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 [13784]. 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, Simplify is next called. If this 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 2023.2.1	95.089	13107	677
Mathematica 14	93.979	12954	830

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 2023.2.1	0.119	276.23	27.412	3807490
Mathematica 14	3.401	238.27	781.250	3284309

The problem which Mathematica produced largest leaf size of \(413606\) is 9727.

The problem which Maple produced largest leaf size of \(949416\) is 12068.

The problem which Mathematica used most CPU time of \(175.525\) seconds is 6197.

The problem which Maple used most CPU time of \(134.110\) seconds is 6839.

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]	806	98.26% [885, 4266, 4275, 11807, 11809, 12590, 12591, 12594, 12615, 12616, 12642, 12645, 12646, 12647]	99.75% [7303, 11674]
[[_linear, ‘class A‘]]	239	100.00%	98.74% [7300, 7301, 11528]
[_separable]	1087	99.26% [944, 2366, 3022, 6264, 8667, 11391, 11425, 13814]	99.45% [408, 409, 6264, 6418, 11425, 13814]
[_Riccati]	317	66.88% [958, 1697, 1698, 1700, 1701, 1702, 2707, 3304, 3324, 3326, 3339, 3639, 4386, 7345, 8447, 10349, 10356, 10369, 10373, 10425, 10442, 10446, 10450, 10455, 10462, 10471, 10486, 10489, 10490, 10491, 10493, 10497, 10511, 10513, 10514, 10515, 10524, 10526, 10527, 10542, 10546, 10548, 10551, 10555, 10559, 10564, 10565, 10566, 10567, 10570, 10572, 10573, 10576, 10579, 10581, 10582, 10585, 10588, 10590, 10591, 10594, 10597, 10599, 10600, 10603, 10607, 10608, 10609, 10613, 10614, 10617, 10619, 10621, 10622, 10623, 10624, 10625, 10626, 10627, 10628, 10630, 10631, 10632, 10633, 10634, 10635, 10636, 10637, 10638, 10639, 10642, 10646, 10647, 10648, 10649, 10650, 10651, 10652, 10653, 10654, 10655, 10656, 10657, 10658, 10659]	72.24% [958, 1697, 1700, 1701, 1702, 2707, 3324, 3326, 3339, 4386, 7345, 8447, 10349, 10356, 10369, 10371, 10373, 10428, 10436, 10442, 10446, 10448, 10450, 10455, 10471, 10479, 10486, 10489, 10490, 10491, 10493, 10497, 10511, 10513, 10524, 10526, 10542, 10555, 10557, 10564, 10572, 10573, 10576, 10581, 10582, 10585, 10590, 10591, 10594, 10599, 10600, 10603, 10607, 10608, 10613, 10614, 10616, 10617, 10619, 10621, 10622, 10623, 10624, 10625, 10626, 10627, 10628, 10630, 10633, 10634, 10635, 10636, 10638, 10642, 10646, 10647, 10648, 10649, 10650, 10651, 10652, 10653, 10654, 10655, 10656, 10657, 10658, 10659]
[[_homogeneous, ‘class G‘]]	63	95.24% [3232, 3236, 11828]	93.65% [3995, 4040, 8704, 8719]
[_linear]	616	99.19% [2006, 6169, 11675, 12384, 13807]	99.19% [2006, 5502, 6169, 12384, 13807]
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	25	100.00%	100.00%
[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	90	100.00%	100.00%
[[_homogeneous, ‘class A‘], _dAlembert]	134	99.25% [11222]	100.00%
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	89	98.88% [6254]	100.00%
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	54	100.00%	100.00%
[[_homogeneous, ‘class A‘], _rational, _dAlembert]	215	99.07% [2085, 5761]	100.00%
[[_homogeneous, ‘class C‘], _dAlembert]	73	93.15% [3000, 4260, 4278, 7102, 11250]	100.00%
[[_homogeneous, ‘class C‘], _Riccati]	22	100.00%	100.00%
[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	69	100.00%	100.00%
[_Bernoulli]	103	97.09% [2012, 5115, 7130]	100.00%
[[_1st_order, _with_linear_symmetries], _Bernoulli]	9	100.00%	100.00%
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	46	100.00%	100.00%
[‘y=_G(x,y’)‘]	138	61.59% [133, 485, 959, 961, 962, 964, 966, 968, 1703, 1706, 1707, 2026, 2316, 2368, 2371, 3363, 3368, 3384, 3463, 4011, 4216, 4261, 4287, 4299, 4951, 4995, 6549, 7063, 7253, 8411, 8416, 8419, 8457, 8706, 8731, 8795, 8796, 8838, 8841, 8845, 8866, 9197, 11229, 11234, 11414, 11894, 11900, 11919, 12316, 12969, 13028, 13726, 13813]	58.70% [133, 485, 959, 961, 962, 964, 966, 968, 1703, 1706, 1707, 2026, 2063, 2316, 3090, 3363, 3368, 3382, 3384, 3395, 3463, 3872, 4011, 4216, 4287, 4298, 4914, 4951, 4995, 6549, 7063, 7253, 8411, 8416, 8419, 8457, 8706, 8731, 8787, 8795, 8796, 8838, 8841, 8845, 8848, 8866, 8878, 11234, 11414, 11894, 11898, 11900, 11919, 12316, 12969, 13028, 13813]
[[_1st_order, _with_linear_symmetries]]	99	91.92% [3229, 3231, 4290, 4294, 5346, 6797, 6807, 11225]	98.99% [8872]
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	32	100.00%	100.00%
[_exact, _rational]	37	97.30% [119]	97.30% [11616]
[_exact]	79	98.73% [3137]	100.00%
[[_1st_order, _with_linear_symmetries], _exact, _rational]	4	100.00%	100.00%
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	4	100.00%	100.00%
[[_homogeneous, ‘class G‘], _exact, _rational]	8	75.00% [146, 11620]	100.00%
[[_2nd_order, _missing_x]]	652	96.63% [2307, 2377, 7411, 9943, 9944, 9945, 9947, 9948, 9950, 9968, 9969, 9971, 9976, 9994, 10040, 10042, 10165, 10168, 11599, 11600, 12250, 12251]	97.09% [7411, 9943, 9944, 9947, 9948, 9950, 9968, 9969, 9971, 9976, 9994, 10040, 10041, 10042, 10168, 11599, 11600, 12250, 12251]
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	93	96.77% [12294, 13249, 13250]	96.77% [12294, 13249, 13250]
[[_Emden, _Fowler]]	306	99.67% [6344]	97.06% [2541, 4718, 5217, 5556, 5588, 5589, 6584, 6617, 12086]
[[_2nd_order, _exact, _linear, _homogeneous]]	216	99.54% [11938]	98.15% [5590, 6460, 6618, 12087]
[[_2nd_order, _missing_y]]	146	96.58% [6856, 6858, 7212, 10159, 11341]	98.63% [6443, 7305]
