Problems 1401 to 1500

Table 2.31: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

1401	$[\begin{matrix} x_{1}^{'} = 3 x_{1} - 2 x_{2} \\ x_{2}^{'} = 4 x_{1} - x_{2} \end{matrix}]$	system_of_ODEs	✓	0.576

1402	$[\begin{matrix} x_{1}^{'} = - x_{1} - 4 x_{2} \\ x_{2}^{'} = x_{1} - x_{2} \end{matrix}]$	system_of_ODEs	✓	0.497

1403	$[\begin{matrix} x_{1}^{'} = 2 x_{1} - 5 x_{2} \\ x_{2}^{'} = x_{1} - 2 x_{2} \end{matrix}]$	system_of_ODEs	✓	0.417

1404	$[\begin{matrix} x_{1}^{'} = 2 x_{1} - \frac{5 x_{2}}{2} \\ x_{2}^{'} = \frac{9 x_{1}}{5} - x_{2} \end{matrix}]$	system_of_ODEs	✓	0.572

1405	$[\begin{matrix} x_{1}^{'} = x_{1} - x_{2} \\ x_{2}^{'} = 5 x_{1} - 3 x_{2} \end{matrix}]$	system_of_ODEs	✓	0.537

1406	$[\begin{matrix} x_{1}^{'} = x_{1} + 2 x_{2} \\ x_{2}^{'} = - 5 x_{1} - x_{2} \end{matrix}]$	system_of_ODEs	✓	0.471

1407	$[\begin{matrix} x_{1}^{'} = x_{1} \\ x_{2}^{'} = 2 x_{1} + x_{2} - 2 x_{3} \\ x_{3}^{'} = 3 x_{1} + 2 x_{2} + x_{3} \end{matrix}]$	system_of_ODEs	✓	0.667

1408	$[\begin{matrix} x_{1}^{'} = - 3 x_{1} + 2 x_{3} \\ x_{2}^{'} = x_{1} - x_{2} \\ x_{3}^{'} = - 2 x_{1} - x_{2} \end{matrix}]$	system_of_ODEs	✓	1.719

1409	$[\begin{matrix} x_{1}^{'} = x_{1} - 5 x_{2} \\ x_{2}^{'} = x_{1} - 3 x_{2} \end{matrix}]$ i.c.	system_of_ODEs	✓	0.589

1410	$[\begin{matrix} x_{1}^{'} = - 3 x_{1} + 2 x_{2} \\ x_{2}^{'} = - x_{1} - x_{2} \end{matrix}]$ i.c.	system_of_ODEs	✓	0.629

1411	$[\begin{matrix} x_{1}^{'} = \frac{3 x_{1}}{4} - 2 x_{2} \\ x_{2}^{'} = x_{1} - \frac{5 x_{2}}{4} \end{matrix}]$	system_of_ODEs	✓	0.581

1412	$[\begin{matrix} x_{1}^{'} = - \frac{4 x_{1}}{5} + 2 x_{2} \\ x_{2}^{'} = - x_{1} + \frac{6 x_{2}}{5} \end{matrix}]$	system_of_ODEs	✓	0.652

1413	$[\begin{matrix} x_{1}^{'} = - \frac{x_{1}}{4} + x_{2} \\ x_{2}^{'} = - x_{1} - \frac{x_{2}}{4} \\ x_{3}^{'} = - \frac{x_{3}}{4} \end{matrix}]$	system_of_ODEs	✓	0.502

1414	$[\begin{matrix} x_{1}^{'} = - \frac{x_{1}}{4} + x_{2} \\ x_{2}^{'} = - x_{1} - \frac{x_{2}}{4} \\ x_{3}^{'} = \frac{x_{3}}{10} \end{matrix}]$	system_of_ODEs	✓	0.576

1415	$[\begin{matrix} x_{1}^{'} = - \frac{x_{1}}{2} - \frac{x_{2}}{8} \\ x_{2}^{'} = 2 x_{1} - \frac{x_{2}}{2} \end{matrix}]$	system_of_ODEs	✓	0.491

1416	$[\begin{matrix} x_{1}^{'} = 3 x_{1} - 4 x_{2} \\ x_{2}^{'} = x_{1} - x_{2} \end{matrix}]$	system_of_ODEs	✓	0.339

