 9872, 9873, 9874, 9875, 9877, 9880, 9881, 9882, 9883, 9885, 9889, 9893, 9894, 9895, 9896, 9897, 9898, 9899, 9900, 9901, 9902, 9903, 9904, 9905, 9906, 9912, 9916, 9918, 9921, 9926, 9927, 9933, 9934, 9935, 9937, 9944, 9945, 9947, 9948, 9949, 9954, 9956, 9957, 9961, 9962, 9965, 9966, 9967, 9968, 9969, 9970, 9972, 9973, 9974, 9975, 9976, 9977, 9978, 9979, 9980, 9981, 9982, 9990, 9991, 9992, 9993, 9994, 9998, 10004, 10005, 10006, 10007, 10008, 10012, 10014, 10015, 10016, 10017, 10018, 10020, 10021, 10023, 10024, 10026, 10027, 10028, 10029, 10031, 10032, 10034, 10035, 10036, 10038, 10039, 10040, 10041, 10042, 10043, 10044, 10048, 10049, 10051, 10052, 10054, 10055, 10056, 10057, 10058, 10059, 10062, 10065, 10069, 10070, 10072, 10073, 10074, 10077, 10079, 10080, 10184, 10210, 10315]