1.2 Results

The current number of partial differential equations in this report is [ 2014 ].

Mathematica solved [ 1462 ] and Maple solved [ 1802 ].

Table 1.1:Percentage solved by each CAS for all problems


Mathematica Maple


72.59% 89.47%


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Table 1.2:Pecentage of solved by each CAS broken down by each chapter




chapter name Number of Problems Mathematica Maple




Miscellaneous PDE’s 142 73.94% 91.55%




Schrodinger PDE 8 100.% 87.5%




Parabolic PDE’s (Diffusion) 131 91.6% 85.5%




Elliptic PDE’s (Laplace, Poisson, Helmholtz) 53 71.7% 75.47%




Hyperbolic PDE’s (Wave) 83 91.57% 85.54%




Handbook of first order partial differential equations 1585 70.28% 90.66%




Handbook of nonlinear partial differential equations 12 8.33% 41.67%




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Table 1.3:Percentage of failed due to time out among all problems that could not be solved


Mathematica Maple


7.25% 12.74%


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Table 1.4:Total real time used to solve all problems


Mathematica Maple


14.46 (hours) 9.07 (hours)


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Table 1.5:Average real time used to solve one problem


Mathematica Maple


25.851 (sec) 16.214 (sec)


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List of problems not solved by Maple nor by Mathematica [175] (8.69%)

32, 48, 57, 61, 112, 119, 124, 128, 129, 130, 170, 171, 274, 279, 280, 281, 309, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 334, 363, 364, 415, 456, 457, 458, 460, 476, 489, 490, 491, 494, 510, 518, 522, 523, 527, 528, 530, 532, 533, 545, 551, 559, 561, 563, 565, 566, 569, 622, 624, 625, 629, 630, 631, 652, 674, 675, 697, 700, 713, 714, 722, 725, 726, 737, 738, 748, 749, 750, 759, 760, 762, 763, 767, 768, 770, 772, 773, 774, 777, 778, 779, 781, 782, 785, 786, 787, 788, 789, 793, 804, 805, 810, 817, 818, 823, 824, 825, 826, 827, 828, 829, 833, 834, 835, 836, 837, 838, 839, 840, 841, 842, 843, 1031, 1174, 1181, 1196, 1368, 1379, 1380, 1382, 1385, 1386, 1387, 1388, 1389, 1415, 1418, 1419, 1423, 1430, 1431, 1452, 1453, 1454, 1455, 1459, 1464, 1465, 1557, 1576, 1579, 1580, 1630, 1631, 1634, 1728, 1738, 1750, 1751, 1802, 1803, 1908, 1909, 1916, 1917, 1918, 1920, 1926, 2003, 2005, 2010, 2011, 2012, 2013, 2014

List of problems solved by Maple but not by Mathematica [377] (18.72%)

16, 29, 34, 40, 67, 78, 93, 94, 95, 96, 97, 98, 100, 101, 109, 110, 111, 113, 114, 117, 120, 121, 123, 125, 126, 131, 133, 175, 183, 205, 215, 231, 299, 306, 312, 361, 396, 397, 410, 431, 451, 455, 459, 461, 462, 466, 467, 468, 471, 478, 482, 484, 486, 487, 488, 492, 495, 496, 501, 506, 507, 508, 509, 520, 521, 524, 526, 529, 531, 534, 539, 544, 553, 556, 560, 562, 572, 576, 578, 579, 580, 581, 585, 586, 591, 592, 593, 594, 595, 600, 601, 602, 603, 614, 617, 620, 623, 627, 636, 637, 638, 644, 645, 646, 648, 649, 650, 651, 654, 658, 659, 660, 661, 662, 663, 664, 665, 666, 670, 671, 673, 677, 678, 679, 680, 681, 684, 685, 686, 693, 698, 699, 701, 702, 703, 704, 707, 709, 711, 712, 719, 721, 723, 724, 731, 733, 735, 743, 745, 747, 755, 757, 758, 761, 771, 776, 780, 784, 790, 792, 794, 795, 797, 798, 800, 802, 803, 806, 807, 808, 809, 811, 812, 813, 814, 815, 816, 819, 820, 821, 822, 831, 832, 877, 886, 887, 903, 904, 909, 919, 931, 996, 1003, 1006, 1020, 1021, 1038, 1039, 1059, 1060, 1067, 1068, 1081, 1086, 1109, 1180, 1182, 1183, 1197, 1210, 1211, 1212, 1213, 1236, 1237, 1264, 1269, 1281, 1354, 1362, 1367, 1376, 1377, 1383, 1384, 1392, 1412, 1416, 1422, 1424, 1425, 1427, 1438, 1439, 1443, 1448, 1449, 1456, 1457, 1458, 1461, 1463, 1470, 1471, 1477, 1482, 1483, 1488, 1489, 1492, 1493, 1494, 1495, 1513, 1514, 1525, 1529, 1531, 1560, 1561, 1565, 1577, 1578, 1588, 1609, 1610, 1620, 1632, 1650, 1652, 1657, 1666, 1668, 1669, 1673, 1680, 1686, 1691, 1697, 1699, 1700, 1701, 1702, 1705, 1706, 1711, 1713, 1716, 1717, 1721, 1722, 1729, 1731, 1732, 1733, 1734, 1735, 1739, 1740, 1742, 1744, 1746, 1747, 1748, 1749, 1759, 1780, 1781, 1785, 1791, 1793, 1801, 1805, 1811, 1816, 1820, 1822, 1826, 1828, 1831, 1837, 1838, 1839, 1842, 1846, 1847, 1849, 1853, 1855, 1860, 1865, 1867, 1868, 1869, 1870, 1873, 1874, 1876, 1879, 1880, 1882, 1885, 1886, 1890, 1891, 1900, 1901, 1902, 1903, 1904, 1907, 1911, 1913, 1915, 1919, 1933, 1940, 1950, 1953, 1960, 1962, 1965, 1966, 1968, 1971, 1972, 1976, 1981, 1986, 1991, 1995, 2000, 2001, 2006, 2007, 2008, 2009

