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 [15472].

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 2024	95.489	14774	698
Mathematica 14	94.577	14633	839

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 2024	0.202	147.54	52.009	2282723
Mathematica 14	3.232	221.31	833.444	3424131

The problem which Mathematica produced largest leaf size of \(413606\) is 9721.

The problem which Maple produced largest leaf size of \(949416\) is 12388.

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

The problem which Maple used most CPU time of \(140.984\) 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. Three different classifications of ODE’s are used. The first uses Maple’s own ode advisor classification. The second uses own ODE classification used in my ode solver. The third classification uses a simplified classification of ODE’s which is based on generic type of the ODE.

Performance using Maple’s ODE types classification

This uses ODE classifications based on Maple’s ode advisor 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]	873	98.05% [885, 4266, 4275, 12127, 12129, 12910, 12911, 12914, 12935, 12936, 12962, 12965, 12966, 12967, 14201, 15125, 15126]	99.77% [7303, 11994]
[[_linear, ‘class A‘]]	304	100.00%	99.01% [7300, 7301, 11518]
[_separable]	1196	99.16% [3022, 6264, 8667, 11415, 14980, 14999, 15000, 15001, 15002, 15006]	99.50% [408, 409, 6264, 6418, 11415, 15001]
[_Riccati]	322	67.39% [958, 1697, 1698, 1700, 1701, 1702, 2707, 3304, 3324, 3326, 3339, 3639, 4386, 7345, 8447, 10339, 10346, 10359, 10363, 10415, 10432, 10436, 10440, 10445, 10452, 10461, 10476, 10479, 10480, 10481, 10483, 10487, 10501, 10503, 10504, 10505, 10514, 10516, 10517, 10532, 10536, 10538, 10541, 10545, 10549, 10554, 10555, 10556, 10557, 10560, 10562, 10563, 10566, 10569, 10571, 10572, 10575, 10578, 10580, 10581, 10584, 10587, 10589, 10590, 10593, 10597, 10598, 10599, 10603, 10604, 10607, 10609, 10611, 10612, 10613, 10614, 10615, 10616, 10617, 10618, 10620, 10621, 10622, 10623, 10624, 10625, 10626, 10627, 10628, 10629, 10632, 10636, 10637, 10638, 10639, 10640, 10641, 10642, 10643, 10644, 10645, 10646, 10647, 10648, 10649]	72.98% [958, 1697, 1700, 1701, 1702, 2707, 3324, 3326, 3339, 4386, 7345, 8447, 10339, 10346, 10359, 10361, 10363, 10418, 10426, 10432, 10436, 10438, 10440, 10445, 10461, 10476, 10479, 10480, 10481, 10483, 10487, 10501, 10503, 10514, 10516, 10532, 10545, 10547, 10554, 10562, 10563, 10566, 10571, 10572, 10575, 10580, 10581, 10584, 10589, 10590, 10593, 10597, 10598, 10603, 10604, 10606, 10607, 10609, 10611, 10612, 10613, 10614, 10615, 10616, 10617, 10618, 10620, 10623, 10624, 10625, 10626, 10628, 10632, 10636, 10637, 10638, 10639, 10640, 10641, 10642, 10643, 10644, 10645, 10646, 10647, 10648, 10649]
[[_homogeneous, ‘class G‘]]	70	94.29% [3232, 3236, 12148, 15095]	94.29% [3995, 4040, 8704, 8719]
[_linear]	688	99.56% [6169, 11995, 15046]	99.56% [5502, 6169, 11995]
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	31	100.00%	100.00%
[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	102	99.02% [14378]	100.00%
[[_homogeneous, ‘class A‘], _dAlembert]	150	99.33% [11212]	100.00%
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	96	100.00%	100.00%
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	60	100.00%	100.00%
[[_homogeneous, ‘class A‘], _rational, _dAlembert]	219	98.63% [2085, 5761, 14384]	100.00%
[[_homogeneous, ‘class C‘], _dAlembert]	81	91.36% [3000, 4260, 4278, 7102, 11240, 14439, 15129]	100.00%
[[_homogeneous, ‘class C‘], _Riccati]	24	100.00%	100.00%
[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	75	100.00%	100.00%
[_Bernoulli]	117	100.00%	100.00%
[[_1st_order, _with_linear_symmetries], _Bernoulli]	10	100.00%	100.00%
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	48	100.00%	100.00%
[‘y=_G(x,y’)‘]	145	62.76% [133, 485, 959, 961, 962, 964, 966, 968, 1703, 1706, 1707, 2026, 2316, 2319, 3363, 3368, 3384, 3463, 4011, 4216, 4261, 4287, 4299, 4951, 4995, 6549, 7063, 7253, 8411, 8416, 8419, 8457, 8706, 8731, 8795, 8796, 8841, 8845, 8866, 11219, 11224, 11404, 12214, 12220, 12239, 12636, 13289, 13348, 14046, 14133, 14296, 14313, 14441, 14941]	57.24% [133, 485, 959, 961, 962, 964, 966, 968, 1703, 1706, 1707, 2026, 2063, 2316, 2319, 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, 8841, 8845, 8848, 8866, 8878, 11224, 11404, 12214, 12218, 12220, 12239, 12636, 13289, 13348, 14133, 14296, 14313, 14441, 14941, 15059]
[[_1st_order, _with_linear_symmetries]]	104	91.35% [3229, 3231, 4290, 4294, 5346, 6797, 6807, 11215, 15124]	99.04% [8872]
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	38	97.37% [15074]	100.00%
[_exact, _rational]	43	97.67% [119]	100.00%
[_exact]	98	93.88% [3137, 14323, 14328, 15066, 15067, 15073]	97.96% [14323, 14328]
[[_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]	11	81.82% [146, 11610]	100.00%
[[_2nd_order, _missing_x]]	833	96.52% [2307, 7411, 9934, 9935, 9936, 9938, 9939, 9941, 9959, 9960, 9962, 9967, 9985, 10031, 10033, 10156, 10159, 11589, 11590, 12570, 12571, 14516, 14517, 15204, 15444, 15446, 15449, 15453, 15459]	97.24% [7411, 9934, 9935, 9938, 9939, 9941, 9959, 9960, 9962, 9967, 9985, 10031, 10032, 10033, 10159, 11589, 11590, 12570, 12571, 15444, 15446, 15449, 15453]
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	121	97.52% [12614, 13569, 13570]	97.52% [12614, 13569, 13570]
[[_Emden, _Fowler]]	348	100.00%	97.41% [2541, 4718, 5217, 5556, 5588, 5589, 6584, 6617, 12406]
[[_2nd_order, _exact, _linear, _homogeneous]]	235	99.57% [12258]	98.30% [5590, 6460, 6618, 12407]
[[_2nd_order, _missing_y]]	201	97.51% [6856, 6858, 7212, 10150, 11331]	99.00% [6443, 7305]
[[_2nd_order, _with_linear_symmetries]]	2852	94.71% [1105, 5010, 5813, 5818, 6581, 7178, 7179, 7182, 7183, 7187, 7189, 7288, 7554, 7556, 7976, 7978, 9353, 9360, 9362, 9364, 9365, 9371, 9405, 9406, 9407, 9409, 9413, 9487, 9535, 9542, 9546, 9565, 9607, 9634, 9690, 9720, 9730, 9736, 9747, 9762, 9767, 9768, 9769, 9771, 9928, 9971, 9981, 9982, 9983, 9986, 9988, 9989, 9990, 9995, 9996, 10000, 10001, 10003, 10005, 10007, 10042, 10065, 10085, 10100, 10102, 10103, 10134, 10141, 10142, 10143, 10154, 10155, 10833, 10841, 10856, 10861, 10872, 10874, 10875, 10876, 10877, 10878, 10881, 10882, 10883, 10884, 10892, 10902, 10908, 10915, 10921, 10922, 10924, 10925, 10926, 10927, 10928, 10943, 10945, 10946, 10966, 10967, 10968, 10972, 11012, 11025, 11029, 11032, 11036, 11039, 11052, 11055, 11056, 11065, 11066, 11067, 11068, 11069, 11070, 11071, 11072, 11073, 11078, 11079, 11081, 11082, 11084, 11085, 11086, 11087, 11095, 11100, 11103, 11118, 11119, 11121, 11310, 11311, 11329, 12050, 12249, 12250, 12252, 12264, 12412, 14050, 14121, 14472, 14473, 15382, 15474]	95.58% [1794, 1797, 1805, 2400, 2920, 4701, 4714, 5003, 5010, 5521, 5526, 5564, 5818, 6042, 6441, 6449, 6581, 6592, 7179, 7187, 7189, 7288, 9353, 9360, 9362, 9364, 9365, 9371, 9405, 9406, 9407, 9409, 9413, 9487, 9535, 9542, 9546, 9565, 9607, 9736, 9767, 9768, 9769, 9771, 9928, 9971, 9981, 9982, 9983, 9986, 9988, 9989, 9990, 9995, 9996, 10000, 10003, 10005, 10007, 10042, 10065, 10085, 10100, 10143, 10154, 10155, 10157, 10856, 10872, 10874, 10876, 10877, 10882, 10883, 10884, 10915, 10921, 10922, 10925, 10926, 10927, 10928, 10946, 10967, 10968, 10972, 11012, 11022, 11023, 11024, 11027, 11032, 11034, 11039, 11055, 11056, 11065, 11066, 11070, 11071, 11072, 11073, 11081, 11082, 11084, 11087, 11104, 11109, 11111, 11116, 11117, 11118, 11121, 11329, 11904, 11905, 12050, 12252, 12264, 12412, 14050, 14121, 14472, 14473, 14803, 15432]
[[_2nd_order, _linear, _nonhomogeneous]]	1111	98.47% [1162, 1186, 7462, 9408, 12248, 12251, 12281, 12352, 12354, 12748, 12749, 14633, 14870, 15384, 15385, 15386, 15436]	97.66% [1162, 1186, 4722, 4723, 5500, 5501, 5833, 6513, 7224, 7225, 7226, 7230, 7231, 7233, 7241, 7306, 7307, 9408, 12248, 12251, 12281, 12352, 12354, 12749, 14633, 14870]
[[_2nd_order, _exact, _linear, _nonhomogeneous]]	73	100.00%	100.00%
system of linear ODEs	828	96.50% [6104, 6542, 6543, 10213, 10228, 10238, 10241, 10242, 10243, 10244, 10245, 10250, 10251, 10254, 10255, 10256, 10257, 10258, 10259, 10261, 12827, 12828, 12829, 12830, 12842, 14043, 15506, 15517, 15524]	96.74% [6104, 6542, 6543, 6716, 6719, 10213, 10228, 10238, 10241, 10242, 10243, 10244, 10245, 10250, 10251, 10254, 10256, 10257, 10259, 10261, 12827, 12828, 12829, 12830, 12842, 14043, 15524]
[_Gegenbauer]	77	100.00%	100.00%
[[_high_order, _missing_x]]	216	100.00%	100.00%
[[_3rd_order, _missing_x]]	195	100.00%	100.00%
[[_3rd_order, _missing_y]]	97	100.00%	100.00%
[[_3rd_order, _exact, _linear, _homogeneous]]	15	100.00%	100.00%
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	76	94.74% [10840, 10933, 11030, 11074]	98.68% [6459]
[_Lienard]	59	100.00%	100.00%