1417	$[\begin{matrix} x_{1}^{'} = 4 x_{1} - 2 x_{2} \\ x_{2}^{'} = 8 x_{1} - 4 x_{2} \end{matrix}]$	system_of_ODEs	✓	0.285

1418	$[\begin{matrix} x_{1}^{'} = - \frac{3 x_{1}}{2} + x_{2} \\ x_{2}^{'} = - \frac{x_{1}}{4} - \frac{x_{2}}{2} \end{matrix}]$	system_of_ODEs	✓	0.327

1419	$[\begin{matrix} x_{1}^{'} = - 3 x_{1} + \frac{5 x_{2}}{2} \\ x_{2}^{'} = - \frac{5 x_{1}}{2} + 2 x_{2} \end{matrix}]$	system_of_ODEs	✓	0.342

1420	$[\begin{matrix} x_{1}^{'} = x_{1} + x_{2} + x_{3} \\ x_{2}^{'} = 2 x_{1} + x_{2} - x_{3} \\ x_{3}^{'} = - x_{2} + x_{3} \end{matrix}]$	system_of_ODEs	✓	0.607

1421	$[\begin{matrix} x_{1}^{'} = x_{2} + x_{3} \\ x_{2}^{'} = x_{1} + x_{3} \\ x_{3}^{'} = x_{1} + x_{2} \end{matrix}]$	system_of_ODEs	✓	0.443

1422	$[\begin{matrix} x_{1}^{'} = x_{1} - 4 x_{2} \\ x_{2}^{'} = 4 x_{1} - 7 x_{2} \end{matrix}]$ i.c.	system_of_ODEs	✓	0.503

1423	$[\begin{matrix} x_{1}^{'} = - \frac{5 x_{1}}{2} + \frac{3 x_{2}}{2} \\ x_{2}^{'} = - \frac{3 x_{1}}{2} + \frac{x_{2}}{2} \end{matrix}]$ i.c.	system_of_ODEs	✓	0.513

1424	$[\begin{matrix} x_{1}^{'} = 2 x_{1} + \frac{3 x_{2}}{2} \\ x_{2}^{'} = - \frac{3 x_{1}}{2} - x_{2} \end{matrix}]$ i.c.	system_of_ODEs	✓	0.546

1425	$[\begin{matrix} x_{1}^{'} = 3 x_{1} + 9 x_{2} \\ x_{2}^{'} = - x_{1} - 3 x_{2} \end{matrix}]$ i.c.	system_of_ODEs	✓	0.363

1426	$[\begin{matrix} x_{1}^{'} = x_{1} \\ x_{2}^{'} = - 4 x_{1} + x_{2} \\ x_{3}^{'} = 3 x_{1} + 6 x_{2} + 2 x_{3} \end{matrix}]$ i.c.	system_of_ODEs	✓	0.481

1427	$[\begin{matrix} x_{1}^{'} = - \frac{5 x_{1}}{2} + x_{2} + x_{3} \\ x_{2}^{'} = x_{1} - \frac{5 x_{2}}{2} + x_{3} \\ x_{3}^{'} = x_{1} + x_{2} - \frac{5 x_{3}}{2} \end{matrix}]$ i.c.	system_of_ODEs	✓	0.550

1428	$[\begin{matrix} x_{1}^{'} = 2 x_{1} - x_{2} + e^{t} \\ x_{2}^{'} = 3 x_{1} - 2 x_{2} + t \end{matrix}]$	system_of_ODEs	✓	0.932

1429	$[\begin{matrix} x_{1}^{'} = x_{1} + \sqrt{3} x_{2} + e^{t} \\ x_{2}^{'} = \sqrt{3} x_{1} - x_{2} + \sqrt{3} e^{- t} \end{matrix}]$	system_of_ODEs	✓	1.969

1430	$[\begin{matrix} x_{1}^{'} = 2 x_{1} - 5 x_{2} - \cos (t) \\ x_{2}^{'} = x_{1} - 2 x_{2} + \sin (t) \end{matrix}]$	system_of_ODEs	✓	1.022

1431	$[\begin{matrix} x_{1}^{'} = x_{1} + x_{2} + e^{- 2 t} \\ x_{2}^{'} = 4 x_{1} - 2 x_{2} - 2 e^{t} \end{matrix}]$	system_of_ODEs	✓	0.705

