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1.2 Results

The current number of partial differential equations in this report is [ 2013 ].

Mathematica solved [ 1318 ] and Maple solved [ 1796 ].

Table 1.1: Percentage solved by each CAS for all problems
Mathematica Maple
65.47% 89.22%

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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 150 66.67% 90.67%
Parabolic PDE’s (Diffusion) 130 40.% 83.85%
Elliptic PDE’s (Laplace, Poisson, Helmholtz) 53 35.85% 75.47%
Hyperbolic PDE’s (Wave) 83 43.37% 85.54%
Handbook of first order partial differential equations 1585 70.03% 90.54%
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
5.04% 16.59%

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Table 1.4: Total real time used to solve all problems
Mathematica Maple
12.35 (hours) 8.63 (hours)

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Table 1.5: Average real time used to solve one problem
Mathematica Maple
22.09 (sec) 15.437 (sec)

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List of problems not solved by Maple nor by Mathematica [198] (9.84%)

32, 33, 49, 58, 62, 120, 127, 132, 136, 137, 138, 170, 171, 176, 177, 195, 204, 227, 265, 266, 268, 269, 270, 271, 272, 273, 276, 277, 278, 279, 280, 308, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 333, 362, 363, 400, 410, 411, 412, 413, 414, 455, 456, 457, 459, 475, 488, 489, 490, 493, 509, 517, 521, 522, 526, 527, 529, 531, 532, 544, 550, 558, 560, 562, 564, 565, 568, 621, 623, 624, 628, 629, 630, 650, 651, 672, 673, 674, 696, 699, 712, 713, 721, 724, 725, 736, 737, 747, 748, 749, 758, 759, 761, 762, 766, 767, 769, 771, 772, 773, 776, 777, 778, 780, 781, 784, 785, 786, 787, 788, 792, 803, 804, 809, 816, 817, 822, 823, 824, 825, 826, 827, 828, 832, 833, 834, 835, 836, 837, 838, 839, 840, 841, 842, 1030, 1173, 1180, 1195, 1367, 1378, 1379, 1381, 1384, 1385, 1386, 1387, 1388, 1414, 1417, 1418, 1422, 1429, 1430, 1451, 1452, 1453, 1454, 1458, 1463, 1464, 1556, 1575, 1578, 1579, 1629, 1630, 1633, 1706, 1707, 1727, 1737, 1749, 1750, 1801, 1907, 1908, 1915, 1916, 1917, 1919, 1949, 2002, 2004, 2009, 2010, 2011, 2012, 2013

List of problems solved by Maple but not by Mathematica [497] (24.69%)

16, 29, 35, 41, 68, 79, 81, 82, 83, 101, 102, 103, 104, 105, 106, 108, 109, 110, 117, 118, 119, 121, 122, 125, 128, 129, 131, 133, 134, 139, 141, 142, 144, 145, 146, 147, 148, 149, 150, 159, 160, 161, 163, 166, 168, 169, 172, 173, 175, 188, 189, 190, 191, 192, 196, 197, 198, 205, 206, 207, 208, 209, 210, 211, 213, 214, 215, 219, 220, 221, 222, 224, 225, 226, 228, 229, 230, 231, 232, 233, 234, 240, 245, 246, 253, 254, 256, 257, 258, 259, 260, 261, 263, 264, 267, 274, 275, 286, 287, 288, 290, 291, 292, 293, 294, 298, 304, 305, 306, 310, 311, 312, 313, 315, 316, 317, 329, 331, 332, 334, 337, 338, 339, 340, 341, 342, 343, 345, 346, 347, 348, 349, 350, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 364, 371, 372, 375, 376, 380, 393, 395, 396, 401, 403, 408, 409, 415, 416, 430, 450, 454, 458, 460, 461, 462, 465, 466, 467, 470, 477, 481, 483, 485, 486, 487, 491, 494, 495, 500, 505, 506, 507, 508, 519, 520, 523, 525, 528, 530, 533, 538, 543, 552, 555, 559, 561, 571, 575, 577, 578, 579, 580, 584, 585, 590, 591, 592, 593, 594, 599, 600, 601, 602, 607, 611, 613, 616, 619, 622, 626, 635, 636, 637, 643, 644, 645, 647, 648, 649, 653, 657, 658, 659, 660, 661, 662, 663, 664, 665, 669, 670, 676, 677, 678, 679, 680, 683, 684, 685, 692, 697, 698, 700, 701, 702, 703, 706, 708, 710, 711, 718, 720, 722, 723, 730, 732, 734, 742, 744, 746, 754, 756, 757, 760, 770, 775, 779, 783, 789, 791, 793, 794, 796, 797, 799, 801, 802, 805, 806, 807, 808, 810, 811, 812, 813, 814, 815, 818, 819, 820, 821, 830, 831, 876, 885, 886, 902, 903, 908, 930, 995, 1002, 1005, 1019, 1020, 1037, 1038, 1058, 1059, 1066, 1067, 1080, 1085, 1108, 1179, 1181, 1182, 1196, 1209, 1211, 1212, 1235, 1236, 1263, 1268, 1280, 1353, 1361, 1366, 1375, 1376, 1382, 1383, 1391, 1411, 1415, 1421, 1423, 1424, 1426, 1431, 1437, 1438, 1442, 1447, 1448, 1455, 1456, 1457, 1460, 1462, 1469, 1470, 1476, 1481, 1482, 1487, 1488, 1491, 1492, 1493, 1494, 1512, 1513, 1524, 1528, 1530, 1559, 1560, 1564, 1576, 1577, 1587, 1608, 1609, 1619, 1631, 1649, 1651, 1656, 1665, 1667, 1668, 1672, 1679, 1685, 1690, 1696, 1698, 1699, 1700, 1701, 1704, 1705, 1710, 1711, 1712, 1715, 1716, 1720, 1721, 1728, 1730, 1731, 1732, 1733, 1734, 1738, 1739, 1741, 1743, 1745, 1746, 1747, 1748, 1758, 1779, 1780, 1784, 1790, 1792, 1800, 1802, 1804, 1810, 1815, 1819, 1821, 1825, 1827, 1830, 1836, 1837, 1838, 1841, 1845, 1846, 1848, 1852, 1854, 1859, 1864, 1866, 1867, 1868, 1869, 1872, 1873, 1875, 1878, 1879, 1881, 1884, 1885, 1889, 1890, 1899, 1900, 1901, 1902, 1903, 1906, 1910, 1912, 1914, 1918, 1932, 1939, 1952, 1959, 1961, 1964, 1965, 1967, 1970, 1971, 1975, 1980, 1985, 1990, 1994, 1999, 2000, 2005, 2006, 2007, 2008