[[_homogeneous, ‘class A‘], _rational, _Riccati]	31	100.00%	100.00%
[‘x=_G(y,y’)‘]	13	61.54% [550, 2713, 6183, 8907, 13034]	61.54% [550, 2713, 6183, 8907, 13034]
[[_Abel, ‘2nd type‘, ‘class B‘]]	15	26.67% [553, 1046, 8586, 10667, 10670, 10690, 10691, 10692, 10712, 10725, 10730]	40.00% [553, 1046, 8586, 10670, 10690, 10691, 10692, 10712, 10725]
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]]	12	100.00%	100.00%
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	29	96.55% [2031]	100.00%
[[_homogeneous, ‘class D‘], _rational]	3	100.00%	100.00%
[[_1st_order, _with_exponential_symmetries]]	9	100.00%	100.00%
[_rational]	111	82.88% [1039, 1075, 1953, 3118, 3192, 3193, 4146, 4315, 6111, 8815, 8817, 8824, 8838, 9219, 9228, 11198, 11604, 14101, 14126]	76.58% [1039, 1075, 1953, 3118, 3192, 3193, 3926, 4146, 4198, 4199, 4315, 6111, 8815, 8817, 8820, 8838, 9219, 9228, 9246, 9254, 11198, 11230, 11604, 12421, 14101, 14126]
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	136	28.68% [1069, 2990, 3092, 3776, 3783, 6185, 7316, 8570, 8573, 8589, 8601, 10653, 10654, 10661, 10662, 10664, 10666, 10669, 10671, 10673, 10674, 10676, 10677, 10678, 10679, 10680, 10683, 10684, 10685, 10687, 10688, 10689, 10696, 10697, 10698, 10699, 10700, 10701, 10704, 10705, 10706, 10707, 10708, 10709, 10710, 10711, 10713, 10714, 10715, 10716, 10717, 10718, 10719, 10731, 10748, 10749, 10752, 10755, 10756, 10757, 10758, 10759, 10760, 10761, 10762, 10764, 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, 10823, 10824]	51.47% [2990, 3092, 3776, 3783, 6185, 7316, 8570, 8573, 8589, 8601, 10661, 10664, 10669, 10676, 10677, 10678, 10679, 10680, 10687, 10688, 10697, 10699, 10700, 10704, 10705, 10708, 10709, 10710, 10711, 10713, 10715, 10716, 10717, 10718, 10719, 10748, 10749, 10755, 10757, 10758, 10759, 10760, 10761, 10762, 10764, 10766, 10767, 10769, 10770, 10771, 10772, 10774, 10775, 10777, 10778, 10779, 10781, 10782, 10783, 10784, 10785, 10786, 10787, 10791, 10792, 10823]
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]]	4	100.00%	100.00%
[NONE]	86	37.21% [710, 1041, 7110, 7214, 8393, 8424, 8538, 8703, 8910, 8911, 9170, 9172, 9918, 9921, 9922, 9926, 9929, 9931, 9932, 9940, 9942, 9946, 9947, 9948, 9951, 9957, 9965, 9966, 9968, 9972, 9998, 10008, 10016, 10025, 10027, 10052, 10055, 10057, 10058, 10061, 10062, 10074, 10080, 10112, 10124, 10125, 10138, 10174, 12238, 12241, 12243, 13529, 14051, 14626]	33.72% [710, 6238, 7110, 7214, 8393, 8424, 8538, 8703, 8910, 8911, 9170, 9172, 9918, 9921, 9922, 9929, 9931, 9932, 9940, 9942, 9946, 9947, 9948, 9951, 9957, 9965, 9966, 9968, 9972, 9998, 10008, 10016, 10021, 10025, 10027, 10028, 10029, 10044, 10052, 10055, 10057, 10058, 10061, 10062, 10074, 10080, 10112, 10124, 10125, 10138, 10174, 12238, 12241, 12243, 13529, 14051, 14626]
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	29	100.00%	96.55% [1984]
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	58	98.28% [2083]	100.00%
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	21	100.00%	100.00%
[[_high_order, _with_linear_symmetries]]	57	87.72% [813, 9865, 9866, 9867, 9868, 9895, 9913]	87.72% [813, 9865, 9866, 9867, 9868, 9905, 9913]
[[_3rd_order, _with_linear_symmetries]]	158	88.61% [5817, 9784, 9785, 9786, 9787, 9788, 9789, 9790, 9800, 9801, 9803, 9811, 9816, 9827, 9840, 9841, 9856, 13559]	89.24% [5817, 9784, 9785, 9786, 9787, 9788, 9789, 9790, 9800, 9801, 9803, 9811, 9816, 9835, 9840, 9856, 13559]
[[_high_order, _linear, _nonhomogeneous]]	89	97.75% [9875, 9904]	98.88% [9904]
[[_1st_order, _with_linear_symmetries], _Clairaut]	76	100.00%	100.00%
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	52	100.00%	100.00%
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	79	98.73% [1985]	98.73% [1985]
[[_homogeneous, ‘class C‘], _rational, _Riccati]	5	100.00%	100.00%
[[_Abel, ‘2nd type‘, ‘class A‘]]	34	14.71% [3676, 3728, 4954, 8542, 8555, 10657, 10658, 10722, 10723, 10724, 10733, 10734, 10735, 10736, 10737, 10751, 10797, 10804, 10805, 10807, 10808, 10810, 10811, 10812, 10813, 10814, 10815, 10816, 10817]	35.29% [3676, 3728, 4954, 8542, 8555, 10722, 10723, 10724, 10733, 10734, 10735, 10736, 10737, 10751, 10797, 10805, 10808, 10812, 10813, 10815, 10816, 10817]
[_rational, _Bernoulli]	46	100.00%	100.00%
[[_homogeneous, ‘class A‘]]	7	100.00%	100.00%
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	162	98.15% [1941, 4451, 10819]	98.77% [1935, 1938]
[[_homogeneous, ‘class G‘], _rational, _Riccati]	21	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‘]]	2	100.00%	100.00%
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	17	100.00%	100.00%
[_exact, [_Abel, ‘2nd type‘, ‘class B‘]]	6	100.00%	100.00%
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	10	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]	7	100.00%	100.00%
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli]	10	100.00%	100.00%
[_rational, [_Abel, ‘2nd type‘, ‘class C‘]]	12	83.33% [4917, 4962]	83.33% [4917, 4962]
[[_homogeneous, ‘class G‘], _rational]	98	98.98% [1986]	97.96% [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% [10349, 10392, 10401, 10405, 10406]	98.04% [10401, 10406]
[[_3rd_order, _linear, _nonhomogeneous]]	93	97.85% [12223, 12227]	100.00%
[[_high_order, _missing_y]]	57	98.25% [9909]	98.25% [9909]
[[_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‘]]	34	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]]	26	100.00%	100.00%
[_Abel]	30	66.67% [1704, 3352, 8384, 8385, 8386, 8387, 12134, 12631, 12938, 13057]	66.67% [1704, 3352, 8384, 8385, 8386, 8387, 12134, 12631, 12938, 13057]
[_Laguerre]	39	100.00%	100.00%
[_Laguerre, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	4	100.00%	100.00%
[_Bessel]	20	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]‘]]	11	100.00%	100.00%
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	6	100.00%	100.00%
[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	36	100.00%	100.00%
[[_homogeneous, ‘class D‘], _Bernoulli]	6	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]	7	100.00%	100.00%
[[_2nd_order, _quadrature]]	61	98.36% [12198]	98.36% [7304]
[[_high_order, _quadrature]]	11	100.00%	100.00%
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	78	89.74% [2308, 2376, 4658, 6100, 6839, 6840, 9914, 15211]	97.44% [2376, 15217]
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]	24	100.00%	100.00%
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]]	10	100.00%	100.00%
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	17	58.82% [4668, 4839, 4840, 4841, 13523, 13524, 15210]	100.00%
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]	29	93.10% [2304, 13520]	93.10% [2304, 2309]
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	11	100.00%	100.00%
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	38	100.00%	97.37% [10131]
[[_2nd_order, _missing_x], [_2nd_order, _with_potential_symmetries], [_2nd_order, _reducible, _mu_xy]]	5	100.00%	100.00%
[[_homogeneous, ‘class C‘], _rational, _dAlembert]	13	100.00%	100.00%
[_dAlembert]	25	100.00%	100.00%
[[_1st_order, _with_linear_symmetries], _dAlembert]	64	82.81% [2350, 4251, 4252, 4253, 4274, 4305, 6811, 6813, 6874, 6878, 7254]	100.00%
[[_homogeneous, ‘class G‘], _rational, _Clairaut]	10	100.00%	100.00%
[[_homogeneous, ‘class G‘], _Clairaut]	3	100.00%	100.00%
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut]	17	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% [10164]	66.67% [10164]
[_Jacobi]	37	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]]	8	100.00%	100.00%
[[_homogeneous, ‘class G‘], _exact]	3	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‘]]	7	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]	3	100.00%	100.00%
[[_homogeneous, ‘class C‘], _exact, _dAlembert]	5	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, 10655, 10659, 10686, 10702, 10720, 10721, 10738, 10740, 10741, 10745, 10747, 10750, 10763, 10794, 10795, 10796, 10798, 10799, 10800, 10801, 10802, 10803, 10820, 10822, 11599]	45.00% [3673, 5247, 8539, 8541, 10655, 10659, 10720, 10721, 10741, 10747, 10750, 10763, 10794, 10795, 10798, 10799, 10800, 10801, 10802, 10820, 10822, 11599]
[[_homogeneous, ‘class G‘], _dAlembert]	7	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]	4	0.00% [3355, 3642, 8392, 14440]	0.00% [3355, 3642, 8392, 14440]
[_rational, [_Riccati, _special]]	9	100.00%	100.00%
[[_1st_order, _with_linear_symmetries], _rational, _Riccati]	3	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]	6	100.00%	100.00%
[_exact, _rational, _Bernoulli]	4	75.00% [14327]	75.00% [14327]
[[_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]	8	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	8	75.00% [8676, 10129]	62.50% [8676, 10129, 10158]
[_rational, _dAlembert]	12	91.67% [8766]	100.00%