[[_2nd_order, _with_linear_symmetries]]	2683	94.04% [1105, 1138, 2380, 5010, 5494, 5495, 5496, 5813, 5818, 6343, 6581, 7096, 7178, 7179, 7182, 7183, 7187, 7189, 7288, 7554, 7556, 7942, 7976, 7978, 9354, 9361, 9363, 9365, 9366, 9367, 9373, 9407, 9408, 9410, 9412, 9416, 9417, 9418, 9434, 9461, 9492, 9540, 9547, 9551, 9571, 9613, 9640, 9696, 9726, 9736, 9742, 9753, 9768, 9773, 9774, 9775, 9777, 9937, 9980, 9990, 9991, 9992, 9995, 9997, 9998, 9999, 10004, 10005, 10009, 10010, 10012, 10014, 10016, 10051, 10074, 10094, 10109, 10111, 10112, 10143, 10150, 10151, 10152, 10163, 10164, 10843, 10851, 10866, 10871, 10882, 10884, 10885, 10886, 10887, 10888, 10891, 10892, 10893, 10894, 10902, 10912, 10918, 10925, 10931, 10932, 10934, 10935, 10936, 10937, 10938, 10953, 10955, 10956, 10976, 10977, 10978, 10982, 11022, 11035, 11039, 11042, 11046, 11049, 11062, 11065, 11066, 11075, 11076, 11077, 11078, 11079, 11080, 11081, 11082, 11083, 11088, 11089, 11091, 11092, 11094, 11095, 11096, 11097, 11105, 11110, 11113, 11128, 11129, 11131, 11320, 11321, 11339, 11730, 11929, 11930, 11932, 11944, 12092, 13730, 13801]	95.53% [1794, 1797, 1805, 2400, 2920, 4701, 4714, 5003, 5010, 5521, 5526, 5564, 5818, 6042, 6441, 6449, 6581, 6592, 7179, 7187, 7189, 7288, 9354, 9361, 9363, 9365, 9366, 9373, 9407, 9408, 9410, 9412, 9416, 9492, 9540, 9547, 9551, 9571, 9613, 9742, 9773, 9774, 9775, 9777, 9937, 9980, 9990, 9991, 9992, 9995, 9997, 9998, 9999, 10004, 10005, 10009, 10012, 10014, 10016, 10051, 10074, 10094, 10109, 10152, 10163, 10164, 10166, 10866, 10882, 10884, 10886, 10887, 10892, 10893, 10894, 10925, 10931, 10932, 10935, 10936, 10937, 10938, 10956, 10977, 10978, 10982, 11022, 11032, 11033, 11034, 11037, 11042, 11044, 11049, 11065, 11066, 11075, 11076, 11080, 11081, 11082, 11083, 11091, 11092, 11094, 11097, 11114, 11119, 11121, 11126, 11127, 11128, 11131, 11339, 11730, 11932, 11944, 12092, 13730, 13801]
[[_2nd_order, _linear, _nonhomogeneous]]	897	98.66% [1162, 1186, 7462, 9411, 11485, 11928, 11931, 11961, 12032, 12034, 12428, 12429]	97.44% [1162, 1186, 4722, 4723, 5500, 5501, 6513, 7224, 7225, 7226, 7230, 7231, 7233, 7241, 7306, 7307, 9411, 11928, 11931, 11961, 12032, 12034, 12429]
[[_2nd_order, _exact, _linear, _nonhomogeneous]]	59	100.00%	100.00%
system of linear ODEs	737	96.34% [6104, 6542, 6543, 10222, 10237, 10247, 10250, 10251, 10252, 10253, 10254, 10259, 10260, 10261, 10264, 10265, 10266, 10267, 10268, 10269, 10271, 12507, 12508, 12509, 12510, 12522, 13723]	96.61% [6104, 6542, 6543, 6719, 10222, 10237, 10247, 10250, 10251, 10252, 10253, 10254, 10259, 10260, 10264, 10266, 10267, 10269, 10271, 12507, 12508, 12509, 12510, 12522, 13723]
[_Gegenbauer]	74	100.00%	100.00%
[[_high_order, _missing_x]]	168	98.21% [9876, 9879, 9908]	100.00%
[[_3rd_order, _missing_x]]	153	100.00%	100.00%
[[_3rd_order, _missing_y]]	68	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)]‘]]	71	90.14% [9409, 9657, 9778, 10850, 10943, 11040, 11084]	97.18% [6459, 11098]
[_Lienard]	54	100.00%	100.00%
[[_homogeneous, ‘class A‘], _rational, _Riccati]	28	100.00%	100.00%
[‘x=_G(y,y’)‘]	13	61.54% [550, 2713, 6183, 8907, 12714]	61.54% [550, 2713, 6183, 8907, 12714]
[[_Abel, ‘2nd type‘, ‘class B‘]]	15	26.67% [553, 1046, 8586, 10677, 10680, 10700, 10701, 10702, 10722, 10735, 10740]	40.00% [553, 1046, 8586, 10680, 10700, 10701, 10702, 10722, 10735]
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]]	11	100.00%	100.00%
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	26	96.15% [2031]	100.00%
[[_homogeneous, ‘class D‘], _rational]	3	100.00%	100.00%
[[_1st_order, _with_exponential_symmetries]]	6	100.00%	100.00%
[_rational]	108	82.41% [1039, 1075, 1953, 2319, 3118, 3192, 3193, 4146, 4315, 6111, 8815, 8817, 8824, 9220, 9229, 11208, 11614, 13781, 13806]	75.93% [1039, 1075, 1953, 2319, 3118, 3192, 3193, 3926, 4146, 4198, 4199, 4315, 6111, 8815, 8817, 9043, 9220, 9229, 9247, 9255, 11208, 11240, 11614, 12101, 13781, 13806]
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	133	27.07% [1069, 2990, 3092, 3776, 3783, 6185, 7316, 8570, 8573, 8589, 8601, 10663, 10664, 10671, 10672, 10674, 10676, 10679, 10681, 10683, 10684, 10686, 10687, 10688, 10689, 10690, 10693, 10694, 10695, 10697, 10698, 10699, 10706, 10707, 10708, 10709, 10710, 10711, 10714, 10715, 10716, 10717, 10718, 10719, 10720, 10721, 10723, 10724, 10725, 10726, 10727, 10728, 10729, 10741, 10758, 10759, 10762, 10765, 10766, 10767, 10768, 10769, 10770, 10771, 10772, 10774, 10775, 10776, 10777, 10778, 10779, 10780, 10781, 10782, 10783, 10784, 10785, 10786, 10787, 10788, 10789, 10790, 10791, 10792, 10793, 10794, 10795, 10796, 10797, 10798, 10799, 10800, 10801, 10802, 10803, 10833, 10834]	51.88% [2990, 3092, 3776, 3783, 6185, 7316, 8570, 8573, 8589, 8601, 10671, 10674, 10679, 10686, 10687, 10688, 10690, 10697, 10698, 10707, 10709, 10710, 10714, 10715, 10718, 10719, 10720, 10721, 10723, 10725, 10726, 10727, 10728, 10729, 10758, 10759, 10765, 10767, 10768, 10769, 10770, 10771, 10774, 10776, 10777, 10779, 10780, 10781, 10782, 10784, 10785, 10787, 10788, 10789, 10791, 10792, 10793, 10794, 10795, 10796, 10797, 10801, 10802, 10833]
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]]	4	100.00%	100.00%
[NONE]	84	34.52% [710, 1041, 2378, 2379, 7110, 7214, 8393, 8424, 8538, 8703, 8910, 8911, 9170, 9172, 9927, 9930, 9931, 9935, 9938, 9940, 9941, 9949, 9951, 9955, 9956, 9957, 9960, 9966, 9974, 9975, 9977, 9981, 10007, 10017, 10025, 10034, 10036, 10061, 10064, 10066, 10067, 10070, 10071, 10083, 10089, 10121, 10133, 10134, 10147, 10183, 11918, 11921, 11923, 13209, 13731]	33.33% [710, 6238, 7110, 7214, 8393, 8424, 8538, 8703, 8910, 8911, 9170, 9172, 9927, 9930, 9931, 9938, 9940, 9941, 9949, 9951, 9955, 9956, 9957, 9960, 9966, 9974, 9975, 9977, 9981, 10007, 10017, 10025, 10030, 10034, 10036, 10037, 10038, 10053, 10061, 10064, 10066, 10067, 10070, 10071, 10083, 10089, 10121, 10133, 10134, 10147, 10183, 11918, 11921, 11923, 13209, 13731]