1432	$[\begin{matrix} x_{1}^{'} = 4 x_{1} - 2 x_{2} + \frac{1}{t^{3}} \\ x_{2}^{'} = 8 x_{1} - 4 x_{2} - \frac{1}{t^{2}} \end{matrix}]$	system_of_ODEs	✓	0.535

1433	$[\begin{matrix} x_{1}^{'} = - 4 x_{1} + 2 x_{2} + \frac{1}{t} \\ x_{2}^{'} = 2 x_{1} - x_{2} + \frac{2}{t} + 4 \end{matrix}]$	system_of_ODEs	✓	0.565

1434	$[\begin{matrix} x_{1}^{'} = x_{1} + x_{2} + 2 e^{t} \\ x_{2}^{'} = 4 x_{1} + x_{2} - e^{t} \end{matrix}]$	system_of_ODEs	✓	0.621

1435	$[\begin{matrix} x_{1}^{'} = 2 x_{1} - x_{2} + e^{t} \\ x_{2}^{'} = 3 x_{1} - 2 x_{2} - e^{t} \end{matrix}]$	system_of_ODEs	✓	0.776

1436	$[\begin{matrix} x_{1}^{'} = - \frac{5 x_{1}}{4} + \frac{3 x_{2}}{4} + 2 t \\ x_{2}^{'} = \frac{3 x_{1}}{4} - \frac{5 x_{2}}{4} + e^{t} \end{matrix}]$	system_of_ODEs	✓	0.884

1437	$[\begin{matrix} x_{1}^{'} = - 3 x_{1} + \sqrt{2} x_{2} + e^{- t} \\ x_{2}^{'} = \sqrt{2} x_{1} - 2 x_{2} - e^{- t} \end{matrix}]$	system_of_ODEs	✓	1.441

1438	$[\begin{matrix} x_{1}^{'} = 2 x_{1} - 5 x_{2} \\ x_{2}^{'} = x_{1} - 2 x_{2} + \cos (t) \end{matrix}]$	system_of_ODEs	✓	1.080

1439	$[\begin{matrix} x_{1}^{'} = 2 x_{1} - 5 x_{2} + \csc (t) \\ x_{2}^{'} = x_{1} - 2 x_{2} + \sec (t) \end{matrix}]$	system_of_ODEs	✓	1.282

1440	$[\begin{matrix} x_{1}^{'} = - \frac{x_{1}}{2} - \frac{x_{2}}{8} + \frac{e^{- \frac{t}{2}}}{2} \\ x_{2}^{'} = 2 x_{1} - \frac{x_{2}}{2} \end{matrix}]$	system_of_ODEs	✓	0.769

1441	$[\begin{matrix} x_{1}^{'} = - 2 x_{1} + x_{2} + 2 e^{- t} \\ x_{2}^{'} = x_{1} - 2 x_{2} + 3 t \end{matrix}]$ i.c.	system_of_ODEs	✓	0.981

1442	$[\begin{matrix} x_{1}^{'} = 3 x_{1} - 2 x_{2} \\ x_{2}^{'} = 2 x_{1} - 2 x_{2} \end{matrix}]$	system_of_ODEs	✓	0.423

1443	$[\begin{matrix} x_{1}^{'} = 5 x_{1} - x_{2} \\ x_{2}^{'} = 3 x_{1} + x_{2} \end{matrix}]$	system_of_ODEs	✓	0.380

1444	$[\begin{matrix} x_{1}^{'} = 2 x_{1} - x_{2} \\ x_{2}^{'} = 3 x_{1} - 2 x_{2} \end{matrix}]$	system_of_ODEs	✓	0.353

1445	$[\begin{matrix} x_{1}^{'} = x_{1} - 4 x_{2} \\ x_{2}^{'} = 4 x_{1} - 7 x_{2} \end{matrix}]$	system_of_ODEs	✓	0.326

1446	$[\begin{matrix} x_{1}^{'} = x_{1} - 5 x_{2} \\ x_{2}^{'} = x_{1} - 3 x_{2} \end{matrix}]$	system_of_ODEs	✓	0.566