List of problems solved by Mathematica but not by Maple [19] (0.94%)

87, 95, 96, 167, 301, 365, 394, 402, 404, 1203, 1410, 1425, 1534, 1639, 1645, 1840, 1874, 1905, 1925

List of problems not solved by Mathematica [695] (34.53%)

16, 29, 32, 33, 35, 41, 49, 58, 62, 68, 79, 81, 82, 83, 101, 102, 103, 104, 105, 106, 108, 109, 110, 117, 118, 119, 120, 121, 122, 125, 127, 128, 129, 131, 132, 133, 134, 136, 137, 138, 139, 141, 142, 144, 145, 146, 147, 148, 149, 150, 159, 160, 161, 163, 166, 168, 169, 170, 171, 172, 173, 175, 176, 177, 188, 189, 190, 191, 192, 195, 196, 197, 198, 204, 205, 206, 207, 208, 209, 210, 211, 213, 214, 215, 219, 220, 221, 222, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 240, 245, 246, 253, 254, 256, 257, 258, 259, 260, 261, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 286, 287, 288, 290, 291, 292, 293, 294, 298, 304, 305, 306, 308, 310, 311, 312, 313, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 329, 331, 332, 333, 334, 337, 338, 339, 340, 341, 342, 343, 345, 346, 347, 348, 349, 350, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 363, 364, 371, 372, 375, 376, 380, 393, 395, 396, 400, 401, 403, 408, 409, 410, 411, 412, 413, 414, 415, 416, 430, 450, 454, 455, 456, 457, 458, 459, 460, 461, 462, 465, 466, 467, 470, 475, 477, 481, 483, 485, 486, 487, 488, 489, 490, 491, 493, 494, 495, 500, 505, 506, 507, 508, 509, 517, 519, 520, 521, 522, 523, 525, 526, 527, 528, 529, 530, 531, 532, 533, 538, 543, 544, 550, 552, 555, 558, 559, 560, 561, 562, 564, 565, 568, 571, 575, 577, 578, 579, 580, 584, 585, 590, 591, 592, 593, 594, 599, 600, 601, 602, 607, 611, 613, 616, 619, 621, 622, 623, 624, 626, 628, 629, 630, 635, 636, 637, 643, 644, 645, 647, 648, 649, 650, 651, 653, 657, 658, 659, 660, 661, 662, 663, 664, 665, 669, 670, 672, 673, 674, 676, 677, 678, 679, 680, 683, 684, 685, 692, 696, 697, 698, 699, 700, 701, 702, 703, 706, 708, 710, 711, 712, 713, 718, 720, 721, 722, 723, 724, 725, 730, 732, 734, 736, 737, 742, 744, 746, 747, 748, 749, 754, 756, 757, 758, 759, 760, 761, 762, 766, 767, 769, 770, 771, 772, 773, 775, 776, 777, 778, 779, 780, 781, 783, 784, 785, 786, 787, 788, 789, 791, 792, 793, 794, 796, 797, 799, 801, 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, 830, 831, 832, 833, 834, 835, 836, 837, 838, 839, 840, 841, 842, 876, 885, 886, 902, 903, 908, 930, 995, 1002, 1005, 1019, 1020, 1030, 1037, 1038, 1058, 1059, 1066, 1067, 1080, 1085, 1108, 1173, 1179, 1180, 1181, 1182, 1195, 1196, 1209, 1211, 1212, 1235, 1236, 1263, 1268, 1280, 1353, 1361, 1366, 1367, 1375, 1376, 1378, 1379, 1381, 1382, 1383, 1384, 1385, 1386, 1387, 1388, 1391, 1411, 1414, 1415, 1417, 1418, 1421, 1422, 1423, 1424, 1426, 1429, 1430, 1431, 1437, 1438, 1442, 1447, 1448, 1451, 1452, 1453, 1454, 1455, 1456, 1457, 1458, 1460, 1462, 1463, 1464, 1469, 1470, 1476, 1481, 1482, 1487, 1488, 1491, 1492, 1493, 1494, 1512, 1513, 1524, 1528, 1530, 1556, 1559, 1560, 1564, 1575, 1576, 1577, 1578, 1579, 1587, 1608, 1609, 1619, 1629, 1630, 1631, 1633, 1649, 1651, 1656, 1665, 1667, 1668, 1672, 1679, 1685, 1690, 1696, 1698, 1699, 1700, 1701, 1704, 1705, 1706, 1707, 1710, 1711, 1712, 1715, 1716, 1720, 1721, 1727, 1728, 1730, 1731, 1732, 1733, 1734, 1737, 1738, 1739, 1741, 1743, 1745, 1746, 1747, 1748, 1749, 1750, 1758, 1779, 1780, 1784, 1790, 1792, 1800, 1801, 1802, 1804, 1810, 1815, 1819, 1821, 1825, 1827, 1830, 1836, 1837, 1838, 1841, 1845, 1846, 1848, 1852, 1854, 1859, 1864, 1866, 1867, 1868, 1869, 1872, 1873, 1875, 1878, 1879, 1881, 1884, 1885, 1889, 1890, 1899, 1900, 1901, 1902, 1903, 1906, 1907, 1908, 1910, 1912, 1914, 1915, 1916, 1917, 1918, 1919, 1932, 1939, 1949, 1952, 1959, 1961, 1964, 1965, 1967, 1970, 1971, 1975, 1980, 1985, 1990, 1994, 1999, 2000, 2002, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013