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert]	9	100.00%	100.00%
[[_homogeneous, ‘class G‘], _rational, _dAlembert]	6	100.00%	100.00%
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	15	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]]	9	100.00%	100.00%
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]]	10	90.00% [12495]	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]	16	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]	39	100.00%	92.31% [9068, 9124, 9125]
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]	6	100.00%	83.33% [15197]
[[_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]]	7	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, 9924, 9987, 10009, 10013, 10015, 10018, 10019, 12256, 13250]	25.00% [7107, 9924, 9987, 10009, 10013, 10015, 10018, 10019, 13250]
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]	3	33.33% [9949, 12269]	33.33% [9949, 12269]
[_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% [9349]	50.00% [9349]
[_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]]	7	100.00%	100.00%
[[_high_order, _fully, _exact, _linear]]	1	100.00%	100.00%
[[_Painleve, ‘1st‘]]	1	0.00% [9916]	0.00% [9916]
[[_Painleve, ‘2nd‘]]	1	0.00% [9919]	0.00% [9919]
[[_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	1	0.00% [9950]	0.00% [9950]
[[_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% [10111]	66.67% [10111]
[[_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]	1	0.00% [10036]	0.00% [10036]
[[_Painleve, ‘4th‘]]	1	0.00% [10060]	0.00% [10060]
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_xy]]	3	100.00%	100.00%
[[_Painleve, ‘3rd‘]]	1	0.00% [10084]	0.00% [10084]
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1]]	1	100.00%	100.00%
[[_Painleve, ‘5th‘]]	1	0.00% [10120]	0.00% [10120]
[[_Painleve, ‘6th‘]]	1	0.00% [10130]	0.00% [10130]
[[_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% [10139]	0.00% [10139]
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_poly_yn]]	1	0.00% [10144]	0.00% [10144]
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1]]	1	0.00% [10148]	0.00% [10148]
[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]]	7	28.57% [10161, 10162, 10163, 10178, 13535]	28.57% [10161, 10162, 10163, 10178, 13535]
[[_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]]	5	100.00%	100.00%
[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries]]	2	50.00% [10173]	50.00% [10173]
[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries], [_high_order, _reducible, _mu_poly_yn]]	2	100.00%	100.00%
	96	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% [12226, 12240]	0.00% [12226, 12240]
[[_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]]	3	100.00%	100.00%
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], [_Abel, ‘2nd type‘, ‘class A‘]]	1	100.00%	100.00%
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]]	1	100.00%	100.00%
[[_2nd_order, _missing_x], _Van_der_Pol]	1	100.00%	100.00%
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]	1	100.00%	100.00%
[[_homogeneous, ‘class D‘], _exact, _rational]	1	100.00%	100.00%
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class A‘]]	1	100.00%	100.00%
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_poly_yn]]	1	100.00%	100.00%
[[_3rd_order, _missing_x], [_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]	1	0.00% [15221]	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	790	97.85% [885, 4266, 4275, 12127, 12129, 12910, 12911, 12914, 12935, 12936, 12962, 12965, 12966, 12967, 14201, 15125, 15126]	99.87% [11994]
linear	69	98.55% [6169]	98.55% [6169]
separable	126	100.00%	100.00%
homogeneous	70	98.57% [5761]	100.00%
homogeneousTypeD2	5	100.00%	100.00%
exact	308	97.40% [119, 146, 3137, 14323, 14328, 15066, 15067, 15073]	99.35% [14323, 14328]
exactWithIntegrationFactor	135	99.26% [8676]	96.30% [1984, 2063, 3090, 8676, 15059]
exactByInspection	19	100.00%	94.74% [3926]
bernoulli	25	100.00%	100.00%
riccati	478	76.99% [958, 1697, 1698, 1700, 1701, 1702, 2707, 3304, 3324, 3326, 3339, 3639, 4386, 7345, 8447, 10339, 10346, 10349, 10359, 10363, 10392, 10401, 10405, 10406, 10415, 10432, 10436, 10440, 10445, 10452, 10461, 10476, 10479, 10480, 10481, 10483, 10487, 10501, 10503, 10504, 10505, 10514, 10516, 10517, 10532, 10536, 10538, 10541, 10545, 10549, 10554, 10555, 10556, 10557, 10560, 10562, 10563, 10566, 10569, 10571, 10572, 10575, 10578, 10580, 10581, 10584, 10587, 10589, 10590, 10593, 10597, 10598, 10599, 10603, 10604, 10607, 10609, 10611, 10612, 10613, 10614, 10615, 10616, 10617, 10618, 10620, 10621, 10622, 10623, 10624, 10625, 10626, 10627, 10628, 10629, 10632, 10636, 10637, 10638, 10639, 10640, 10641, 10642, 10643, 10644, 10645, 10646, 10647, 10648, 10649]	80.96% [958, 1697, 1700, 1701, 1702, 2707, 3324, 3326, 3339, 4386, 7345, 8447, 9068, 9125, 10339, 10346, 10359, 10361, 10363, 10401, 10406, 10418, 10426, 10432, 10436, 10438, 10440, 10445, 10461, 10476, 10479, 10480, 10481, 10483, 10487, 10501, 10503, 10514, 10516, 10532, 10545, 10547, 10554, 10562, 10563, 10566, 10571, 10572, 10575, 10580, 10581, 10584, 10589, 10590, 10593, 10597, 10598, 10603, 10604, 10606, 10607, 10609, 10611, 10612, 10613, 10614, 10615, 10616, 10617, 10618, 10620, 10623, 10624, 10625, 10626, 10628, 10632, 10636, 10637, 10638, 10639, 10640, 10641, 10642, 10643, 10644, 10645, 10646, 10647, 10648, 10649]
clairaut	115	100.00%	99.13% [4343]
dAlembert	253	92.89% [2350, 3000, 4251, 4252, 4253, 4260, 4274, 4278, 4305, 6811, 6813, 6874, 6878, 7254, 8766, 11212, 11240, 15129]	100.00%
isobaric	13	100.00%	100.00%
polynomial	16	100.00%	100.00%
abelFirstKind	58	82.76% [1704, 1897, 3352, 8384, 8385, 8387, 12134, 12631, 12938, 13057]	84.48% [1704, 3352, 8384, 8385, 8387, 12134, 12631, 12938, 13057]
first order ode series method. Taylor series method	12	100.00%	100.00%
first order ode series method. Regular singular point	8	100.00%	100.00%
first order ode series method. Irregular singular point	3	100.00%	0.00% [408, 409, 6418]
first_order_laplace	77	100.00%	100.00%
first_order_ode_lie_symmetry_calculated	498	95.98% [1941, 1986, 2083, 3229, 3231, 3232, 3236, 4290, 4294, 4451, 5346, 6797, 6807, 7102, 10819, 11215, 12148, 14439, 15095, 15124]	97.59% [3995, 4040, 4163, 4199, 6820, 8704, 8719, 8820, 8872, 9246, 11230, 12421]
system of linear ODEs	802	96.88% [6104, 6542, 6543, 10228, 10238, 10241, 10242, 10243, 10244, 10245, 10254, 10255, 10256, 10257, 10258, 10259, 10261, 12827, 12828, 12829, 12830, 12842, 14043, 15506, 15524]	97.01% [6104, 6542, 6543, 6716, 6719, 10228, 10238, 10241, 10242, 10243, 10244, 10245, 10254, 10256, 10257, 10259, 10261, 12827, 12828, 12829, 12830, 12842, 14043, 15524]
second_order_laplace	330	100.00%	99.70% [6513]
reduction_of_order	160	98.12% [12050, 14472, 14473]	98.12% [12050, 14472, 14473]
second_order_linear_constant_coeff	2	100.00%	0.00% [7306, 7307]
second_order_airy	15	100.00%	100.00%
second_order_change_of_variable_on_x_method_1	1	100.00%	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	18	83.33% [9747, 10927, 15436]	94.44% [10927]
second_order_change_of_variable_on_y_method_1	4	100.00%	100.00%
second_order_integrable_as_is	12	83.33% [10144, 12269]	83.33% [10144, 12269]
second_order_ode_lagrange_adjoint_equation_method	9	88.89% [10881]	100.00%
second_order_nonlinear_solved_by_mainardi_lioville_method	14	100.00%	100.00%
second_order_bessel_ode	136	91.18% [7288, 9349, 9634, 9690, 10833, 10892, 10943, 10945, 11036, 11079, 12412, 12748]	97.79% [7288, 9349, 12412]
second_order_bessel_ode_form_A	7	100.00%	100.00%
second_order_ode_missing_x	168	86.90% [2307, 2308, 9934, 9935, 9936, 9939, 9941, 9959, 9960, 9962, 9985, 10031, 10033, 10156, 10159, 12495, 12570, 12571, 15211, 15444, 15446, 15449]	88.69% [9934, 9935, 9939, 9941, 9959, 9960, 9962, 9985, 10031, 10032, 10033, 10131, 10159, 12570, 12571, 15217, 15444, 15446, 15449]
second_order_ode_missing_y	60	88.33% [2304, 6856, 6858, 7212, 10150, 11331, 13520]	96.67% [2304, 2309]
second order series method. Taylor series method	8	87.50% [2376]	87.50% [2376]
second order series method. Regular singular point. Difference not integer	266	100.00%	97.74% [7224, 7225, 7226, 7230, 7231, 7233]
second order series method. Regular singular point. Repeated root	208	100.00%	99.52% [7241]
second order series method. Regular singular point. Difference is integer	322	100.00%	99.69% [5501]
second order series method. Irregular singular point	38	94.74% [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, 11904, 11905, 12406, 12407, 14803]
second order series method. Regular singular point. Complex roots	30	100.00%	100.00%
second_order_ode_high_degree	1	100.00%	100.00%
higher_order_linear_constant_coefficients_ODE	728	100.00%	100.00%
higher_order_ODE_non_constant_coefficients_of_type_Euler	96	100.00%	100.00%
higher_order_laplace	29	100.00%	100.00%