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	26	100.00%	96.15% [1984]
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	55	98.18% [2083]	100.00%
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	18	100.00%	100.00%
[[_high_order, _with_linear_symmetries]]	47	85.11% [813, 9872, 9873, 9874, 9875, 9904, 9922]	85.11% [813, 9872, 9873, 9874, 9875, 9914, 9922]
[[_3rd_order, _with_linear_symmetries]]	132	84.85% [5817, 9791, 9792, 9793, 9794, 9795, 9796, 9797, 9807, 9808, 9810, 9818, 9823, 9834, 9847, 9848, 9863, 12463, 13239, 13541]	87.12% [5817, 9791, 9792, 9793, 9794, 9795, 9796, 9797, 9807, 9808, 9810, 9818, 9823, 9842, 9847, 9863, 13239]
[[_high_order, _linear, _nonhomogeneous]]	72	97.22% [9884, 9913]	98.61% [9913]
[[_1st_order, _with_linear_symmetries], _Clairaut]	64	98.44% [11236]	100.00%
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	51	100.00%	100.00%
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	76	98.68% [1985]	98.68% [1985]
[[_homogeneous, ‘class C‘], _rational, _Riccati]	5	100.00%	100.00%
[[_Abel, ‘2nd type‘, ‘class A‘]]	34	14.71% [3676, 3728, 4954, 8542, 8555, 10667, 10668, 10732, 10733, 10734, 10743, 10744, 10745, 10746, 10747, 10761, 10807, 10814, 10815, 10817, 10818, 10820, 10821, 10822, 10823, 10824, 10825, 10826, 10827]	35.29% [3676, 3728, 4954, 8542, 8555, 10732, 10733, 10734, 10743, 10744, 10745, 10746, 10747, 10761, 10807, 10815, 10818, 10822, 10823, 10825, 10826, 10827]
[_rational, _Bernoulli]	44	100.00%	100.00%
[[_homogeneous, ‘class A‘]]	7	100.00%	100.00%
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	143	97.90% [1941, 4451, 10829]	99.30% [1938]
[[_homogeneous, ‘class G‘], _rational, _Riccati]	20	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‘]]	5	100.00%	100.00%
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	9	100.00%	100.00%
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]]	4	100.00%	100.00%
[_exact, _Bernoulli]	6	100.00%	100.00%
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli]	9	100.00%	100.00%
[_rational, [_Abel, ‘2nd type‘, ‘class C‘]]	12	83.33% [4917, 4962]	83.33% [4917, 4962]
[[_homogeneous, ‘class G‘], _rational]	90	98.89% [1986]	97.78% [4163, 6820]
[[_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]	102	95.10% [10359, 10402, 10411, 10415, 10416]	97.06% [10411, 10415, 10416]
[[_3rd_order, _linear, _nonhomogeneous]]	75	97.33% [11903, 11907]	100.00%
[[_high_order, _missing_y]]	36	97.22% [9918]	97.22% [9918]
[[_3rd_order, _exact, _linear, _nonhomogeneous]]	6	100.00%	100.00%
[[_high_order, _exact, _linear, _nonhomogeneous]]	7	100.00%	100.00%
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	24	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]]	23	100.00%	100.00%
[_Abel]	30	66.67% [1704, 3352, 8384, 8385, 8386, 8387, 11814, 12311, 12618, 12737]	66.67% [1704, 3352, 8384, 8385, 8386, 8387, 11814, 12311, 12618, 12737]
[_Laguerre]	38	100.00%	100.00%
[_Laguerre, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	4	100.00%	100.00%
[_Bessel]	19	100.00%	100.00%
[_rational, _Abel]	21	95.24% [1897]	100.00%
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]	3	100.00%	100.00%
[[_homogeneous, ‘class D‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	5	100.00%	100.00%
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	8	100.00%	100.00%
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	8	100.00%	100.00%
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	6	100.00%	100.00%
[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	30	100.00%	100.00%
[[_homogeneous, ‘class D‘], _Bernoulli]	4	100.00%	100.00%
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	11	100.00%	100.00%
[[_homogeneous, ‘class A‘], _exact, _dAlembert]	4	100.00%	100.00%
[[_2nd_order, _quadrature]]	51	98.04% [11878]	98.04% [7304]
[[_high_order, _quadrature]]	8	100.00%	100.00%
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	71	90.14% [2308, 2376, 4658, 6100, 6839, 6840, 9923]	98.59% [2376]
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]	21	100.00%	100.00%
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]]	7	100.00%	100.00%
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	16	62.50% [4668, 4839, 4840, 4841, 13203, 13204]	100.00%
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]	29	89.66% [2304, 7217, 13200]	93.10% [2304, 2309]
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	10	100.00%	100.00%
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	36	97.22% [4666]	97.22% [10140]
[[_2nd_order, _missing_x], [_2nd_order, _with_potential_symmetries], [_2nd_order, _reducible, _mu_xy]]	4	100.00%	100.00%
[[_homogeneous, ‘class C‘], _rational, _dAlembert]	13	100.00%	100.00%
[_dAlembert]	21	100.00%	100.00%
[[_1st_order, _with_linear_symmetries], _dAlembert]	58	81.03% [2350, 4251, 4252, 4253, 4274, 4305, 6811, 6813, 6874, 6878, 7254]	100.00%
[[_homogeneous, ‘class G‘], _rational, _Clairaut]	9	100.00%	100.00%
[[_homogeneous, ‘class G‘], _Clairaut]	3	100.00%	100.00%
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut]	16	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]	6	100.00%	100.00%
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]]	11	100.00%	100.00%
[[_3rd_order, _exact, _nonlinear]]	3	66.67% [10173]	66.67% [10173]
[_Jacobi]	33	100.00%	100.00%
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]]	6	100.00%	100.00%
[[_3rd_order, _quadrature]]	5	100.00%	100.00%
[[_homogeneous, ‘class G‘], _exact]	2	100.00%	100.00%
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli]	12	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%
[[_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]	26	100.00%	100.00%