List of problems not solved by Maple [217] (10.78%)

32, 33, 49, 58, 62, 87, 95, 96, 120, 127, 132, 136, 137, 138, 167, 170, 171, 176, 177, 195, 204, 227, 265, 266, 268, 269, 270, 271, 272, 273, 276, 277, 278, 279, 280, 301, 308, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 333, 362, 363, 365, 394, 400, 402, 404, 410, 411, 412, 413, 414, 455, 456, 457, 459, 475, 488, 489, 490, 493, 509, 517, 521, 522, 526, 527, 529, 531, 532, 544, 550, 558, 560, 562, 564, 565, 568, 621, 623, 624, 628, 629, 630, 650, 651, 672, 673, 674, 696, 699, 712, 713, 721, 724, 725, 736, 737, 747, 748, 749, 758, 759, 761, 762, 766, 767, 769, 771, 772, 773, 776, 777, 778, 780, 781, 784, 785, 786, 787, 788, 792, 803, 804, 809, 816, 817, 822, 823, 824, 825, 826, 827, 828, 832, 833, 834, 835, 836, 837, 838, 839, 840, 841, 842, 1030, 1173, 1180, 1195, 1203, 1367, 1378, 1379, 1381, 1384, 1385, 1386, 1387, 1388, 1410, 1414, 1417, 1418, 1422, 1425, 1429, 1430, 1451, 1452, 1453, 1454, 1458, 1463, 1464, 1534, 1556, 1575, 1578, 1579, 1629, 1630, 1633, 1639, 1645, 1706, 1707, 1727, 1737, 1749, 1750, 1801, 1840, 1874, 1905, 1907, 1908, 1915, 1916, 1917, 1919, 1925, 1949, 2002, 2004, 2009, 2010, 2011, 2012, 2013

List of problems that are hand solved [195] (9.69%)

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, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 92, 93, 110, 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, 268, 269, 270, 271, 272, 273, 275, 276, 281, 282, 283, 288, 290, 291, 292, 293, 307, 308, 310, 311, 313, 316, 327, 329, 333, 334, 335, 336, 337, 338, 343, 348, 349, 350, 353, 354, 355, 356, 357, 358, 359, 360, 364, 365, 366, 373, 374, 383, 388, 389, 391, 392, 393, 395, 396, 397, 398, 402, 405, 407, 410, 411, 412, 413, 414, 419, 421, 423, 424, 425, 426, 427, 428, 429, 1368, 1369, 1370, 1371, 1515, 1516, 1585, 1586

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, 269, 270, 272, 273, 275, 276, 335, 336, 337, 350, 355, 357, 358, 359, 364, 373, 374, 383, 388, 389, 391, 392, 396, 397, 398, 407, 412, 413

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