1447	$[\begin{matrix} x_{1}^{'} = 2 x_{1} - 5 x_{2} \\ x_{2}^{'} = x_{1} - 2 x_{2} \end{matrix}]$	system_of_ODEs	✓	0.465

1448	$[\begin{matrix} x_{1}^{'} = 3 x_{1} - 2 x_{2} \\ x_{2}^{'} = 4 x_{1} - x_{2} \end{matrix}]$	system_of_ODEs	✓	0.549

1449	$[\begin{matrix} x_{1}^{'} = - x_{1} - x_{2} \\ x_{2}^{'} = - \frac{5 x_{2}}{2} \end{matrix}]$	system_of_ODEs	✓	0.418

1450	$[\begin{matrix} x_{1}^{'} = 3 x_{1} - 4 x_{2} \\ x_{2}^{'} = x_{1} - x_{2} \end{matrix}]$	system_of_ODEs	✓	0.354

1451	$[\begin{matrix} x_{1}^{'} = x_{1} + 2 x_{2} \\ x_{2}^{'} = - 5 x_{1} \end{matrix}]$	system_of_ODEs	✓	0.717

1452	$[\begin{matrix} x_{1}^{'} = - x_{1} \\ x_{2}^{'} = - x_{2} \end{matrix}]$	system_of_ODEs	✓	0.234

1453	$[\begin{matrix} x_{1}^{'} = 2 x_{1} - \frac{5 x_{2}}{2} \\ x_{2}^{'} = \frac{9 x_{1}}{5} - x_{2} \end{matrix}]$	system_of_ODEs	✓	0.622

1454	$[\begin{matrix} x_{1}^{'} = x_{1} + x_{2} - 2 \\ x_{2}^{'} = x_{1} - x_{2} \end{matrix}]$	system_of_ODEs	✓	0.829

1455	$[\begin{matrix} x_{1}^{'} = - 2 x_{1} + x_{2} - 2 \\ x_{2}^{'} = x_{1} - 2 x_{2} + 1 \end{matrix}]$	system_of_ODEs	✓	0.742

1456	$[\begin{matrix} x_{1}^{'} = - x_{1} - x_{2} - 1 \\ x_{2}^{'} = 2 x_{1} - x_{2} + 5 \end{matrix}]$	system_of_ODEs	✓	0.927

1457	$[\begin{matrix} x^{'} = - x \\ y^{'} = - 2 y \end{matrix}]$ i.c.	system_of_ODEs	✓	0.388

1458	$[\begin{matrix} x^{'} = - x \\ y^{'} = 2 y \end{matrix}]$ i.c.	system_of_ODEs	✓	0.361

1459	$[\begin{matrix} x^{'} = - x \\ y^{'} = 2 y \end{matrix}]$ i.c.	system_of_ODEs	✓	0.407

1460	$[\begin{matrix} x^{'} = - y \\ y^{'} = x \end{matrix}]$ i.c.	system_of_ODEs	✓	0.482

1461	$[\begin{matrix} x^{'} = - y \\ y^{'} = x \end{matrix}]$ i.c.	system_of_ODEs	✓	0.418

1462	$y^{''''} + 4 y^{'''} + 3 y = t$	[[_high_order, _with_linear_symmetries]]	✓	0.198

1463	$t (t - 1) y^{''''} + e^{t} y^{''} + 4 t^{2} y = 0$	[[_high_order, _with_linear_symmetries]]	✗	0.094

1464	$y^{''''} + y^{''} = 0$	[[_high_order, _missing_x]]	✓	0.081

1465	$y^{'''} + 2 y^{''} - y^{'} - 2 y = 0$	[[_3rd_order, _missing_x]]	✓	0.080

1466	$x y^{'''} - y^{''} = 0$	[[_3rd_order, _missing_y]]	✓	1.074

1467	$x^{3} y^{'''} + x^{2} y^{''} - 2 y^{'} x + 2 y = 0$	[[_3rd_order, _exact, _linear, _homogeneous]]	✓	0.148

1468	$y^{'''} + 2 y^{''} - y^{'} - 3 y = 0$	[[_3rd_order, _missing_x]]	✓	0.141

1469	$t y^{'''} + 2 y^{''} - y^{'} + t y = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.065