[[_homogeneous, ‘class D‘], _rational, _Riccati]	20	100.00%	100.00%
[[_1st_order, _with_linear_symmetries], _exact]	2	100.00%	100.00%
[[_homogeneous, ‘class C‘], _exact, _dAlembert]	4	100.00%	100.00%
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class A‘]]	2	100.00%	100.00%
[[_homogeneous, ‘class D‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	2	100.00%	100.00%
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]]	40	27.50% [3673, 5247, 8539, 8541, 10665, 10669, 10696, 10712, 10730, 10731, 10748, 10750, 10751, 10755, 10757, 10760, 10773, 10804, 10805, 10806, 10808, 10809, 10810, 10811, 10812, 10813, 10830, 10832, 11609]	45.00% [3673, 5247, 8539, 8541, 10665, 10669, 10730, 10731, 10751, 10757, 10760, 10773, 10804, 10805, 10808, 10809, 10810, 10811, 10812, 10830, 10832, 11609]
[[_homogeneous, ‘class G‘], _dAlembert]	5	100.00%	100.00%
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli]	5	100.00%	100.00%
[[_homogeneous, ‘class G‘], _Abel]	4	100.00%	100.00%
[[_homogeneous, ‘class G‘], _Chini]	4	100.00%	100.00%
[_Chini]	3	0.00% [3355, 3642, 8392]	0.00% [3355, 3642, 8392]
[_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 A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]	4	100.00%	100.00%
[_exact, _rational, _Bernoulli]	3	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% [3843, 8605]	71.43% [3843, 8605]
[[_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	66.67% [8676, 10138]	0.00% [3980, 8676, 8688, 10138, 10167, 10487]
[_rational, _dAlembert]	10	90.00% [8766]	100.00%
[[_homogeneous, ‘class G‘], _rational, _dAlembert]	8	100.00%	100.00%
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert]	10	100.00%	100.00%
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	14	100.00%	100.00%
[_Clairaut]	7	100.00%	85.71% [4343]
[[_homogeneous, ‘class D‘], _exact, _rational, _Bernoulli]	1	100.00%	100.00%
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	6	100.00%	100.00%
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]]	10	90.00% [12175]	100.00%
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_xy]]	3	66.67% [6246]	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%
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_y_y1]]	3	100.00%	100.00%
[[_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]]	4	100.00%	100.00%
[[_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]]	3	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% [9068, 9124, 9125]
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]	5	100.00%	100.00%
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_poly_yn]]	3	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_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]]	6	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]]	2	100.00%	100.00%
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]]	12	8.33% [7107, 7108, 9933, 9996, 10018, 10022, 10024, 10027, 10028, 11936, 12930]	25.00% [7107, 9933, 9996, 10018, 10022, 10024, 10027, 10028, 12930]
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]	3	33.33% [9958, 11949]	33.33% [9958, 11949]
[_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]	2	50.00% [9350]	50.00% [9350]
[_ellipsoidal]	2	100.00%	100.00%
[_Jacobi, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	1	100.00%	100.00%
[_Halm]	4	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% [9925]	0.00% [9925]
[[_Painleve, ‘2nd‘]]	1	0.00% [9928]	0.00% [9928]
[[_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	1	0.00% [9959]	0.00% [9959]
[[_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% [10120]	66.67% [10120]
[[_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]	1	0.00% [10045]	0.00% [10045]
[[_Painleve, ‘4th‘]]	1	0.00% [10069]	0.00% [10069]
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_xy]]	3	100.00%	100.00%
[[_Painleve, ‘3rd‘]]	1	0.00% [10093]	0.00% [10093]
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1]]	1	100.00%	100.00%
[[_Painleve, ‘5th‘]]	1	0.00% [10129]	0.00% [10129]
[[_Painleve, ‘6th‘]]	1	0.00% [10139]	0.00% [10139]
[[_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% [10148]	0.00% [10148]
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_poly_yn]]	1	0.00% [10153]	0.00% [10153]
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1]]	1	0.00% [10157]	0.00% [10157]
[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]]	7	28.57% [10170, 10171, 10172, 10187, 13215]	28.57% [10170, 10171, 10172, 10187, 13215]
[[_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]]	4	100.00%	100.00%
[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries]]	2	50.00% [10182]	50.00% [10182]
[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries], [_high_order, _reducible, _mu_poly_yn]]	2	100.00%	100.00%
	82	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%
[_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% [11906, 11920]	0.00% [11906, 11920]
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]	2	100.00%	100.00%
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]	1	100.00%	100.00%
[[_2nd_order, _missing_x], _Duffing, [_2nd_order, _reducible, _mu_x_y1]]	2	100.00%	100.00%
[[_1st_order, _with_exponential_symmetries], _exact]	1	100.00%	100.00%
[[_homogeneous, ‘class C‘], _exact, _rational, _dAlembert]	1	100.00%	100.00%
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_poly_yn]]	2	100.00%	100.00%
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_poly_yn]]	1	100.00%	100.00%
[[_high_order, _exact, _linear, _homogeneous]]	2	100.00%	100.00%
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], [_Abel, ‘2nd type‘, ‘class A‘]]	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 1.5: Percentage solved per own ODE type