List of problems solved by Mathematica but not by Maple [37] (1.84%)

87, 88, 148, 167, 204, 227, 265, 266, 267, 269, 270, 271, 272, 273, 277, 278, 302, 366, 395, 401, 403, 405, 411, 412, 413, 414, 1204, 1411, 1426, 1535, 1640, 1646, 1707, 1708, 1841, 1875, 1906

List of problems not solved by Mathematica [552] (27.41%)

16, 29, 32, 34, 40, 48, 57, 61, 67, 78, 93, 94, 95, 96, 97, 98, 100, 101, 109, 110, 111, 112, 113, 114, 117, 119, 120, 121, 123, 124, 125, 126, 128, 129, 130, 131, 133, 170, 171, 175, 183, 205, 215, 231, 274, 279, 280, 281, 299, 306, 309, 312, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 334, 361, 363, 364, 396, 397, 410, 415, 431, 451, 455, 456, 457, 458, 459, 460, 461, 462, 466, 467, 468, 471, 476, 478, 482, 484, 486, 487, 488, 489, 490, 491, 492, 494, 495, 496, 501, 506, 507, 508, 509, 510, 518, 520, 521, 522, 523, 524, 526, 527, 528, 529, 530, 531, 532, 533, 534, 539, 544, 545, 551, 553, 556, 559, 560, 561, 562, 563, 565, 566, 569, 572, 576, 578, 579, 580, 581, 585, 586, 591, 592, 593, 594, 595, 600, 601, 602, 603, 614, 617, 620, 622, 623, 624, 625, 627, 629, 630, 631, 636, 637, 638, 644, 645, 646, 648, 649, 650, 651, 652, 654, 658, 659, 660, 661, 662, 663, 664, 665, 666, 670, 671, 673, 674, 675, 677, 678, 679, 680, 681, 684, 685, 686, 693, 697, 698, 699, 700, 701, 702, 703, 704, 707, 709, 711, 712, 713, 714, 719, 721, 722, 723, 724, 725, 726, 731, 733, 735, 737, 738, 743, 745, 747, 748, 749, 750, 755, 757, 758, 759, 760, 761, 762, 763, 767, 768, 770, 771, 772, 773, 774, 776, 777, 778, 779, 780, 781, 782, 784, 785, 786, 787, 788, 789, 790, 792, 793, 794, 795, 797, 798, 800, 802, 803, 804, 805, 806, 807, 808, 809, 810, 811, 812, 813, 814, 815, 816, 817, 818, 819, 820, 821, 822, 823, 824, 825, 826, 827, 828, 829, 831, 832, 833, 834, 835, 836, 837, 838, 839, 840, 841, 842, 843, 877, 886, 887, 903, 904, 909, 919, 931, 996, 1003, 1006, 1020, 1021, 1031, 1038, 1039, 1059, 1060, 1067, 1068, 1081, 1086, 1109, 1174, 1180, 1181, 1182, 1183, 1196, 1197, 1210, 1211, 1212, 1213, 1236, 1237, 1264, 1269, 1281, 1354, 1362, 1367, 1368, 1376, 1377, 1379, 1380, 1382, 1383, 1384, 1385, 1386, 1387, 1388, 1389, 1392, 1412, 1415, 1416, 1418, 1419, 1422, 1423, 1424, 1425, 1427, 1430, 1431, 1438, 1439, 1443, 1448, 1449, 1452, 1453, 1454, 1455, 1456, 1457, 1458, 1459, 1461, 1463, 1464, 1465, 1470, 1471, 1477, 1482, 1483, 1488, 1489, 1492, 1493, 1494, 1495, 1513, 1514, 1525, 1529, 1531, 1557, 1560, 1561, 1565, 1576, 1577, 1578, 1579, 1580, 1588, 1609, 1610, 1620, 1630, 1631, 1632, 1634, 1650, 1652, 1657, 1666, 1668, 1669, 1673, 1680, 1686, 1691, 1697, 1699, 1700, 1701, 1702, 1705, 1706, 1711, 1713, 1716, 1717, 1721, 1722, 1728, 1729, 1731, 1732, 1733, 1734, 1735, 1738, 1739, 1740, 1742, 1744, 1746, 1747, 1748, 1749, 1750, 1751, 1759, 1780, 1781, 1785, 1791, 1793, 1801, 1802, 1803, 1805, 1811, 1816, 1820, 1822, 1826, 1828, 1831, 1837, 1838, 1839, 1842, 1846, 1847, 1849, 1853, 1855, 1860, 1865, 1867, 1868, 1869, 1870, 1873, 1874, 1876, 1879, 1880, 1882, 1885, 1886, 1890, 1891, 1900, 1901, 1902, 1903, 1904, 1907, 1908, 1909, 1911, 1913, 1915, 1916, 1917, 1918, 1919, 1920, 1926, 1933, 1940, 1950, 1953, 1960, 1962, 1965, 1966, 1968, 1971, 1972, 1976, 1981, 1986, 1991, 1995, 2000, 2001, 2003, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014