1470	$(2 - t) y^{'''} + (2 t - 3) y^{''} - y^{'} t + y = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.089

1471	$t^{2} (t + 3) y^{'''} - 3 t (t + 2) y^{''} + 6 (1 + t) y^{'} - 6 y = 0$	[[_3rd_order, _with_linear_symmetries]]	✗	0.093

1472	$y^{'''} - y^{''} - y^{'} + y = 0$	[[_3rd_order, _missing_x]]	✓	0.085

1473	$y^{'''} - 3 y^{''} + 3 y^{'} + y = 0$	[[_3rd_order, _missing_x]]	✓	0.106

1474	$y^{''''} - 4 y^{'''} + 4 y^{''} = 0$	[[_high_order, _missing_x]]	✓	0.085

1475	$y^{(6)} + y = 0$	[[_high_order, _missing_x]]	✓	0.131

1476	$y^{(6)} - 3 y^{''''} + 3 y^{''} - y = 0$	[[_high_order, _missing_x]]	✓	0.095

1477	$y^{(6)} - y^{''} = 0$	[[_high_order, _missing_x]]	✓	0.088

1478	$y^{(5)} - 3 y^{''''} + 3 y^{'''} - 3 y^{''} + 2 y^{'} = 0$	[[_high_order, _missing_x]]	✓	0.097

1479	$y^{(8)} + 8 y^{''''} + 16 y = 0$	[[_high_order, _missing_x]]	✓	0.115

1480	$y^{''''} + 2 y^{''} + y = 0$	[[_high_order, _missing_x]]	✓	0.101

1481	$y^{'''} + 5 y^{''} + 6 y^{'} + 2 y = 0$	[[_3rd_order, _missing_x]]	✓	0.091

1482	$y^{''''} - 7 y^{'''} + 6 y^{''} + 30 y^{'} - 36 y = 0$	[[_high_order, _missing_x]]	✓	0.095

1483	$y^{''} - y^{'} - 6 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.318

1484	$y^{''} + 3 y^{'} + 2 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.310

1485	$y^{''} - 2 y^{'} + 2 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.359

1486	$y^{''} - 2 y^{'} + 4 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.488

1487	$y^{''} + 2 y^{'} + 5 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.458

1488	$y^{''''} - 4 y^{'''} + 6 y^{''} - 4 y^{'} + y = 0$ i.c.	[[_high_order, _missing_x]]	✓	0.472

1489	$y^{''''} - 4 y = 0$ i.c.	[[_high_order, _missing_x]]	✓	0.558

1490	$y^{''} + ω^{2} y = \cos (2 t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.454

1491	$y^{''} - 2 y^{'} + 2 y = e^{- t}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.528

1492	$y^{''} + 4 y = {\begin{array}{cc} 1 & 0 \leq t < π \\ 0 & π \leq t < \infty \end{array}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.067

1493	$y^{''} + 4 y = {\begin{array}{cc} 1 & 0 \leq t < 1 \\ 0 & 1 \leq t < \infty \end{array}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.215

1494	$y^{''} + y = {\begin{array}{cc} t & 0 \leq t < 1 \\ 2 - t & 1 \leq t < 2 \\ 0 & 2 \leq t < \infty \end{array}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.424

1495	$y^{''} + y = {\begin{array}{cc} 1 & 0 \leq t < 3 π \\ 0 & 3 π \leq t < \infty \end{array}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.246

1496	$y^{''} + 2 y^{'} + 2 y = {\begin{array}{cc} 1 & π \leq t < 2 π \\ 0 & otherwise \end{array}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	2.664

1497	$y^{''} + 4 y = \sin (t) - Heaviside (t - 2 π) \sin (t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.823

1498	$y^{''} + 3 y^{'} + 2 y = {\begin{array}{cc} 1 & 0 \leq t < 10 \\ 0 & otherwise \end{array}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.552

1499	$y^{''} + y^{'} + \frac{5 y}{4} = t - Heaviside (t - \frac{π}{2}) (t - \frac{π}{2})$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	2.004

1500	$y^{''} + y^{'} + \frac{5 y}{4} = {\begin{array}{cc} \sin (t) & 0 \leq t < π \\ 0 & otherwise \end{array}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	2.119

2.2.15 Problems 1401 to 1500