Performance using simplified ODE types classification

This chapter shows how each CAS performed based on the following basic differential equations types. A differential equation is classified as one of the following types.

1. First order ode.
2. Second and higher order ode.

For first order ode, the following are the main classifications used.

1. First order ode \(f(x,y,y')=0\) which is linear in \(y'(x)\).

2. First order ode not linear in \(y'(x)\) (such as d’Alembert, Clairaut). But it is important to note that in this case the ode is nonlinear in \(y'\) when written in the form \(y=g(x,y')\). For an example, lets look at this ode \[ y' = -\frac {x}{2}-1+\frac {\sqrt {x^{2}+4 x +4 y}}{2} \] Which is linear in \(y'\) as it stands. But in d’Alembert, Clairaut we always look at the ode in the form \(y=g(x,y')\). Hence, if we solve for \(y\) first, the above ode now becomes \begin {align*} y &= x y' + \left ( (y')^{2}+ 2 y' + 1 \right )\\ &= g(x,y') \end {align*}

   Now we see that \(g(x,y')\) is nonlinear in \(y'\). The above ode happens to be of type Clairaut.

For second order and higher order ode’s, further classification is

1. Linear ode.
2. non-linear ode.

Another classification for second order and higher order ode’s is

1. Constant coefficients ode.
2. Varying coefficients ode

Another classification for second order and higher order ode’s is

1. Homogeneous ode. (the right side is zero).
2. Non-homogeneous ode. (the right side is not zero).

All of the above can be combined to give this classification

1. First order ode.

   1. First order ode linear in \(y'(x)\).
   2. First order ode not linear in \(y'(x)\) (such as d’Alembert, Clairaut).

2. Second and higher order ode

   1. Linear second order ode.

      1. Linear homogeneous ode. (the right side is zero).
      2. Linear homogeneous and constant coefficients ode.
      3. Linear homogeneous and non-constant coefficients ode.
      4. Linear non-homogeneous ode. (the right side is not zero).
      5. Linear non-homogeneous and constant coefficients ode.
      6. Linear non-homogeneous and non-constant coefficients ode.

   2. Nonlinear second order ode.

      1. Nonlinear homogeneous ode.
      2. Nonlinear non-homogeneous ode.

For system of differential equation the following classification is used.

1. System of first order odes.

   1. Linear system of odes.
   2. non-linear system of odes.

2. System of second order odes.

   1. Linear system of odes.
   2. non-linear system of odes.

The following gives count of the number of ODE’s for each ODE type as specified above, 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.

1. First order ode.

   Number of problems 6876.

   Solved by Mathematica: 93.22%

   Solved by Maple: 94.90%

   Links to problems not solved by Mathematica:

   [119, 133, 146, 485, 550, 553, 885, 958, 959, 961, 962, 964, 966, 968, 1039, 1041, 1046, 1069, 1075, 1697, 1698, 1700, 1701, 1702, 1703, 1704, 1706, 1707, 1897, 1941, 1953, 1985, 1986, 2026, 2031, 2083, 2085, 2316, 2319, 2350, 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, 4917, 4951, 4954, 4962, 4995, 5247, 5346, 5761, 6111, 6169, 6183, 6185, 6264, 6549, 6797, 6807, 6811, 6813, 6874, 6878, 7063, 7102, 7253, 7254, 7316, 7345, 8384, 8385, 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, 9219, 9228, 10339, 10346, 10349, 10359, 10363, 10392, 10401, 10405, 10406, 10415, 10432, 10436, 10440, 10445, 10452, 10461, 10476, 10479, 10480, 10481, 10483, 10487, 10501, 10503, 10504, 10505, 10514, 10516, 10517, 10532, 10536, 10538, 10541, 10545, 10549, 10554, 10555, 10556, 10557, 10560, 10562, 10563, 10566, 10569, 10571, 10572, 10575, 10578, 10580, 10581, 10584, 10587, 10589, 10590, 10593, 10597, 10598, 10599, 10603, 10604, 10607, 10609, 10611, 10612, 10613, 10614, 10615, 10616, 10617, 10618, 10620, 10621, 10622, 10623, 10624, 10625, 10626, 10627, 10628, 10629, 10632, 10636, 10637, 10638, 10639, 10640, 10641, 10642, 10643, 10644, 10645, 10646, 10647, 10648, 10649, 10653, 10654, 10655, 10657, 10658, 10659, 10661, 10662, 10664, 10666, 10667, 10669, 10670, 10671, 10673, 10674, 10676, 10677, 10678, 10679, 10680, 10683, 10684, 10685, 10686, 10687, 10688, 10689, 10690, 10691, 10692, 10696, 10697, 10698, 10699, 10700, 10701, 10702, 10704, 10705, 10706, 10707, 10708, 10709, 10710, 10711, 10712, 10713, 10714, 10715, 10716, 10717, 10718, 10719, 10720, 10721, 10722, 10723, 10724, 10730, 10731, 10733, 10734, 10735, 10736, 10737, 10738, 10740, 10741, 10745, 10747, 10748, 10749, 10750, 10751, 10752, 10755, 10756, 10757, 10758, 10759, 10760, 10761, 10762, 10763, 10764, 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, 10807, 10808, 10810, 10811, 10812, 10813, 10814, 10815, 10816, 10817, 10819, 10820, 10822, 10823, 10824, 11198, 11212, 11215, 11219, 11224, 11240, 11404, 11415, 11599, 11604, 11610, 11995, 12127, 12129, 12134, 12148, 12214, 12220, 12239, 12631, 12636, 12910, 12911, 12914, 12935, 12936, 12938, 12962, 12965, 12966, 12967, 13034, 13057, 13289, 13348, 14046, 14101, 14126, 14133, 14201, 14296, 14313, 14323, 14327, 14328, 14378, 14384, 14439, 14440, 14441, 14941, 14980, 14999, 15000, 15001, 15002, 15006, 15046, 15066, 15067, 15073, 15074, 15095, 15124, 15125, 15126, 15129]

   Links to problems not solved by Maple:

   [133, 485, 550, 553, 958, 959, 961, 962, 964, 966, 968, 1039, 1046, 1075, 1697, 1700, 1701, 1702, 1703, 1704, 1706, 1707, 1935, 1938, 1953, 1984, 1985, 2026, 2063, 2316, 2319, 2707, 2713, 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, 3995, 4011, 4040, 4146, 4163, 4198, 4199, 4216, 4287, 4298, 4315, 4343, 4386, 4914, 4917, 4951, 4954, 4962, 4995, 5247, 6111, 6169, 6183, 6185, 6264, 6549, 6820, 7063, 7253, 7316, 7345, 8384, 8385, 8387, 8392, 8393, 8411, 8416, 8419, 8424, 8447, 8457, 8538, 8539, 8541, 8542, 8555, 8570, 8573, 8586, 8589, 8601, 8605, 8676, 8703, 8704, 8706, 8719, 8731, 8787, 8795, 8796, 8815, 8817, 8820, 8838, 8841, 8845, 8848, 8866, 8872, 8878, 8907, 8910, 8911, 9068, 9124, 9125, 9170, 9172, 9219, 9228, 9246, 9254, 10339, 10346, 10359, 10361, 10363, 10401, 10406, 10418, 10426, 10432, 10436, 10438, 10440, 10445, 10461, 10476, 10479, 10480, 10481, 10483, 10487, 10501, 10503, 10514, 10516, 10532, 10545, 10547, 10554, 10562, 10563, 10566, 10571, 10572, 10575, 10580, 10581, 10584, 10589, 10590, 10593, 10597, 10598, 10603, 10604, 10606, 10607, 10609, 10611, 10612, 10613, 10614, 10615, 10616, 10617, 10618, 10620, 10623, 10624, 10625, 10626, 10628, 10632, 10636, 10637, 10638, 10639, 10640, 10641, 10642, 10643, 10644, 10645, 10646, 10647, 10648, 10649, 10655, 10659, 10661, 10664, 10669, 10670, 10676, 10677, 10678, 10679, 10680, 10687, 10688, 10690, 10691, 10692, 10697, 10699, 10700, 10704, 10705, 10708, 10709, 10710, 10711, 10712, 10713, 10715, 10716, 10717, 10718, 10719, 10720, 10721, 10722, 10723, 10724, 10733, 10734, 10735, 10736, 10737, 10741, 10747, 10748, 10749, 10750, 10751, 10755, 10757, 10758, 10759, 10760, 10761, 10762, 10763, 10764, 10766, 10767, 10769, 10770, 10771, 10772, 10774, 10775, 10777, 10778, 10779, 10781, 10782, 10783, 10784, 10785, 10786, 10787, 10791, 10792, 10794, 10795, 10797, 10798, 10799, 10800, 10801, 10802, 10805, 10808, 10812, 10813, 10815, 10816, 10817, 10820, 10822, 10823, 11198, 11224, 11230, 11404, 11415, 11518, 11599, 11604, 11994, 11995, 12134, 12214, 12218, 12220, 12239, 12421, 12631, 12636, 12938, 13034, 13057, 13289, 13348, 14101, 14126, 14133, 14296, 14313, 14323, 14327, 14328, 14440, 14441, 14941, 15001, 15059]

2. Second order linear ODE.

   Number of problems 4610.

   Solved by Mathematica: 96.79%

   Solved by Maple: 97.83%

   Links to problems not solved by Mathematica:

   [1105, 1162, 1186, 5813, 5818, 7178, 7179, 7182, 7183, 7187, 7189, 7288, 7462, 7554, 7556, 7976, 7978, 9349, 9353, 9360, 9364, 9365, 9371, 9405, 9406, 9407, 9408, 9409, 9487, 9535, 9542, 9546, 9565, 9607, 9634, 9690, 9720, 9730, 9736, 9747, 9762, 9767, 9768, 9769, 9771, 10833, 10840, 10841, 10856, 10861, 10872, 10874, 10875, 10876, 10877, 10878, 10881, 10882, 10883, 10884, 10892, 10902, 10908, 10915, 10921, 10922, 10924, 10925, 10926, 10927, 10928, 10933, 10943, 10945, 10946, 10966, 10967, 10968, 10972, 11012, 11025, 11029, 11030, 11032, 11036, 11039, 11052, 11055, 11056, 11065, 11066, 11067, 11068, 11069, 11070, 11071, 11072, 11073, 11074, 11078, 11079, 11081, 11082, 11084, 11085, 11086, 11087, 11095, 11100, 11103, 11118, 11119, 11121, 11310, 11311, 11329, 11589, 11590, 12050, 12198, 12248, 12249, 12250, 12251, 12252, 12258, 12264, 12281, 12352, 12354, 12412, 12614, 12748, 12749, 13569, 13570, 14121, 14472, 14473, 14633, 14870, 15382, 15384, 15385, 15386, 15436, 15453, 15459]

   Links to problems not solved by Maple:

   [1162, 1186, 5818, 5833, 6513, 7179, 7187, 7189, 7288, 9349, 9353, 9360, 9364, 9365, 9371, 9405, 9406, 9407, 9408, 9409, 9487, 9535, 9542, 9546, 9565, 9607, 9736, 9767, 9768, 9769, 9771, 10856, 10872, 10874, 10876, 10877, 10882, 10883, 10884, 10915, 10921, 10922, 10925, 10926, 10927, 10928, 10946, 10967, 10968, 10972, 11012, 11022, 11023, 11024, 11027, 11032, 11034, 11039, 11055, 11056, 11065, 11066, 11070, 11071, 11072, 11073, 11081, 11082, 11084, 11087, 11104, 11109, 11111, 11116, 11117, 11118, 11121, 11329, 11589, 11590, 12050, 12248, 12251, 12252, 12264, 12281, 12352, 12354, 12412, 12614, 12749, 13569, 13570, 14121, 14472, 14473, 14633, 14870, 15432, 15453]

3. Second order ode.

   Number of problems 5160.