List of problems not solved by Maple [212] (10.53%)

32, 48, 57, 61, 87, 88, 112, 119, 124, 128, 129, 130, 148, 167, 170, 171, 204, 227, 265, 266, 267, 269, 270, 271, 272, 273, 274, 277, 278, 279, 280, 281, 302, 309, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 334, 363, 364, 366, 395, 401, 403, 405, 411, 412, 413, 414, 415, 456, 457, 458, 460, 476, 489, 490, 491, 494, 510, 518, 522, 523, 527, 528, 530, 532, 533, 545, 551, 559, 561, 563, 565, 566, 569, 622, 624, 625, 629, 630, 631, 652, 674, 675, 697, 700, 713, 714, 722, 725, 726, 737, 738, 748, 749, 750, 759, 760, 762, 763, 767, 768, 770, 772, 773, 774, 777, 778, 779, 781, 782, 785, 786, 787, 788, 789, 793, 804, 805, 810, 817, 818, 823, 824, 825, 826, 827, 828, 829, 833, 834, 835, 836, 837, 838, 839, 840, 841, 842, 843, 1031, 1174, 1181, 1196, 1204, 1368, 1379, 1380, 1382, 1385, 1386, 1387, 1388, 1389, 1411, 1415, 1418, 1419, 1423, 1426, 1430, 1431, 1452, 1453, 1454, 1455, 1459, 1464, 1465, 1535, 1557, 1576, 1579, 1580, 1630, 1631, 1634, 1640, 1646, 1707, 1708, 1728, 1738, 1750, 1751, 1802, 1803, 1841, 1875, 1906, 1908, 1909, 1916, 1917, 1918, 1920, 1926, 2003, 2005, 2010, 2011, 2012, 2013, 2014

List of problems that are hand solved [195] (9.68%)

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 24, 26, 27, 28, 29, 30, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 84, 85, 102, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 167, 169, 172, 173, 176, 177, 178, 179, 181, 182, 184, 185, 186, 192, 195, 196, 199, 200, 201, 202, 203, 204, 207, 208, 209, 210, 211, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 233, 235, 236, 237, 238, 248, 253, 254, 259, 260, 263, 264, 265, 269, 270, 271, 272, 273, 274, 276, 277, 282, 283, 284, 289, 291, 292, 293, 294, 308, 309, 311, 312, 314, 317, 328, 330, 334, 335, 336, 337, 338, 339, 344, 349, 350, 351, 354, 355, 356, 357, 358, 359, 360, 361, 365, 366, 367, 374, 375, 384, 389, 390, 392, 393, 394, 396, 397, 398, 399, 403, 406, 408, 411, 412, 413, 414, 415, 420, 422, 424, 425, 426, 427, 428, 429, 430, 1369, 1370, 1371, 1372, 1516, 1517, 1586, 1587

List of problems that are animated [60] (2.98%)

2, 3, 4, 5, 6, 7, 8, 9, 10, 152, 153, 155, 160, 162, 164, 177, 182, 192, 200, 203, 209, 210, 211, 220, 223, 228, 230, 236, 238, 260, 264, 265, 270, 271, 273, 274, 276, 277, 336, 337, 338, 351, 356, 358, 359, 360, 365, 374, 375, 384, 389, 390, 392, 393, 397, 398, 399, 408, 413, 414