Problems 1501 to 1600

Table 2.33: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

1501	$y^{''} + 4 y = Heaviside (t - π) - Heaviside (t - 3 π)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.811

1502	$y^{''''} + 5 y^{''} + 4 y = 1 - Heaviside (t - π)$ i.c.	[[_high_order, _linear, _nonhomogeneous]]	✓	5.174

1503	$u^{''} + \frac{u^{'}}{4} + u = k (Heaviside (t - \frac{3}{2}) - Heaviside (t - \frac{5}{2}))$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	4.664

1504	$u^{''} + \frac{u^{'}}{4} + u = \frac{Heaviside (t - \frac{3}{2})}{2} - \frac{Heaviside (t - \frac{5}{2})}{2}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	4.540

1505	$u^{''} + \frac{u^{'}}{4} + u = \frac{Heaviside (t - 5) (t - 5) - Heaviside (t - 5 - k) (t - 5 - k)}{k}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	5.308

1506	$y^{''} + 2 y^{'} + 2 y = δ (t - π)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.983

1507	$y^{''} + 4 y = δ (t - π) - δ (t - 2 π)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.732

1508	$y^{''} + 3 y^{'} + 2 y = δ (t - 5) + Heaviside (t - 10)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.136

1509	$y^{''} + 2 y^{'} + 3 y = \sin (t) + δ (t - 3 π)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	2.086

1510	$y^{''} + y = δ (t - 2 π) \cos (t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.658

1511	$y^{''} + 4 y = 2 δ (t - \frac{π}{4})$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.602

1512	$y^{''} + 2 y^{'} + 2 y = \cos (t) + δ (t - \frac{π}{2})$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.383

1513	$y^{''''} - y = δ (t - 1)$ i.c.	[[_high_order, _linear, _nonhomogeneous]]	✓	5.467

1514	$y^{''} + \frac{y^{'}}{2} + y = δ (t - 1)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.294

1515	$y^{''} + \frac{y^{'}}{4} + y = δ (t - 1)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.368

1516	$y^{''} + y = \frac{Heaviside (t - 4 + k) - Heaviside (t - 4 - k)}{2 k}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	5.070

1517	$y^{''} + 2 y^{'} + 2 y = f (t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.833

1518	$y^{''} + 2 y^{'} + 2 y = δ (t - π)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.780

1519	$y^{'} = 2 y$	[_quadrature]	✓	1.636

1520	$x y^{'} + y = x^{2}$	[_linear]	✓	1.458

1521	$y^{'} + 2 x y = x$	[_separable]	✓	1.482

1522	$2 y^{'} + x (y^{2} - 1) = 0$	[_separable]	✓	2.076

1523	$y^{'} = x^{2} (1 + y^{2})$	[_separable]	✓	2.003

1524	$y^{'} = - x$	[_quadrature]	✓	0.442

1525	$y^{'} = - x \sin (x)$	[_quadrature]	✓	0.569

1526	$y^{'} = \ln (x) x$	[_quadrature]	✓	0.424

1527	$y^{'} = - x e^{x}$ i.c.	[_quadrature]	✓	0.703

1528	$y^{'} = x \sin (x^{2})$ i.c.	[_quadrature]	✓	0.845

1529	$y^{'} = \tan (x)$ i.c.	[_quadrature]	✓	1.175

1530	$y^{'} = \cos (x) - y \tan (x)$ i.c.	[_linear]	✓	2.088

1531	$y^{'} = \frac{x^{2} - 2 x^{2} y + 2}{x^{3}}$ i.c.	[_linear]	✓	1.642

1532	$y^{'} = x (1 + y^{2})$ i.c.	[_separable]	✓	2.535

1533	$y^{'} = - \frac{y (y + 1)}{x}$ i.c.	[_separable]	✓	2.583

1534	$y^{'} = a y^{\frac{a - 1}{a}}$	[_quadrature]	✓	1.316

1535	$y^{'} = \| y \| + 1$ i.c.	[_quadrature]	✓	2.090

1536	$y^{'} = - \frac{x}{2} - 1 + \frac{\sqrt{x^{2} + 4 x + 4 y}}{2}$	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	1.851