   Solved by Mathematica: 94.28%

   Solved by Maple: 95.72%

   Links to problems not solved by Mathematica:

   [710, 1105, 1162, 1186, 2304, 2307, 2308, 4658, 4668, 4839, 4840, 4841, 5813, 5818, 6100, 6246, 6839, 6840, 6856, 6858, 7107, 7108, 7110, 7178, 7179, 7182, 7183, 7187, 7189, 7212, 7214, 7288, 7411, 7462, 7554, 7556, 7976, 7978, 8386, 9349, 9353, 9360, 9364, 9365, 9371, 9405, 9406, 9407, 9408, 9409, 9487, 9535, 9542, 9546, 9565, 9607, 9634, 9690, 9720, 9730, 9736, 9747, 9762, 9767, 9768, 9769, 9771, 9914, 9916, 9918, 9919, 9921, 9922, 9924, 9926, 9928, 9929, 9931, 9932, 9934, 9935, 9936, 9938, 9939, 9940, 9941, 9942, 9946, 9947, 9948, 9949, 9950, 9951, 9957, 9959, 9960, 9962, 9965, 9966, 9967, 9968, 9971, 9972, 9981, 9982, 9983, 9985, 9986, 9987, 9988, 9989, 9990, 9995, 9996, 9998, 10000, 10001, 10003, 10005, 10007, 10008, 10009, 10013, 10015, 10016, 10018, 10019, 10025, 10027, 10031, 10033, 10036, 10042, 10052, 10055, 10057, 10058, 10060, 10061, 10062, 10065, 10074, 10080, 10084, 10085, 10100, 10102, 10103, 10111, 10112, 10120, 10124, 10125, 10129, 10130, 10134, 10138, 10139, 10141, 10142, 10143, 10144, 10148, 10150, 10154, 10155, 10156, 10159, 10725, 10833, 10840, 10841, 10856, 10861, 10872, 10874, 10875, 10876, 10877, 10878, 10881, 10882, 10883, 10884, 10892, 10902, 10908, 10915, 10921, 10922, 10924, 10925, 10926, 10927, 10928, 10933, 10943, 10945, 10946, 10966, 10967, 10968, 10972, 11012, 11025, 11029, 11030, 11032, 11036, 11039, 11052, 11055, 11056, 11065, 11066, 11067, 11068, 11069, 11070, 11071, 11072, 11073, 11074, 11078, 11079, 11081, 11082, 11084, 11085, 11086, 11087, 11095, 11100, 11103, 11118, 11119, 11121, 11310, 11311, 11329, 11331, 11589, 11590, 12050, 12198, 12241, 12248, 12249, 12250, 12251, 12252, 12256, 12258, 12264, 12269, 12281, 12352, 12354, 12412, 12495, 12570, 12571, 12614, 12748, 12749, 13250, 13520, 13523, 13524, 13529, 13569, 13570, 14050, 14051, 14121, 14472, 14473, 14516, 14517, 14626, 14633, 14870, 15204, 15210, 15211, 15382, 15384, 15385, 15386, 15436, 15444, 15446, 15449, 15453, 15459]

   Links to problems not solved by Maple:

   [710, 1162, 1186, 2304, 2309, 5818, 5833, 6238, 6513, 7107, 7110, 7179, 7187, 7189, 7214, 7288, 7411, 8386, 9349, 9353, 9360, 9364, 9365, 9371, 9405, 9406, 9407, 9408, 9409, 9487, 9535, 9542, 9546, 9565, 9607, 9736, 9767, 9768, 9769, 9771, 9916, 9918, 9919, 9921, 9922, 9924, 9928, 9929, 9931, 9932, 9934, 9935, 9938, 9939, 9940, 9941, 9942, 9946, 9947, 9948, 9949, 9950, 9951, 9957, 9959, 9960, 9962, 9965, 9966, 9967, 9968, 9971, 9972, 9981, 9982, 9983, 9985, 9986, 9987, 9988, 9989, 9990, 9995, 9996, 9998, 10000, 10003, 10005, 10007, 10008, 10009, 10013, 10015, 10016, 10018, 10019, 10021, 10025, 10027, 10028, 10029, 10031, 10032, 10033, 10036, 10042, 10044, 10052, 10055, 10057, 10058, 10060, 10061, 10062, 10065, 10074, 10080, 10084, 10085, 10100, 10111, 10112, 10120, 10124, 10125, 10129, 10130, 10131, 10138, 10139, 10143, 10144, 10148, 10154, 10155, 10157, 10158, 10159, 10725, 10856, 10872, 10874, 10876, 10877, 10882, 10883, 10884, 10915, 10921, 10922, 10925, 10926, 10927, 10928, 10946, 10967, 10968, 10972, 11012, 11022, 11023, 11024, 11027, 11032, 11034, 11039, 11055, 11056, 11065, 11066, 11070, 11071, 11072, 11073, 11081, 11082, 11084, 11087, 11104, 11109, 11111, 11116, 11117, 11118, 11121, 11329, 11589, 11590, 12050, 12241, 12248, 12251, 12252, 12264, 12269, 12281, 12352, 12354, 12412, 12570, 12571, 12614, 12749, 13250, 13529, 13569, 13570, 14050, 14051, 14121, 14472, 14473, 14626, 14633, 14870, 15217, 15432, 15444, 15446, 15449, 15453]

4. Second ODE homogeneous ODE.

   Number of problems 3169.

   Solved by Mathematica: 92.84%

   Solved by Maple: 94.79%

   Links to problems not solved by Mathematica:

   [1105, 2304, 2307, 2308, 4658, 4668, 4839, 4840, 4841, 5813, 5818, 6100, 6246, 6839, 6840, 6858, 7214, 7288, 7411, 7554, 7556, 7976, 7978, 9349, 9353, 9360, 9364, 9365, 9371, 9405, 9406, 9407, 9409, 9487, 9535, 9542, 9546, 9565, 9607, 9634, 9690, 9720, 9730, 9736, 9747, 9762, 9767, 9768, 9769, 9771, 9914, 9924, 9926, 9928, 9929, 9934, 9935, 9936, 9938, 9939, 9940, 9942, 9946, 9948, 9949, 9957, 9959, 9960, 9962, 9965, 9966, 9967, 9968, 9971, 9972, 9981, 9982, 9983, 9985, 9986, 9987, 9988, 9989, 9990, 9995, 9996, 9998, 10001, 10003, 10009, 10013, 10015, 10016, 10025, 10027, 10031, 10033, 10036, 10042, 10055, 10058, 10061, 10065, 10074, 10080, 10084, 10085, 10100, 10111, 10112, 10120, 10129, 10130, 10134, 10138, 10139, 10141, 10142, 10143, 10144, 10150, 10154, 10156, 10159, 10833, 10840, 10841, 10856, 10861, 10872, 10874, 10875, 10876, 10877, 10878, 10881, 10882, 10883, 10884, 10892, 10902, 10908, 10915, 10921, 10922, 10924, 10925, 10926, 10927, 10928, 10933, 10943, 10945, 10946, 10966, 10967, 10968, 10972, 11012, 11025, 11029, 11030, 11032, 11036, 11039, 11052, 11055, 11056, 11065, 11066, 11067, 11068, 11069, 11070, 11071, 11072, 11073, 11074, 11078, 11079, 11081, 11082, 11084, 11085, 11086, 11087, 11095, 11100, 11103, 11118, 11119, 11121, 11310, 11311, 11329, 11331, 11589, 11590, 12050, 12241, 12249, 12250, 12256, 12258, 12264, 12412, 12495, 12570, 12571, 12614, 13520, 13523, 13524, 13529, 13569, 13570, 14472, 14473, 14516, 14517, 15204, 15210, 15211, 15444, 15446, 15449, 15453]

   Links to problems not solved by Maple:

   [2304, 2309, 5818, 6238, 7214, 7288, 7411, 9349, 9353, 9360, 9364, 9365, 9371, 9405, 9406, 9407, 9409, 9487, 9535, 9542, 9546, 9565, 9607, 9736, 9767, 9768, 9769, 9771, 9924, 9928, 9929, 9934, 9935, 9938, 9939, 9940, 9942, 9946, 9948, 9949, 9957, 9959, 9960, 9962, 9965, 9966, 9967, 9968, 9971, 9972, 9981, 9982, 9983, 9985, 9986, 9987, 9988, 9989, 9990, 9995, 9996, 9998, 10003, 10009, 10013, 10015, 10016, 10025, 10027, 10028, 10029, 10031, 10032, 10033, 10036, 10042, 10044, 10055, 10058, 10061, 10065, 10074, 10080, 10084, 10085, 10100, 10111, 10112, 10120, 10129, 10130, 10131, 10138, 10139, 10143, 10144, 10154, 10157, 10158, 10159, 10856, 10872, 10874, 10876, 10877, 10882, 10883, 10884, 10915, 10921, 10922, 10925, 10926, 10927, 10928, 10946, 10967, 10968, 10972, 11012, 11022, 11023, 11024, 11027, 11032, 11034, 11039, 11055, 11056, 11065, 11066, 11070, 11071, 11072, 11073, 11081, 11082, 11084, 11087, 11104, 11109, 11111, 11116, 11117, 11118, 11121, 11329, 11589, 11590, 12050, 12241, 12264, 12412, 12570, 12571, 12614, 13529, 13569, 13570, 14472, 14473, 15444, 15446, 15449, 15453]

5. Second ODE non-homogeneous ODE.

   Number of problems 1991.