Type of ODE	Count	Mathematica	Maple
quadrature	724	98.07% [885, 4266, 4275, 11807, 11809, 12590, 12591, 12594, 12615, 12616, 12642, 12645, 12646, 12647]	99.86% [11674]
linear	69	98.55% [6169]	98.55% [6169]
separable	135	100.00%	100.00%
homogeneous	70	98.57% [5761]	100.00%
homogeneousTypeD2	9	100.00%	100.00%
exact	275	98.91% [119, 146, 3137]	98.91% [3980, 8688, 11616]
exactWithIntegrationFactor	134	99.25% [8676]	97.01% [1984, 2063, 3090, 8676]
exactByInspection	19	100.00%	94.74% [3926]
bernoulli	25	100.00%	100.00%
riccati	470	76.60% [958, 1697, 1698, 1700, 1701, 1702, 2707, 3304, 3324, 3326, 3339, 3639, 4386, 7345, 8447, 10349, 10356, 10359, 10369, 10373, 10402, 10411, 10415, 10416, 10425, 10442, 10446, 10450, 10455, 10462, 10471, 10486, 10489, 10490, 10491, 10493, 10497, 10511, 10513, 10514, 10515, 10524, 10526, 10527, 10542, 10546, 10548, 10551, 10555, 10559, 10564, 10565, 10566, 10567, 10570, 10572, 10573, 10576, 10579, 10581, 10582, 10585, 10588, 10590, 10591, 10594, 10597, 10599, 10600, 10603, 10607, 10608, 10609, 10613, 10614, 10617, 10619, 10621, 10622, 10623, 10624, 10625, 10626, 10627, 10628, 10630, 10631, 10632, 10633, 10634, 10635, 10636, 10637, 10638, 10639, 10642, 10646, 10647, 10648, 10649, 10650, 10651, 10652, 10653, 10654, 10655, 10656, 10657, 10658, 10659]	80.00% [958, 1697, 1700, 1701, 1702, 2707, 3324, 3326, 3339, 4386, 7345, 8447, 9068, 9125, 10349, 10356, 10369, 10371, 10373, 10411, 10415, 10416, 10428, 10436, 10442, 10446, 10448, 10450, 10455, 10471, 10479, 10486, 10487, 10489, 10490, 10491, 10493, 10497, 10511, 10513, 10524, 10526, 10542, 10555, 10557, 10564, 10572, 10573, 10576, 10581, 10582, 10585, 10590, 10591, 10594, 10599, 10600, 10603, 10607, 10608, 10613, 10614, 10616, 10617, 10619, 10621, 10622, 10623, 10624, 10625, 10626, 10627, 10628, 10630, 10633, 10634, 10635, 10636, 10638, 10642, 10646, 10647, 10648, 10649, 10650, 10651, 10652, 10653, 10654, 10655, 10656, 10657, 10658, 10659]
clairaut	101	99.01% [11236]	99.01% [4343]
dAlembert	252	93.25% [2350, 3000, 4251, 4252, 4253, 4260, 4274, 4278, 4305, 6811, 6813, 6874, 6878, 7254, 8766, 11222, 11250]	100.00%
isobaric	13	100.00%	100.00%
polynomial	16	100.00%	100.00%
abelFirstKind	58	82.76% [1704, 1897, 3352, 8384, 8385, 8387, 11814, 12311, 12618, 12737]	84.48% [1704, 3352, 8384, 8385, 8387, 11814, 12311, 12618, 12737]
first order ode series method. Taylor series method	10	70.00% [2366, 2368, 2371]	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, 6418]
first_order_laplace	72	100.00%	100.00%
first_order_ode_lie_symmetry_calculated	338	96.15% [1986, 2083, 3229, 3231, 3232, 3236, 4290, 4294, 5346, 6797, 6807, 11225, 11828]	96.75% [3995, 4040, 4163, 4199, 6820, 8704, 8719, 8872, 9247, 11240, 12101]
system of linear ODEs	714	96.78% [6104, 6542, 6543, 10237, 10247, 10250, 10251, 10252, 10253, 10254, 10264, 10265, 10266, 10267, 10268, 10269, 10271, 12507, 12508, 12509, 12510, 12522, 13723]	96.92% [6104, 6542, 6543, 6719, 10237, 10247, 10250, 10251, 10252, 10253, 10254, 10264, 10266, 10267, 10269, 10271, 12507, 12508, 12509, 12510, 12522, 13723]
second_order_laplace	318	100.00%	99.69% [6513]
reduction_of_order	125	96.80% [1138, 6343, 6344, 11730]	99.20% [11730]
second_order_linear_constant_coeff	2	100.00%	0.00% [7306, 7307]
second_order_airy	15	100.00%	100.00%
exact nonlinear second order ode	7	28.57% [9938, 9940, 9941, 9951, 13731]	28.57% [9938, 9940, 9941, 9951, 13731]
second_order_change_of_variable_on_x_method_1	2	50.00% [9409]	100.00%
second_order_change_of_variable_on_x_method_2	5	100.00%	100.00%
second_order_change_of_variable_on_y_method_2	15	86.67% [9753, 10937]	93.33% [10937]
second_order_change_of_variable_on_y_method_1	3	100.00%	100.00%
second_order_integrable_as_is	11	81.82% [10153, 11949]	81.82% [10153, 11949]
second_order_ode_lagrange_adjoint_equation_method	8	87.50% [10891]	87.50% [11098]
second_order_nonlinear_solved_by_mainardi_lioville_method	14	100.00%	100.00%
second_order_bessel_ode	130	90.77% [7288, 9350, 9640, 9696, 10843, 10902, 10953, 10955, 11046, 11089, 12092, 12428]	97.69% [7288, 9350, 12092]
second_order_bessel_ode_form_A	7	100.00%	100.00%
second_order_ode_missing_x	152	88.16% [2307, 2308, 4666, 9943, 9944, 9945, 9948, 9968, 9969, 9971, 9994, 10040, 10042, 10165, 10168, 12175, 12250, 12251]	90.79% [9943, 9944, 9948, 9968, 9969, 9971, 9994, 10040, 10041, 10042, 10140, 10168, 12250, 12251]
second_order_ode_missing_y	58	86.21% [2304, 6856, 6858, 7212, 7217, 10159, 11341, 13200]	96.55% [2304, 2309]
second order series method. Taylor series method	6	33.33% [2376, 2377, 2378, 2379]	83.33% [2376]
second order series method. Regular singular point. Difference not integer	246	99.59% [2380]	97.56% [7224, 7225, 7226, 7230, 7231, 7233]
second order series method. Regular singular point. Repeated root	198	100.00%	99.49% [7241]
second order series method. Regular singular point. Difference is integer	302	100.00%	99.67% [5501]
second order series method. Irregular singular point	35	94.29% [5010, 6581]	0.00% [1794, 1797, 1805, 2400, 2541, 2920, 4701, 4714, 4718, 4722, 4723, 5003, 5010, 5217, 5500, 5521, 5526, 5556, 5564, 5588, 5589, 5590, 6042, 6441, 6443, 6449, 6459, 6460, 6581, 6584, 6592, 6617, 6618, 12086, 12087]
second order series method. Regular singular point. Complex roots	28	89.29% [5494, 5495, 5496]	100.00%
second_order_ode_high_degree	1	100.00%	100.00%
higher_order_linear_constant_coefficients_ODE	549	99.27% [9876, 9879, 9908, 12463]	100.00%
higher_order_ODE_non_constant_coefficients_of_type_Euler	67	100.00%	100.00%
higher_order_laplace	29	96.55% [13541]	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