1537	$y^{'} + a y = 0$	[_quadrature]	✓	0.820

1538	$y^{'} + 3 x^{2} y = 0$	[_separable]	✓	1.615

1539	$x y^{'} + y \ln (x) = 0$	[_separable]	✓	1.878

1540	$x y^{'} + 3 y = 0$	[_separable]	✓	2.214

1541	$x^{2} y^{'} + y = 0$	[_separable]	✓	1.762

1542	$y^{'} + \frac{(x + 1) y}{x} = 0$ i.c.	[_separable]	✓	2.191

1543	$x y^{'} + (1 + \frac{1}{\ln (x)}) y = 0$ i.c.	[_separable]	✓	2.335

1544	$x y^{'} + (1 + x \cot (x)) y = 0$ i.c.	[_separable]	✓	2.600

1545	$y^{'} - \frac{2 x y}{x^{2} + 1} = 0$ i.c.	[_separable]	✓	1.951

1546	$y^{'} + \frac{k y}{x} = 0$ i.c.	[_separable]	✓	1.344

1547	$y^{'} + \tan (k x) y = 0$ i.c.	[_separable]	✓	2.803

1548	$y^{'} + 3 y = 1$	[_quadrature]	✓	1.590

1549	$y^{'} + (\frac{1}{x} - 1) y = - \frac{2}{x}$	[_linear]	✓	1.243

1550	$y^{'} + 2 x y = x e^{- x^{2}}$	[_linear]	✓	2.644

1551	$y^{'} + \frac{2 x y}{x^{2} + 1} = \frac{e^{- x^{2}}}{x^{2} + 1}$	[_linear]	✓	1.673

1552	$y^{'} + \frac{y}{x} = \frac{7}{x^{2}} + 3$	[_linear]	✓	1.275

1553	$y^{'} + \frac{4 y}{- 1 + x} = \frac{1}{{(- 1 + x)}^{5}} + \frac{\sin (x)}{{(- 1 + x)}^{4}}$	[_linear]	✓	4.993

1554	$x y^{'} + (2 x^{2} + 1) y = x^{3} e^{- x^{2}}$	[_linear]	✓	2.922

1555	$x y^{'} + 2 y = \frac{2}{x^{2}} + 1$	[_linear]	✓	1.289

1556	$y^{'} + y \tan (x) = \cos (x)$	[_linear]	✓	1.872

1557	$(x + 1) y^{'} + 2 y = \frac{\sin (x)}{x + 1}$	[_linear]	✓	2.848

1558	$(- 2 + x) (- 1 + x) y^{'} - (4 x - 3) y = {(- 2 + x)}^{3}$	[_linear]	✓	3.202

1559	$y^{'} + 2 \sin (x) \cos (x) y = e^{- \sin {(x)}^{2}}$	[_linear]	✓	2.300

1560	$x^{2} y^{'} + 3 x y = e^{x}$	[_linear]	✓	1.354

1561	$y^{'} + 7 y = e^{3 x}$ i.c.	[[_linear, ‘class A‘]]	✓	1.676

1562	$(x^{2} + 1) y^{'} + 4 x y = \frac{2}{x^{2} + 1}$ i.c.	[_linear]	✓	3.235

1563	$x y^{'} + 3 y = \frac{2}{x (x^{2} + 1)}$ i.c.	[_linear]	✓	2.049

1564	$y^{'} + \cot (x) y = \cos (x)$ i.c.	[_linear]	✓	2.186

1565	$y^{'} + \frac{y}{x} = \frac{2}{x^{2}} + 1$ i.c.	[_linear]	✓	1.382

1566	$(- 1 + x) y^{'} + 3 y = \frac{1}{{(- 1 + x)}^{3}} + \frac{\sin (x)}{{(- 1 + x)}^{2}}$ i.c.	[_linear]	✓	4.314

1567	$x y^{'} + 2 y = 8 x^{2}$ i.c.	[_linear]	✓	2.026

1568	$x y^{'} - 2 y = - x^{2}$ i.c.	[_linear]	✓	1.654

1569	$y^{'} + 2 x y = x$ i.c.	[_separable]	✓	1.950

1570	$(- 1 + x) y^{'} + 3 y = \frac{1 + (- 1 + x) \sec {(x)}^{2}}{{(- 1 + x)}^{3}}$ i.c.	[_linear]	✓	10.086