   Solved by Mathematica: 96.58%

   Solved by Maple: 97.19%

   Links to problems not solved by Mathematica:

   [710, 1162, 1186, 6856, 7107, 7108, 7110, 7178, 7179, 7182, 7183, 7187, 7189, 7212, 7462, 8386, 9408, 9916, 9918, 9919, 9921, 9922, 9931, 9932, 9941, 9947, 9950, 9951, 10000, 10005, 10007, 10008, 10018, 10019, 10052, 10057, 10060, 10062, 10102, 10103, 10124, 10125, 10148, 10155, 10725, 12198, 12248, 12251, 12252, 12269, 12281, 12352, 12354, 12748, 12749, 13250, 14050, 14051, 14121, 14626, 14633, 14870, 15382, 15384, 15385, 15386, 15436, 15459]

   Links to problems not solved by Maple:

   [710, 1162, 1186, 5833, 6513, 7107, 7110, 7179, 7187, 7189, 8386, 9408, 9916, 9918, 9919, 9921, 9922, 9931, 9932, 9941, 9947, 9950, 9951, 10000, 10005, 10007, 10008, 10018, 10019, 10021, 10052, 10057, 10060, 10062, 10124, 10125, 10148, 10155, 10725, 12248, 12251, 12252, 12269, 12281, 12352, 12354, 12749, 13250, 14050, 14051, 14121, 14626, 14633, 14870, 15217, 15432]

6. Second order non-linear ODE.

   Number of problems 550.

   Solved by Mathematica: 73.27%

   Solved by Maple: 78.00%

   Links to problems not solved by Mathematica:

   [710, 2304, 2307, 2308, 4658, 4668, 4839, 4840, 4841, 6100, 6246, 6839, 6840, 6856, 6858, 7107, 7108, 7110, 7212, 7214, 7411, 8386, 9914, 9916, 9918, 9919, 9921, 9922, 9924, 9926, 9928, 9929, 9931, 9932, 9934, 9935, 9936, 9938, 9939, 9940, 9941, 9942, 9946, 9947, 9948, 9949, 9950, 9951, 9957, 9959, 9960, 9962, 9965, 9966, 9967, 9968, 9971, 9972, 9981, 9982, 9983, 9985, 9986, 9987, 9988, 9989, 9990, 9995, 9996, 9998, 10000, 10001, 10003, 10005, 10007, 10008, 10009, 10013, 10015, 10016, 10018, 10019, 10025, 10027, 10031, 10033, 10036, 10042, 10052, 10055, 10057, 10058, 10060, 10061, 10062, 10065, 10074, 10080, 10084, 10085, 10100, 10102, 10103, 10111, 10112, 10120, 10124, 10125, 10129, 10130, 10134, 10138, 10139, 10141, 10142, 10143, 10144, 10148, 10150, 10154, 10155, 10156, 10159, 10725, 11331, 12241, 12256, 12269, 12495, 12570, 12571, 13250, 13520, 13523, 13524, 13529, 14050, 14051, 14516, 14517, 14626, 15204, 15210, 15211, 15444, 15446, 15449]

   Links to problems not solved by Maple:

   [710, 2304, 2309, 6238, 7107, 7110, 7214, 7411, 8386, 9916, 9918, 9919, 9921, 9922, 9924, 9928, 9929, 9931, 9932, 9934, 9935, 9938, 9939, 9940, 9941, 9942, 9946, 9947, 9948, 9949, 9950, 9951, 9957, 9959, 9960, 9962, 9965, 9966, 9967, 9968, 9971, 9972, 9981, 9982, 9983, 9985, 9986, 9987, 9988, 9989, 9990, 9995, 9996, 9998, 10000, 10003, 10005, 10007, 10008, 10009, 10013, 10015, 10016, 10018, 10019, 10021, 10025, 10027, 10028, 10029, 10031, 10032, 10033, 10036, 10042, 10044, 10052, 10055, 10057, 10058, 10060, 10061, 10062, 10065, 10074, 10080, 10084, 10085, 10100, 10111, 10112, 10120, 10124, 10125, 10129, 10130, 10131, 10138, 10139, 10143, 10144, 10148, 10154, 10155, 10157, 10158, 10159, 10725, 12241, 12269, 12570, 12571, 13250, 13529, 14050, 14051, 14626, 15217, 15444, 15446, 15449]

7. Solved using series method.

   Number of problems 1555.

   Solved by Mathematica: 99.74%

   Solved by Maple: 96.27%

   Links to problems not solved by Mathematica:

   [2376, 5010, 6581, 15474]

   Links to problems not solved by Maple:

   [408, 409, 1794, 1797, 1805, 2376, 2400, 2541, 2920, 4701, 4714, 4718, 4722, 4723, 5003, 5010, 5217, 5500, 5501, 5502, 5521, 5526, 5556, 5564, 5588, 5589, 5590, 6042, 6418, 6441, 6443, 6449, 6459, 6460, 6581, 6584, 6592, 6617, 6618, 7224, 7225, 7226, 7230, 7231, 7233, 7241, 7300, 7301, 7303, 7304, 7305, 7306, 7307, 11904, 11905, 12406, 12407, 14803]

8. Third and higher order ode.

   Number of problems 1054.

   Solved by Mathematica: 95.73%

   Solved by Maple: 96.11%

   Links to problems not solved by Mathematica:

   [813, 5817, 9362, 9413, 9784, 9785, 9786, 9787, 9788, 9789, 9790, 9800, 9801, 9803, 9811, 9816, 9827, 9840, 9841, 9856, 9865, 9866, 9867, 9868, 9875, 9895, 9904, 9909, 9913, 10161, 10162, 10163, 10164, 10173, 10174, 10178, 12223, 12226, 12227, 12238, 12240, 12243, 13535, 13559, 15221]

   Links to problems not solved by Maple:

   [813, 5817, 9362, 9413, 9784, 9785, 9786, 9787, 9788, 9789, 9790, 9800, 9801, 9803, 9811, 9816, 9835, 9840, 9856, 9865, 9866, 9867, 9868, 9904, 9905, 9909, 9913, 10161, 10162, 10163, 10164, 10173, 10174, 10178, 12226, 12238, 12240, 12243, 13535, 13559, 15197]

9. First order ode linear in derivative.

   Number of problems 5933.

   Solved by Mathematica: 93.22%

   Solved by Maple: 94.77%

   Links to problems not solved by Mathematica:

   [119, 133, 146, 485, 550, 553, 885, 958, 959, 961, 962, 964, 966, 968, 1039, 1041, 1046, 1069, 1075, 1697, 1698, 1700, 1701, 1702, 1703, 1704, 1706, 1707, 1897, 1941, 1953, 1985, 1986, 2026, 2031, 2083, 2085, 2707, 2713, 2990, 3022, 3092, 3118, 3137, 3192, 3193, 3304, 3324, 3326, 3339, 3352, 3355, 3363, 3368, 3384, 3463, 3639, 3642, 3673, 3676, 3728, 3776, 3783, 3843, 4386, 4451, 4917, 4951, 4954, 4962, 4995, 5247, 5761, 6111, 6169, 6183, 6185, 6264, 6549, 7063, 7102, 7316, 7345, 8384, 8385, 8387, 8392, 8393, 8411, 8416, 8419, 8424, 8447, 8457, 8538, 8539, 8541, 8542, 8555, 8570, 8573, 8586, 8589, 8601, 8605, 8667, 8676, 8703, 9170, 9172, 9219, 9228, 10339, 10346, 10349, 10359, 10363, 10392, 10401, 10405, 10406, 10415, 10432, 10436, 10440, 10445, 10452, 10461, 10476, 10479, 10480, 10481, 10483, 10487, 10501, 10503, 10504, 10505, 10514, 10516, 10517, 10532, 10536, 10538, 10541, 10545, 10549, 10554, 10555, 10556, 10557, 10560, 10562, 10563, 10566, 10569, 10571, 10572, 10575, 10578, 10580, 10581, 10584, 10587, 10589, 10590, 10593, 10597, 10598, 10599, 10603, 10604, 10607, 10609, 10611, 10612, 10613, 10614, 10615, 10616, 10617, 10618, 10620, 10621, 10622, 10623, 10624, 10625, 10626, 10627, 10628, 10629, 10632, 10636, 10637, 10638, 10639, 10640, 10641, 10642, 10643, 10644, 10645, 10646, 10647, 10648, 10649, 10653, 10654, 10655, 10657, 10658, 10659, 10661, 10662, 10664, 10666, 10667, 10669, 10670, 10671, 10673, 10674, 10676, 10677, 10678, 10679, 10680, 10683, 10684, 10685, 10686, 10687, 10688, 10689, 10690, 10691, 10692, 10696, 10697, 10698, 10699, 10700, 10701, 10702, 10704, 10705, 10706, 10707, 10708, 10709, 10710, 10711, 10712, 10713, 10714, 10715, 10716, 10717, 10718, 10719, 10720, 10721, 10722, 10723, 10724, 10730, 10731, 10733, 10734, 10735, 10736, 10737, 10738, 10740, 10741, 10745, 10747, 10748, 10749, 10750, 10751, 10752, 10755, 10756, 10757, 10758, 10759, 10760, 10761, 10762, 10763, 10764, 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, 10807, 10808, 10810, 10811, 10812, 10813, 10814, 10815, 10816, 10817, 10819, 10820, 10822, 10823, 10824, 11198, 11415, 11599, 11604, 11610, 11995, 12134, 12214, 12220, 12631, 12636, 12910, 12911, 12914, 12935, 12936, 12938, 12962, 12965, 12966, 12967, 13034, 13057, 13289, 13348, 14046, 14101, 14126, 14133, 14201, 14296, 14313, 14323, 14327, 14328, 14378, 14384, 14439, 14440, 14441, 14941, 14980, 14999, 15000, 15001, 15002, 15006, 15046, 15066, 15067, 15073, 15074, 15126]

   Links to problems not solved by Maple:

   [133, 485, 550, 553, 958, 959, 961, 962, 964, 966, 968, 1039, 1046, 1075, 1697, 1700, 1701, 1702, 1703, 1704, 1706, 1707, 1935, 1938, 1953, 1984, 1985, 2026, 2063, 2707, 2713, 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, 4386, 4914, 4917, 4951, 4954, 4962, 4995, 5247, 6111, 6169, 6183, 6185, 6264, 6549, 7063, 7316, 7345, 8384, 8385, 8387, 8392, 8393, 8411, 8416, 8419, 8424, 8447, 8457, 8538, 8539, 8541, 8542, 8555, 8570, 8573, 8586, 8589, 8601, 8605, 8676, 8703, 9068, 9124, 9125, 9170, 9172, 9219, 9228, 9246, 9254, 10339, 10346, 10359, 10361, 10363, 10401, 10406, 10418, 10426, 10432, 10436, 10438, 10440, 10445, 10461, 10476, 10479, 10480, 10481, 10483, 10487, 10501, 10503, 10514, 10516, 10532, 10545, 10547, 10554, 10562, 10563, 10566, 10571, 10572, 10575, 10580, 10581, 10584, 10589, 10590, 10593, 10597, 10598, 10603, 10604, 10606, 10607, 10609, 10611, 10612, 10613, 10614, 10615, 10616, 10617, 10618, 10620, 10623, 10624, 10625, 10626, 10628, 10632, 10636, 10637, 10638, 10639, 10640, 10641, 10642, 10643, 10644, 10645, 10646, 10647, 10648, 10649, 10655, 10659, 10661, 10664, 10669, 10670, 10676, 10677, 10678, 10679, 10680, 10687, 10688, 10690, 10691, 10692, 10697, 10699, 10700, 10704, 10705, 10708, 10709, 10710, 10711, 10712, 10713, 10715, 10716, 10717, 10718, 10719, 10720, 10721, 10722, 10723, 10724, 10733, 10734, 10735, 10736, 10737, 10741, 10747, 10748, 10749, 10750, 10751, 10755, 10757, 10758, 10759, 10760, 10761, 10762, 10763, 10764, 10766, 10767, 10769, 10770, 10771, 10772, 10774, 10775, 10777, 10778, 10779, 10781, 10782, 10783, 10784, 10785, 10786, 10787, 10791, 10792, 10794, 10795, 10797, 10798, 10799, 10800, 10801, 10802, 10805, 10808, 10812, 10813, 10815, 10816, 10817, 10820, 10822, 10823, 11198, 11415, 11518, 11599, 11604, 11994, 11995, 12134, 12214, 12218, 12220, 12631, 12636, 12938, 13034, 13057, 13289, 13348, 14101, 14126, 14133, 14296, 14313, 14323, 14327, 14328, 14440, 14441, 14941, 15001, 15059]

10. System of differential equations.

    Number of problems 827.