(830) [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, 1941, 1953, 1985, 1986, 2006, 2012, 2026, 2031, 2083, 2085, 2304, 2307, 2308, 2316, 2319, 2350, 2366, 2368, 2371, 2376, 2377, 2378, 2379, 2380, 2707, 2713, 2990, 3000, 3022, 3092, 3118, 3137, 3192, 3193, 3229, 3231, 3232, 3236, 3304, 3324, 3326, 3339, 3352, 3355, 3363, 3368, 3384, 3463, 3639, 3642, 3673, 3676, 3728, 3776, 3783, 3843, 4011, 4146, 4216, 4251, 4252, 4253, 4260, 4261, 4266, 4274, 4275, 4278, 4287, 4290, 4294, 4299, 4305, 4315, 4386, 4451, 4658, 4666, 4668, 4839, 4840, 4841, 4917, 4951, 4954, 4962, 4995, 5010, 5115, 5247, 5346, 5494, 5495, 5496, 5761, 5813, 5817, 5818, 6100, 6104, 6111, 6169, 6183, 6185, 6246, 6254, 6264, 6343, 6344, 6542, 6543, 6549, 6581, 6797, 6807, 6811, 6813, 6839, 6840, 6856, 6858, 6874, 6878, 7063, 7096, 7102, 7107, 7108, 7110, 7130, 7178, 7179, 7182, 7183, 7187, 7189, 7212, 7214, 7217, 7253, 7254, 7288, 7316, 7345, 7411, 7462, 7554, 7556, 7942, 7976, 7978, 8384, 8385, 8386, 8387, 8392, 8393, 8411, 8416, 8419, 8424, 8447, 8457, 8538, 8539, 8541, 8542, 8555, 8570, 8573, 8586, 8589, 8601, 8605, 8667, 8676, 8703, 8706, 8731, 8766, 8795, 8796, 8815, 8817, 8824, 8838, 8841, 8845, 8866, 8907, 8910, 8911, 9170, 9172, 9197, 9220, 9229, 9350, 9354, 9361, 9363, 9365, 9366, 9367, 9373, 9407, 9408, 9409, 9410, 9411, 9412, 9416, 9417, 9418, 9434, 9461, 9492, 9540, 9547, 9551, 9571, 9613, 9640, 9657, 9696, 9726, 9736, 9742, 9753, 9768, 9773, 9774, 9775, 9777, 9778, 9791, 9792, 9793, 9794, 9795, 9796, 9797, 9807, 9808, 9810, 9818, 9823, 9834, 9847, 9848, 9863, 9872, 9873, 9874, 9875, 9876, 9879, 9884, 9904, 9908, 9913, 9918, 9922, 9923, 9925, 9927, 9928, 9930, 9931, 9933, 9935, 9937, 9938, 9940, 9941, 9943, 9944, 9945, 9947, 9948, 9949, 9950, 9951, 9955, 9956, 9957, 9958, 9959, 9960, 9966, 9968, 9969, 9971, 9974, 9975, 9976, 9977, 9980, 9981, 9990, 9991, 9992, 9994, 9995, 9996, 9997, 9998, 9999, 10004, 10005, 10007, 10009, 10010, 10012, 10014, 10016, 10017, 10018, 10022, 10024, 10025, 10027, 10028, 10034, 10036, 10040, 10042, 10045, 10051, 10061, 10064, 10066, 10067, 10069, 10070, 10071, 10074, 10083, 10089, 10093, 10094, 10109, 10111, 10112, 10120, 10121, 10129, 10133, 10134, 10138, 10139, 10143, 10147, 10148, 10150, 10151, 10152, 10153, 10157, 10159, 10163, 10164, 10165, 10168, 10170, 10171, 10172, 10173, 10182, 10183, 10187, 10222, 10237, 10247, 10250, 10251, 10252, 10253, 10254, 10259, 10260, 10261, 10264, 10265, 10266, 10267, 10268, 10269, 10271, 10349, 10356, 10359, 10369, 10373, 10402, 10411, 10415, 10416, 10425, 10442, 10446, 10450, 10455, 10462, 10471, 10486, 10489, 10490, 10491, 10493, 10497, 10511, 10513, 10514, 10515, 10524, 10526, 10527, 10542, 10546, 10548, 10551, 10555, 10559, 10564, 10565, 10566, 10567, 10570, 10572, 10573, 10576, 10579, 10581, 10582, 10585, 10588, 10590, 10591, 10594, 10597, 10599, 10600, 10603, 10607, 10608, 10609, 10613, 10614, 10617, 10619, 10621, 10622, 10623, 10624, 10625, 10626, 10627, 10628, 10630, 10631, 10632, 10633, 10634, 10635, 10636, 10637, 10638, 10639, 10642, 10646, 10647, 10648, 10649, 10650, 10651, 10652, 10653, 10654, 10655, 10656, 10657, 10658, 10659, 10663, 10664, 10665, 10667, 10668, 10669, 10671, 10672, 10674, 10676, 10677, 10679, 10680, 10681, 10683, 10684, 10686, 10687, 10688, 10689, 10690, 10693, 10694, 10695, 10696, 10697, 10698, 10699, 10700, 10701, 10702, 10706, 10707, 10708, 10709, 10710, 10711, 10712, 10714, 10715, 10716, 10717, 10718, 10719, 10720, 10721, 10722, 10723, 10724, 10725, 10726, 10727, 10728, 10729, 10730, 10731, 10732, 10733, 10734, 10735, 10740, 10741, 10743, 10744, 10745, 10746, 10747, 10748, 10750, 10751, 10755, 10757, 10758, 10759, 10760, 10761, 10762, 10765, 10766, 10767, 10768, 10769, 10770, 10771, 10772, 10773, 10774, 10775, 10776, 10777, 10778, 10779, 10780, 10781, 10782, 10783, 10784, 10785, 10786, 10787, 10788, 10789, 10790, 10791, 10792, 10793, 10794, 10795, 10796, 10797, 10798, 10799, 10800, 10801, 10802, 10803, 10804, 10805, 10806, 10807, 10808, 10809, 10810, 10811, 10812, 10813, 10814, 10815, 10817, 10818, 10820, 10821, 10822, 10823, 10824, 10825, 10826, 10827, 10829, 10830, 10832, 10833, 10834, 10843, 10850, 10851, 10866, 10871, 10882, 10884, 10885, 10886, 10887, 10888, 10891, 10892, 10893, 10894, 10902, 10912, 10918, 10925, 10931, 10932, 10934, 10935, 10936, 10937, 10938, 10943, 10953, 10955, 10956, 10976, 10977, 10978, 10982, 11022, 11035, 11039, 11040, 11042, 11046, 11049, 11062, 11065, 11066, 11075, 11076, 11077, 11078, 11079, 11080, 11081, 11082, 11083, 11084, 11088, 11089, 11091, 11092, 11094, 11095, 11096, 11097, 11105, 11110, 11113, 11128, 11129, 11131, 11208, 11222, 11225, 11229, 11234, 11236, 11250, 11320, 11321, 11339, 11341, 11391, 11414, 11425, 11485, 11599, 11600, 11609, 11614, 11620, 11675, 11730, 11807, 11809, 11814, 11828, 11878, 11894, 11900, 11903, 11906, 11907, 11918, 11919, 11920, 11921, 11923, 11928, 11929, 11930, 11931, 11932, 11936, 11938, 11944, 11949, 11961, 12032, 12034, 12092, 12175, 12250, 12251, 12294, 12311, 12316, 12384, 12428, 12429, 12463, 12507, 12508, 12509, 12510, 12522, 12590, 12591, 12594, 12615, 12616, 12618, 12642, 12645, 12646, 12647, 12714, 12737, 12930, 12969, 13028, 13200, 13203, 13204, 13209, 13215, 13239, 13249, 13250, 13541, 13723, 13726, 13730, 13731, 13781, 13801, 13806, 13807, 13813, 13814]