1571	$(x + 2) y^{'} + 4 y = \frac{2 x^{2} + 1}{x {(x + 2)}^{3}}$ i.c.	[_linear]	✓	1.660

1572	$(x^{2} - 1) y^{'} - 2 x y = x (x^{2} - 1)$ i.c.	[_linear]	✓	1.952

1573	$x y^{'} - 2 y = - 1$ i.c.	[_separable]	✓	2.415

1574	$\sec {(y)}^{2} y^{'} - 3 \tan (y) = - 1$	[_quadrature]	✓	2.165

1575	$e^{y^{2}} (2 y y^{'} + \frac{2}{x}) = \frac{1}{x^{2}}$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	2.149

1576	$\frac{x y^{'}}{y} + 2 \ln (y) = 4 x^{2}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	2.544

1577	$\frac{y^{'}}{{(y + 1)}^{2}} - \frac{1}{x (y + 1)} = - \frac{3}{x^{2}}$	[[_homogeneous, ‘class C‘], _rational, _Riccati]	✓	1.936

1578	$y^{'} = \frac{3 x^{2} + 2 x + 1}{- 2 + y}$	[_separable]	✓	1.930

1579	$\sin (x) \sin (y) + \cos (y) y^{'} = 0$	[_separable]	✓	3.681

1580	$x y^{'} + y^{2} + y = 0$	[_separable]	✓	2.232

1581	$(3 y^{3} + 3 y \cos (y) + 1) y^{'} + \frac{(2 x + 1) y}{x^{2} + 1} = 0$	[_separable]	✓	3.691

1582	$x^{2} y y^{'} = {(y^{2} - 1)}^{3 / 2}$	[_separable]	✓	8.691

1583	$y^{'} = x^{2} (1 + y^{2})$	[_separable]	✓	2.178

1584	$(x^{2} + 1) y^{'} + x y = 0$	[_separable]	✓	1.674

1585	$y^{'} = (- 1 + x) (y - 1) (- 2 + y)$	[_separable]	✓	3.009

1586	${(y - 1)}^{2} y^{'} = 2 x + 3$	[_separable]	✓	2.050

1587	$y^{'} = \frac{x^{2} + 3 x + 2}{- 2 + y}$ i.c.	[_separable]	✓	2.398

1588	$y^{'} + x (y^{2} + y) = 0$ i.c.	[_separable]	✓	2.826

1589	$(3 y^{2} + 4 y) y^{'} + 2 x + \cos (x) = 0$ i.c.	[_separable]	✓	692.329

1590	$y^{'} + \frac{(y + 1) (y - 1) (- 2 + y)}{x + 1} = 0$ i.c.	[_separable]	✓	16.816

1591	$y^{'} + 2 x (y + 1) = 0$ i.c.	[_separable]	✓	1.925

1592	$y^{'} = 2 x y (1 + y^{2})$ i.c.	[_separable]	✓	11.476

1593	$y^{'} (x^{2} + 2) = 4 x (y^{2} + 2 y + 1)$	[_separable]	✓	2.602

1594	$y^{'} = - 2 x (y^{3} - 3 y + 2)$ i.c.	[_separable]	✓	4.819

1595	$y^{'} = \frac{2 x}{2 y + 1}$ i.c.	[_separable]	✓	3.513

1596	$y^{'} = 2 y - y^{2}$ i.c.	[_quadrature]	✓	2.688

1597	$x + y y^{'} = 0$ i.c.	[_separable]	✓	4.448

1598	$y^{'} + x^{2} (y + 1) {(- 2 + y)}^{2} = 0$	[_separable]	✓	3.488

1599	$(x + 1) (- 2 + x) y^{'} + y = 0$ i.c.	[_separable]	✓	2.164

1600	$y^{'} = \frac{1 + y^{2}}{x^{2} + 1}$	[_separable]	✓	2.283

2.2.16 Problems 1501 to 1600