    Solved by Mathematica: 96.49%

    Solved by Maple: 96.74%

    Links to problems not solved by Mathematica:

    [6104, 6542, 6543, 10213, 10228, 10238, 10241, 10242, 10243, 10244, 10245, 10250, 10251, 10254, 10255, 10256, 10257, 10258, 10259, 10261, 12827, 12828, 12829, 12830, 12842, 14043, 15506, 15517, 15524]

    Links to problems not solved by Maple:

    [6104, 6542, 6543, 6716, 6719, 10213, 10228, 10238, 10241, 10242, 10243, 10244, 10245, 10250, 10251, 10254, 10256, 10257, 10259, 10261, 12827, 12828, 12829, 12830, 12842, 14043, 15524]

11. Third and higher order homogeneous ODE.

    Number of problems 599.

    Solved by Mathematica: 94.32%

    Solved by Maple: 94.49%

    Links to problems not solved by Mathematica:

    [813, 5817, 9362, 9413, 9784, 9785, 9786, 9787, 9788, 9789, 9790, 9800, 9801, 9803, 9811, 9816, 9827, 9840, 9841, 9856, 9865, 9866, 9867, 9868, 9895, 9913, 10162, 10163, 10173, 10174, 10178, 13535, 13559, 15221]

    Links to problems not solved by Maple:

    [813, 5817, 9362, 9413, 9784, 9785, 9786, 9787, 9788, 9789, 9790, 9800, 9801, 9803, 9811, 9816, 9835, 9840, 9856, 9865, 9866, 9867, 9868, 9905, 9913, 10162, 10163, 10173, 10174, 10178, 13535, 13559, 15197]

12. Third and higher order linear ODE.

    Number of problems 1016.

    Solved by Mathematica: 96.85%

    Solved by Maple: 97.24%

    Links to problems not solved by Mathematica:

    [813, 5817, 9362, 9413, 9784, 9785, 9786, 9787, 9788, 9789, 9790, 9800, 9801, 9803, 9811, 9816, 9827, 9840, 9841, 9856, 9865, 9866, 9867, 9868, 9875, 9895, 9904, 9909, 9913, 12223, 12227, 13559]

    Links to problems not solved by Maple:

    [813, 5817, 9362, 9413, 9784, 9785, 9786, 9787, 9788, 9789, 9790, 9800, 9801, 9803, 9811, 9816, 9835, 9840, 9856, 9865, 9866, 9867, 9868, 9904, 9905, 9909, 9913, 13559]

13. Third and higher order non-linear ODE.

    Number of problems 38.

    Solved by Mathematica: 65.79%

    Solved by Maple: 65.79%

    Links to problems not solved by Mathematica:

    [10161, 10162, 10163, 10164, 10173, 10174, 10178, 12226, 12238, 12240, 12243, 13535, 15221]

    Links to problems not solved by Maple:

    [10161, 10162, 10163, 10164, 10173, 10174, 10178, 12226, 12238, 12240, 12243, 13535, 15197]

14. First order ode non-linear in derivative.

    Number of problems 943.

    Solved by Mathematica: 93.21%

    Solved by Maple: 95.65%

    Links to problems not solved by Mathematica:

    [2316, 2319, 2350, 3000, 3229, 3231, 3232, 3236, 4011, 4146, 4216, 4251, 4252, 4253, 4260, 4261, 4266, 4274, 4275, 4278, 4287, 4290, 4294, 4299, 4305, 4315, 5346, 6797, 6807, 6811, 6813, 6874, 6878, 7253, 7254, 8706, 8731, 8766, 8795, 8796, 8815, 8817, 8824, 8838, 8841, 8845, 8866, 8907, 8910, 8911, 11212, 11215, 11219, 11224, 11240, 11404, 12127, 12129, 12148, 12239, 15095, 15124, 15125, 15129]

    Links to problems not solved by Maple:

    [2316, 2319, 3995, 4011, 4040, 4146, 4163, 4198, 4199, 4216, 4287, 4298, 4315, 4343, 6820, 7253, 8704, 8706, 8719, 8731, 8787, 8795, 8796, 8815, 8817, 8820, 8838, 8841, 8845, 8848, 8866, 8872, 8878, 8907, 8910, 8911, 11224, 11230, 11404, 12239, 12421]

15. Higher order, non-linear and homogeneous.

    Number of problems 26.

    Solved by Mathematica: 73.08%

    Solved by Maple: 73.08%

    Links to problems not solved by Mathematica:

    [10162, 10163, 10173, 10174, 10178, 13535, 15221]

    Links to problems not solved by Maple:

    [10162, 10163, 10173, 10174, 10178, 13535, 15197]

16. Higher order, non-linear and non-homogeneous.

    Number of problems 12.

    Solved by Mathematica: 50.00%

    Solved by Maple: 50.00%

    Links to problems not solved by Mathematica:

    [10161, 10164, 12226, 12238, 12240, 12243]

    Links to problems not solved by Maple:

    [10161, 10164, 12226, 12238, 12240, 12243]

17. Second order, non-linear and homogeneous.

    Number of problems 422.

    Solved by Mathematica: 74.64%

    Solved by Maple: 80.09%

    Links to problems not solved by Mathematica:

    [2304, 2307, 2308, 4658, 4668, 4839, 4840, 4841, 6100, 6246, 6839, 6840, 6858, 7214, 7411, 9914, 9924, 9926, 9928, 9929, 9934, 9935, 9936, 9938, 9939, 9940, 9942, 9946, 9948, 9949, 9957, 9959, 9960, 9962, 9965, 9966, 9967, 9968, 9971, 9972, 9981, 9982, 9983, 9985, 9986, 9987, 9988, 9989, 9990, 9995, 9996, 9998, 10001, 10003, 10009, 10013, 10015, 10016, 10025, 10027, 10031, 10033, 10036, 10042, 10055, 10058, 10061, 10065, 10074, 10080, 10084, 10085, 10100, 10111, 10112, 10120, 10129, 10130, 10134, 10138, 10139, 10141, 10142, 10143, 10144, 10150, 10154, 10156, 10159, 11331, 12241, 12256, 12495, 12570, 12571, 13520, 13523, 13524, 13529, 14516, 14517, 15204, 15210, 15211, 15444, 15446, 15449]

    Links to problems not solved by Maple:

    [2304, 2309, 6238, 7214, 7411, 9924, 9928, 9929, 9934, 9935, 9938, 9939, 9940, 9942, 9946, 9948, 9949, 9957, 9959, 9960, 9962, 9965, 9966, 9967, 9968, 9971, 9972, 9981, 9982, 9983, 9985, 9986, 9987, 9988, 9989, 9990, 9995, 9996, 9998, 10003, 10009, 10013, 10015, 10016, 10025, 10027, 10028, 10029, 10031, 10032, 10033, 10036, 10042, 10044, 10055, 10058, 10061, 10065, 10074, 10080, 10084, 10085, 10100, 10111, 10112, 10120, 10129, 10130, 10131, 10138, 10139, 10143, 10144, 10154, 10157, 10158, 10159, 12241, 12570, 12571, 13529, 15444, 15446, 15449]

18. Second order, non-linear and non-homogeneous.

    Number of problems 128.

    Solved by Mathematica: 68.75%

    Solved by Maple: 71.09%

    Links to problems not solved by Mathematica:

    [710, 6856, 7107, 7108, 7110, 7212, 8386, 9916, 9918, 9919, 9921, 9922, 9931, 9932, 9941, 9947, 9950, 9951, 10000, 10005, 10007, 10008, 10018, 10019, 10052, 10057, 10060, 10062, 10102, 10103, 10124, 10125, 10148, 10155, 10725, 12269, 13250, 14050, 14051, 14626]

    Links to problems not solved by Maple:

    [710, 7107, 7110, 8386, 9916, 9918, 9919, 9921, 9922, 9931, 9932, 9941, 9947, 9950, 9951, 10000, 10005, 10007, 10008, 10018, 10019, 10021, 10052, 10057, 10060, 10062, 10124, 10125, 10148, 10155, 10725, 12269, 13250, 14050, 14051, 14626, 15217]

19. Third and higher order non-homogeneous ODE.

    Number of problems 455.

    Solved by Mathematica: 97.58%

    Solved by Maple: 98.24%

    Links to problems not solved by Mathematica:

    [9875, 9904, 9909, 10161, 10164, 12223, 12226, 12227, 12238, 12240, 12243]

    Links to problems not solved by Maple:

    [9904, 9909, 10161, 10164, 12226, 12238, 12240, 12243]

20. Second or higher order ODE with constant coefficients.

    Number of problems 2834.

    Solved by Mathematica: 99.61%

    Solved by Maple: 99.79%

    Links to problems not solved by Mathematica:

    [11589, 11590, 12198, 14121, 14870, 15382, 15384, 15385, 15386, 15453, 15459]

    Links to problems not solved by Maple:

    [6513, 11589, 11590, 14121, 14870, 15453]

21. Higher order, Linear, Homogeneous and constant coefficients.

    Number of problems 389.

    Solved by Mathematica: 100.00%

    Solved by Maple: 100.00%

    Links to problems not solved by Mathematica:

    []

    Links to problems not solved by Maple:

    []

22. Higher order, Linear, Homogeneous and non-constant coefficients.

    Number of problems 184.