Not solved by Maple

(677) [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, 1938, 1953, 1984, 1985, 2006, 2026, 2063, 2304, 2309, 2316, 2319, 2376, 2400, 2541, 2707, 2713, 2920, 2990, 3090, 3092, 3118, 3192, 3193, 3324, 3326, 3339, 3352, 3355, 3363, 3368, 3382, 3384, 3395, 3463, 3642, 3673, 3676, 3728, 3776, 3783, 3843, 3872, 3926, 3980, 3995, 4011, 4040, 4146, 4163, 4198, 4199, 4216, 4287, 4298, 4315, 4343, 4386, 4701, 4714, 4718, 4722, 4723, 4914, 4917, 4951, 4954, 4962, 4995, 5003, 5010, 5217, 5247, 5500, 5501, 5502, 5521, 5526, 5556, 5564, 5588, 5589, 5590, 5817, 5818, 6042, 6104, 6111, 6169, 6183, 6185, 6238, 6264, 6418, 6441, 6443, 6449, 6459, 6460, 6513, 6542, 6543, 6549, 6581, 6584, 6592, 6617, 6618, 6719, 6820, 7063, 7107, 7110, 7179, 7187, 7189, 7214, 7224, 7225, 7226, 7230, 7231, 7233, 7241, 7253, 7288, 7300, 7301, 7303, 7304, 7305, 7306, 7307, 7316, 7345, 7411, 8384, 8385, 8386, 8387, 8392, 8393, 8411, 8416, 8419, 8424, 8447, 8457, 8538, 8539, 8541, 8542, 8555, 8570, 8573, 8586, 8589, 8601, 8605, 8676, 8688, 8703, 8704, 8706, 8719, 8731, 8787, 8795, 8796, 8815, 8817, 8838, 8841, 8845, 8848, 8866, 8872, 8878, 8907, 8910, 8911, 9043, 9068, 9124, 9125, 9170, 9172, 9220, 9229, 9247, 9255, 9350, 9354, 9361, 9363, 9365, 9366, 9373, 9407, 9408, 9410, 9411, 9412, 9416, 9492, 9540, 9547, 9551, 9571, 9613, 9742, 9773, 9774, 9775, 9777, 9791, 9792, 9793, 9794, 9795, 9796, 9797, 9807, 9808, 9810, 9818, 9823, 9842, 9847, 9863, 9872, 9873, 9874, 9875, 9913, 9914, 9918, 9922, 9925, 9927, 9928, 9930, 9931, 9933, 9937, 9938, 9940, 9941, 9943, 9944, 9947, 9948, 9949, 9950, 9951, 9955, 9956, 9957, 9958, 9959, 9960, 9966, 9968, 9969, 9971, 9974, 9975, 9976, 9977, 9980, 9981, 9990, 9991, 9992, 9994, 9995, 9996, 9997, 9998, 9999, 10004, 10005, 10007, 10009, 10012, 10014, 10016, 10017, 10018, 10022, 10024, 10025, 10027, 10028, 10030, 10034, 10036, 10037, 10038, 10040, 10041, 10042, 10045, 10051, 10053, 10061, 10064, 10066, 10067, 10069, 10070, 10071, 10074, 10083, 10089, 10093, 10094, 10109, 10120, 10121, 10129, 10133, 10134, 10138, 10139, 10140, 10147, 10148, 10152, 10153, 10157, 10163, 10164, 10166, 10167, 10168, 10170, 10171, 10172, 10173, 10182, 10183, 10187, 10222, 10237, 10247, 10250, 10251, 10252, 10253, 10254, 10259, 10260, 10264, 10266, 10267, 10269, 10271, 10349, 10356, 10369, 10371, 10373, 10411, 10415, 10416, 10428, 10436, 10442, 10446, 10448, 10450, 10455, 10471, 10479, 10486, 10487, 10489, 10490, 10491, 10493, 10497, 10511, 10513, 10524, 10526, 10542, 10555, 10557, 10564, 10572, 10573, 10576, 10581, 10582, 10585, 10590, 10591, 10594, 10599, 10600, 10603, 10607, 10608, 10613, 10614, 10616, 10617, 10619, 10621, 10622, 10623, 10624, 10625, 10626, 10627, 10628, 10630, 10633, 10634, 10635, 10636, 10638, 10642, 10646, 10647, 10648, 10649, 10650, 10651, 10652, 10653, 10654, 10655, 10656, 10657, 10658, 10659, 10665, 10669, 10671, 10674, 10679, 10680, 10686, 10687, 10688, 10690, 10697, 10698, 10700, 10701, 10702, 10707, 10709, 10710, 10714, 10715, 10718, 10719, 10720, 10721, 10722, 10723, 10725, 10726, 10727, 10728, 10729, 10730, 10731, 10732, 10733, 10734, 10735, 10743, 10744, 10745, 10746, 10747, 10751, 10757, 10758, 10759, 10760, 10761, 10765, 10767, 10768, 10769, 10770, 10771, 10773, 10774, 10776, 10777, 10779, 10780, 10781, 10782, 10784, 10785, 10787, 10788, 10789, 10791, 10792, 10793, 10794, 10795, 10796, 10797, 10801, 10802, 10804, 10805, 10807, 10808, 10809, 10810, 10811, 10812, 10815, 10818, 10822, 10823, 10825, 10826, 10827, 10830, 10832, 10833, 10866, 10882, 10884, 10886, 10887, 10892, 10893, 10894, 10925, 10931, 10932, 10935, 10936, 10937, 10938, 10956, 10977, 10978, 10982, 11022, 11032, 11033, 11034, 11037, 11042, 11044, 11049, 11065, 11066, 11075, 11076, 11080, 11081, 11082, 11083, 11091, 11092, 11094, 11097, 11098, 11114, 11119, 11121, 11126, 11127, 11128, 11131, 11208, 11234, 11240, 11339, 11414, 11425, 11528, 11599, 11600, 11609, 11614, 11616, 11674, 11730, 11814, 11894, 11898, 11900, 11906, 11918, 11919, 11920, 11921, 11923, 11928, 11931, 11932, 11944, 11949, 11961, 12032, 12034, 12086, 12087, 12092, 12101, 12250, 12251, 12294, 12311, 12316, 12384, 12429, 12507, 12508, 12509, 12510, 12522, 12618, 12714, 12737, 12930, 12969, 13028, 13209, 13215, 13239, 13249, 13250, 13723, 13730, 13731, 13781, 13801, 13806, 13807, 13813, 13814]

Solved by Maple but not by Mathematica

(275) [119, 146, 885, 944, 1041, 1069, 1105, 1138, 1698, 1897, 1941, 1986, 2012, 2031, 2083, 2085, 2307, 2308, 2350, 2366, 2368, 2371, 2377, 2378, 2379, 2380, 3000, 3022, 3137, 3229, 3231, 3232, 3236, 3304, 3639, 4251, 4252, 4253, 4260, 4261, 4266, 4274, 4275, 4278, 4290, 4294, 4299, 4305, 4451, 4658, 4666, 4668, 4839, 4840, 4841, 5115, 5346, 5494, 5495, 5496, 5761, 5813, 6100, 6246, 6254, 6343, 6344, 6797, 6807, 6811, 6813, 6839, 6840, 6856, 6858, 6874, 6878, 7096, 7102, 7108, 7130, 7178, 7182, 7183, 7212, 7217, 7254, 7462, 7554, 7556, 7942, 7976, 7978, 8667, 8766, 8824, 9197, 9367, 9409, 9417, 9418, 9434, 9461, 9640, 9657, 9696, 9726, 9736, 9753, 9768, 9778, 9834, 9848, 9876, 9879, 9884, 9904, 9908, 9923, 9935, 9945, 10010, 10111, 10112, 10143, 10150, 10151, 10159, 10165, 10261, 10265, 10268, 10359, 10402, 10425, 10462, 10514, 10515, 10527, 10546, 10548, 10551, 10559, 10565, 10566, 10567, 10570, 10579, 10588, 10597, 10609, 10631, 10632, 10637, 10639, 10663, 10664, 10667, 10668, 10672, 10676, 10677, 10681, 10683, 10684, 10689, 10693, 10694, 10695, 10696, 10699, 10706, 10708, 10711, 10712, 10716, 10717, 10724, 10740, 10741, 10748, 10750, 10755, 10762, 10766, 10772, 10775, 10778, 10783, 10786, 10790, 10798, 10799, 10800, 10803, 10806, 10813, 10814, 10817, 10820, 10821, 10824, 10829, 10834, 10843, 10850, 10851, 10871, 10885, 10888, 10891, 10902, 10912, 10918, 10934, 10943, 10953, 10955, 10976, 11035, 11039, 11040, 11046, 11062, 11077, 11078, 11079, 11084, 11088, 11089, 11095, 11096, 11105, 11110, 11113, 11129, 11222, 11225, 11229, 11236, 11250, 11320, 11321, 11341, 11391, 11485, 11620, 11675, 11807, 11809, 11828, 11878, 11903, 11907, 11929, 11930, 11936, 11938, 12175, 12428, 12463, 12590, 12591, 12594, 12615, 12616, 12642, 12645, 12646, 12647, 13200, 13203, 13204, 13541, 13726]

Solved by Mathematica but not by Maple

(122) [408, 409, 1794, 1797, 1805, 1938, 1984, 2063, 2309, 2400, 2541, 2920, 3090, 3382, 3395, 3872, 3926, 3980, 3995, 4040, 4163, 4198, 4199, 4298, 4343, 4701, 4714, 4718, 4722, 4723, 4914, 5003, 5217, 5500, 5501, 5502, 5521, 5526, 5556, 5564, 5588, 5589, 5590, 6042, 6238, 6418, 6441, 6443, 6449, 6459, 6460, 6513, 6584, 6592, 6617, 6618, 6719, 6820, 7224, 7225, 7226, 7230, 7231, 7233, 7241, 7300, 7301, 7303, 7304, 7305, 7306, 7307, 8688, 8704, 8719, 8787, 8848, 8872, 8878, 9043, 9068, 9124, 9125, 9247, 9255, 9842, 9914, 10030, 10037, 10038, 10041, 10053, 10140, 10166, 10167, 10371, 10428, 10436, 10448, 10479, 10487, 10557, 10616, 11032, 11033, 11034, 11037, 11044, 11098, 11114, 11119, 11121, 11126, 11127, 11240, 11528, 11616, 11674, 11898, 12086, 12087, 12101]

Both systems unable to solve

(555) [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, 1953, 1985, 2006, 2026, 2304, 2316, 2319, 2376, 2707, 2713, 2990, 3092, 3118, 3192, 3193, 3324, 3326, 3339, 3352, 3355, 3363, 3368, 3384, 3463, 3642, 3673, 3676, 3728, 3776, 3783, 3843, 4011, 4146, 4216, 4287, 4315, 4386, 4917, 4951, 4954, 4962, 4995, 5010, 5247, 5817, 5818, 6104, 6111, 6169, 6183, 6185, 6264, 6542, 6543, 6549, 6581, 7063, 7107, 7110, 7179, 7187, 7189, 7214, 7253, 7288, 7316, 7345, 7411, 8384, 8385, 8386, 8387, 8392, 8393, 8411, 8416, 8419, 8424, 8447, 8457, 8538, 8539, 8541, 8542, 8555, 8570, 8573, 8586, 8589, 8601, 8605, 8676, 8703, 8706, 8731, 8795, 8796, 8815, 8817, 8838, 8841, 8845, 8866, 8907, 8910, 8911, 9170, 9172, 9220, 9229, 9350, 9354, 9361, 9363, 9365, 9366, 9373, 9407, 9408, 9410, 9411, 9412, 9416, 9492, 9540, 9547, 9551, 9571, 9613, 9742, 9773, 9774, 9775, 9777, 9791, 9792, 9793, 9794, 9795, 9796, 9797, 9807, 9808, 9810, 9818, 9823, 9847, 9863, 9872, 9873, 9874, 9875, 9913, 9918, 9922, 9925, 9927, 9928, 9930, 9931, 9933, 9937, 9938, 9940, 9941, 9943, 9944, 9947, 9948, 9949, 9950, 9951, 9955, 9956, 9957, 9958, 9959, 9960, 9966, 9968, 9969, 9971, 9974, 9975, 9976, 9977, 9980, 9981, 9990, 9991, 9992, 9994, 9995, 9996, 9997, 9998, 9999, 10004, 10005, 10007, 10009, 10012, 10014, 10016, 10017, 10018, 10022, 10024, 10025, 10027, 10028, 10034, 10036, 10040, 10042, 10045, 10051, 10061, 10064, 10066, 10067, 10069, 10070, 10071, 10074, 10083, 10089, 10093, 10094, 10109, 10120, 10121, 10129, 10133, 10134, 10138, 10139, 10147, 10148, 10152, 10153, 10157, 10163, 10164, 10168, 10170, 10171, 10172, 10173, 10182, 10183, 10187, 10222, 10237, 10247, 10250, 10251, 10252, 10253, 10254, 10259, 10260, 10264, 10266, 10267, 10269, 10271, 10349, 10356, 10369, 10373, 10411, 10415, 10416, 10442, 10446, 10450, 10455, 10471, 10486, 10489, 10490, 10491, 10493, 10497, 10511, 10513, 10524, 10526, 10542, 10555, 10564, 10572, 10573, 10576, 10581, 10582, 10585, 10590, 10591, 10594, 10599, 10600, 10603, 10607, 10608, 10613, 10614, 10617, 10619, 10621, 10622, 10623, 10624, 10625, 10626, 10627, 10628, 10630, 10633, 10634, 10635, 10636, 10638, 10642, 10646, 10647, 10648, 10649, 10650, 10651, 10652, 10653, 10654, 10655, 10656, 10657, 10658, 10659, 10665, 10669, 10671, 10674, 10679, 10680, 10686, 10687, 10688, 10690, 10697, 10698, 10700, 10701, 10702, 10707, 10709, 10710, 10714, 10715, 10718, 10719, 10720, 10721, 10722, 10723, 10725, 10726, 10727, 10728, 10729, 10730, 10731, 10732, 10733, 10734, 10735, 10743, 10744, 10745, 10746, 10747, 10751, 10757, 10758, 10759, 10760, 10761, 10765, 10767, 10768, 10769, 10770, 10771, 10773, 10774, 10776, 10777, 10779, 10780, 10781, 10782, 10784, 10785, 10787, 10788, 10789, 10791, 10792, 10793, 10794, 10795, 10796, 10797, 10801, 10802, 10804, 10805, 10807, 10808, 10809, 10810, 10811, 10812, 10815, 10818, 10822, 10823, 10825, 10826, 10827, 10830, 10832, 10833, 10866, 10882, 10884, 10886, 10887, 10892, 10893, 10894, 10925, 10931, 10932, 10935, 10936, 10937, 10938, 10956, 10977, 10978, 10982, 11022, 11042, 11049, 11065, 11066, 11075, 11076, 11080, 11081, 11082, 11083, 11091, 11092, 11094, 11097, 11128, 11131, 11208, 11234, 11339, 11414, 11425, 11599, 11600, 11609, 11614, 11730, 11814, 11894, 11900, 11906, 11918, 11919, 11920, 11921, 11923, 11928, 11931, 11932, 11944, 11949, 11961, 12032, 12034, 12092, 12250, 12251, 12294, 12311, 12316, 12384, 12429, 12507, 12508, 12509, 12510, 12522, 12618, 12714, 12737, 12930, 12969, 13028, 13209, 13215, 13239, 13249, 13250, 13723, 13730, 13731, 13781, 13801, 13806, 13807, 13813, 13814]