    Solved by Mathematica: 85.33%

    Solved by Maple: 85.87%

    Links to problems not solved by Mathematica:

    [813, 5817, 9362, 9413, 9784, 9785, 9786, 9787, 9788, 9789, 9790, 9800, 9801, 9803, 9811, 9816, 9827, 9840, 9841, 9856, 9865, 9866, 9867, 9868, 9895, 9913, 13559]

    Links to problems not solved by Maple:

    [813, 5817, 9362, 9413, 9784, 9785, 9786, 9787, 9788, 9789, 9790, 9800, 9801, 9803, 9811, 9816, 9835, 9840, 9856, 9865, 9866, 9867, 9868, 9905, 9913, 13559]

23. Higher order, Linear, non-homogeneous and constant coefficients.

    Number of problems 373.

    Solved by Mathematica: 100.00%

    Solved by Maple: 100.00%

    Links to problems not solved by Mathematica:

    []

    Links to problems not solved by Maple:

    []

24. Second or higher order ODE with non-constant coefficients.

    Number of problems 3380.

    Solved by Mathematica: 90.27%

    Solved by Maple: 92.43%

    Links to problems not solved by Mathematica:

    [710, 813, 1105, 1162, 1186, 2304, 2307, 2308, 4658, 4668, 4839, 4840, 4841, 5813, 5817, 5818, 6100, 6246, 6839, 6840, 6856, 6858, 7107, 7108, 7110, 7178, 7179, 7182, 7183, 7187, 7189, 7212, 7214, 7288, 7411, 7462, 7554, 7556, 7976, 7978, 8386, 9349, 9353, 9360, 9362, 9364, 9365, 9371, 9405, 9406, 9407, 9408, 9409, 9413, 9487, 9535, 9542, 9546, 9565, 9607, 9634, 9690, 9720, 9730, 9736, 9747, 9762, 9767, 9768, 9769, 9771, 9784, 9785, 9786, 9787, 9788, 9789, 9790, 9800, 9801, 9803, 9811, 9816, 9827, 9840, 9841, 9856, 9865, 9866, 9867, 9868, 9875, 9895, 9904, 9909, 9913, 9914, 9916, 9918, 9919, 9921, 9922, 9924, 9926, 9928, 9929, 9931, 9932, 9934, 9935, 9936, 9938, 9939, 9940, 9941, 9942, 9946, 9947, 9948, 9949, 9950, 9951, 9957, 9959, 9960, 9962, 9965, 9966, 9967, 9968, 9971, 9972, 9981, 9982, 9983, 9985, 9986, 9987, 9988, 9989, 9990, 9995, 9996, 9998, 10000, 10001, 10003, 10005, 10007, 10008, 10009, 10013, 10015, 10016, 10018, 10019, 10025, 10027, 10031, 10033, 10036, 10042, 10052, 10055, 10057, 10058, 10060, 10061, 10062, 10065, 10074, 10080, 10084, 10085, 10100, 10102, 10103, 10111, 10112, 10120, 10124, 10125, 10129, 10130, 10134, 10138, 10139, 10141, 10142, 10143, 10144, 10148, 10150, 10154, 10155, 10156, 10159, 10161, 10162, 10163, 10164, 10173, 10174, 10178, 10725, 10833, 10840, 10841, 10856, 10861, 10872, 10874, 10875, 10876, 10877, 10878, 10881, 10882, 10883, 10884, 10892, 10902, 10908, 10915, 10921, 10922, 10924, 10925, 10926, 10927, 10928, 10933, 10943, 10945, 10946, 10966, 10967, 10968, 10972, 11012, 11025, 11029, 11030, 11032, 11036, 11039, 11052, 11055, 11056, 11065, 11066, 11067, 11068, 11069, 11070, 11071, 11072, 11073, 11074, 11078, 11079, 11081, 11082, 11084, 11085, 11086, 11087, 11095, 11100, 11103, 11118, 11119, 11121, 11310, 11311, 11329, 11331, 12050, 12223, 12226, 12227, 12238, 12240, 12241, 12243, 12248, 12249, 12250, 12251, 12252, 12256, 12258, 12264, 12269, 12281, 12352, 12354, 12412, 12495, 12570, 12571, 12614, 12748, 12749, 13250, 13520, 13523, 13524, 13529, 13535, 13559, 13569, 13570, 14050, 14051, 14472, 14473, 14516, 14517, 14626, 14633, 15204, 15210, 15211, 15221, 15436, 15444, 15446, 15449]

    Links to problems not solved by Maple:

    [710, 813, 1162, 1186, 2304, 2309, 5817, 5818, 5833, 6238, 7107, 7110, 7179, 7187, 7189, 7214, 7288, 7411, 8386, 9349, 9353, 9360, 9362, 9364, 9365, 9371, 9405, 9406, 9407, 9408, 9409, 9413, 9487, 9535, 9542, 9546, 9565, 9607, 9736, 9767, 9768, 9769, 9771, 9784, 9785, 9786, 9787, 9788, 9789, 9790, 9800, 9801, 9803, 9811, 9816, 9835, 9840, 9856, 9865, 9866, 9867, 9868, 9904, 9905, 9909, 9913, 9916, 9918, 9919, 9921, 9922, 9924, 9928, 9929, 9931, 9932, 9934, 9935, 9938, 9939, 9940, 9941, 9942, 9946, 9947, 9948, 9949, 9950, 9951, 9957, 9959, 9960, 9962, 9965, 9966, 9967, 9968, 9971, 9972, 9981, 9982, 9983, 9985, 9986, 9987, 9988, 9989, 9990, 9995, 9996, 9998, 10000, 10003, 10005, 10007, 10008, 10009, 10013, 10015, 10016, 10018, 10019, 10021, 10025, 10027, 10028, 10029, 10031, 10032, 10033, 10036, 10042, 10044, 10052, 10055, 10057, 10058, 10060, 10061, 10062, 10065, 10074, 10080, 10084, 10085, 10100, 10111, 10112, 10120, 10124, 10125, 10129, 10130, 10131, 10138, 10139, 10143, 10144, 10148, 10154, 10155, 10157, 10158, 10159, 10161, 10162, 10163, 10164, 10173, 10174, 10178, 10725, 10856, 10872, 10874, 10876, 10877, 10882, 10883, 10884, 10915, 10921, 10922, 10925, 10926, 10927, 10928, 10946, 10967, 10968, 10972, 11012, 11022, 11023, 11024, 11027, 11032, 11034, 11039, 11055, 11056, 11065, 11066, 11070, 11071, 11072, 11073, 11081, 11082, 11084, 11087, 11104, 11109, 11111, 11116, 11117, 11118, 11121, 11329, 12050, 12226, 12238, 12240, 12241, 12243, 12248, 12251, 12252, 12264, 12269, 12281, 12352, 12354, 12412, 12570, 12571, 12614, 12749, 13250, 13529, 13535, 13559, 13569, 13570, 14050, 14051, 14472, 14473, 14626, 14633, 15197, 15217, 15432, 15444, 15446, 15449]

25. Second order, Linear, Homogeneous and constant coefficients.

    Number of problems 665.

    Solved by Mathematica: 99.55%

    Solved by Maple: 99.55%

    Links to problems not solved by Mathematica:

    [11589, 11590, 15453]

    Links to problems not solved by Maple:

    [11589, 11590, 15453]

26. Second order, Linear, Homogeneous and non-constant coefficients.

    Number of problems 2082.

    Solved by Mathematica: 94.38%

    Solved by Maple: 96.25%

    Links to problems not solved by Mathematica:

    [1105, 5813, 5818, 7288, 7554, 7556, 7976, 7978, 9349, 9353, 9360, 9364, 9365, 9371, 9405, 9406, 9407, 9409, 9487, 9535, 9542, 9546, 9565, 9607, 9634, 9690, 9720, 9730, 9736, 9747, 9762, 9767, 9768, 9769, 9771, 10833, 10840, 10841, 10856, 10861, 10872, 10874, 10875, 10876, 10877, 10878, 10881, 10882, 10883, 10884, 10892, 10902, 10908, 10915, 10921, 10922, 10924, 10925, 10926, 10927, 10928, 10933, 10943, 10945, 10946, 10966, 10967, 10968, 10972, 11012, 11025, 11029, 11030, 11032, 11036, 11039, 11052, 11055, 11056, 11065, 11066, 11067, 11068, 11069, 11070, 11071, 11072, 11073, 11074, 11078, 11079, 11081, 11082, 11084, 11085, 11086, 11087, 11095, 11100, 11103, 11118, 11119, 11121, 11310, 11311, 11329, 12050, 12249, 12250, 12258, 12264, 12412, 12614, 13569, 13570, 14472, 14473]

    Links to problems not solved by Maple:

    [5818, 7288, 9349, 9353, 9360, 9364, 9365, 9371, 9405, 9406, 9407, 9409, 9487, 9535, 9542, 9546, 9565, 9607, 9736, 9767, 9768, 9769, 9771, 10856, 10872, 10874, 10876, 10877, 10882, 10883, 10884, 10915, 10921, 10922, 10925, 10926, 10927, 10928, 10946, 10967, 10968, 10972, 11012, 11022, 11023, 11024, 11027, 11032, 11034, 11039, 11055, 11056, 11065, 11066, 11070, 11071, 11072, 11073, 11081, 11082, 11084, 11087, 11104, 11109, 11111, 11116, 11117, 11118, 11121, 11329, 12050, 12264, 12412, 12614, 13569, 13570, 14472, 14473]

27. Second order, Linear, non-homogeneous and constant coefficients.

    Number of problems 1407.

    Solved by Mathematica: 99.43%

    Solved by Maple: 99.79%

    Links to problems not solved by Mathematica:

    [12198, 14121, 14870, 15382, 15384, 15385, 15386, 15459]

    Links to problems not solved by Maple:

    [6513, 14121, 14870]

28. Higher order, Linear, non-homogeneous and non-constant coefficients.

    Number of problems 70.

    Solved by Mathematica: 92.86%

    Solved by Maple: 97.14%

    Links to problems not solved by Mathematica:

    [9875, 9904, 9909, 12223, 12227]

    Links to problems not solved by Maple:

    [9904, 9909]

29. Second order, Linear, non-homogeneous and non-constant coefficients.

    Number of problems 456.

    Solved by Mathematica: 95.61%

    Solved by Maple: 96.49%

    Links to problems not solved by Mathematica:

    [1162, 1186, 7178, 7179, 7182, 7183, 7187, 7189, 7462, 9408, 12248, 12251, 12252, 12281, 12352, 12354, 12748, 12749, 14633, 15436]

    Links to problems not solved by Maple:

    [1162, 1186, 5833, 7179, 7187, 7189, 9408, 12248, 12251, 12252, 12281, 12352, 12354, 12749, 14633, 15432]