Problems 1601 to 1700

Table 2.35: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

1601	$y^{'} \sqrt{- x^{2} + 1} + \sqrt{1 - y^{2}} = 0$	[_separable]	✓	18.720

1602	$y^{'} = \frac{\cos (x)}{\sin (y)}$ i.c.	[_separable]	✓	2.329

1603	$y^{'} = a y - b y^{2}$ i.c.	[_quadrature]	✓	9.767

1604	$y^{'} + y = \frac{2 x e^{- x}}{1 + y e^{x}}$	[[_Abel, ‘2nd type‘, ‘class B‘]]	✓	2.479

1605	$y^{'} x - 2 y = \frac{x^{6}}{y + x^{2}}$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	4.616

1606	$y^{'} - y = \frac{(x + 1) e^{4 x}}{{(y + e^{x})}^{2}}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	2.705

1607	$y^{'} - 2 y = \frac{x e^{2 x}}{1 - y e^{- 2 x}}$	[[_Abel, ‘2nd type‘, ‘class A‘]]	✓	2.527

1608	$y^{'} = \frac{x^{2} + y^{2}}{\sin (x)}$	[_Riccati]	✗	7.978

1609	$y^{'} = \frac{y + e^{x}}{x^{2} + y^{2}}$	[‘y=_G(x,y’)‘]	✗	1.922

1610	$y^{'} = \tan (x y)$	[‘y=_G(x,y’)‘]	✗	1.462

1611	$y^{'} = \frac{x^{2} + y^{2}}{\ln (x y)}$	[‘y=_G(x,y’)‘]	✗	2.146

1612	$y^{'} = (x^{2} + y^{2}) y^{1 / 3}$	[‘y=_G(x,y’)‘]	✗	1.201

1613	$y^{'} = 2 x y$	[_separable]	✓	1.090

1614	$y^{'} = \ln (x^{2} + y^{2} + 1)$	[‘y=_G(x,y’)‘]	✗	1.220

1615	$y^{'} = \frac{2 x + 3 y}{x - 4 y}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	5.337

1616	$y^{'} = \sqrt{x^{2} + y^{2}}$	[‘y=_G(x,y’)‘]	✗	1.239

1617	$y^{'} = x {(- 1 + y^{2})}^{2 / 3}$	[_separable]	✓	1.606

1618	$y^{'} = {(x^{2} + y^{2})}^{2}$	[‘y=_G(x,y’)‘]	✗	0.985

1619	$y^{'} = \sqrt{x + y}$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	2.971

1620	$y^{'} = \frac{\tan (y)}{x - 1}$	[_separable]	✓	2.636

1621	$y^{'} = y^{2 / 5}$ i.c.	[_quadrature]	✓	1.449

1622	$y^{'} = 3 x {(- 1 + y)}^{1 / 3}$ i.c.	[_separable]	✓	6.931

1623	$y^{'} = 3 x {(- 1 + y)}^{1 / 3}$ i.c.	[_separable]	✓	11.231

1624	$y^{'} = 3 x {(- 1 + y)}^{1 / 3}$ i.c.	[_separable]	✓	8.339

1625	$y^{'} - y = x y^{2}$	[_Bernoulli]	✓	1.525

1626	$y^{'} = \frac{y + e^{- \frac{y}{x}} x}{x}$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	6.137

1627	$x^{2} y^{'} = y^{2} + x y - x^{2}$	[[_homogeneous, ‘class A‘], _rational, _Riccati]	✓	0.236

1628	$x^{2} y^{'} = y^{2} + x y - x^{2}$ i.c.	[[_homogeneous, ‘class A‘], _rational, _Riccati]	✓	2.991

1629	$y^{'} + y = y^{2}$	[_quadrature]	✓	0.219

1630	$7 y^{'} x - 2 y = - \frac{x^{2}}{y^{6}}$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	0.276

1631	$x^{2} y^{'} + 2 y = 2 e^{\frac{1}{x}} \sqrt{y}$	[_Bernoulli]	✓	0.654

1632	$(x^{2} + 1) y^{'} + 2 x y = \frac{1}{(x^{2} + 1) y}$	[_rational, _Bernoulli]	✓	0.629

1633	$y^{'} - x y = x^{3} y^{3}$	[_Bernoulli]	✓	0.575

1634	$y^{'} - \frac{(x + 1) y}{3 x} = y^{4}$	[_rational, _Bernoulli]	✓	0.951

1635	$y^{'} - 2 y = x y^{3}$ i.c.	[_Bernoulli]	✓	0.593

1636	$y^{'} - x y = x y^{3 / 2}$ i.c.	[_separable]	✓	4.777

1637	$y^{'} x + y = x^{4} y^{4}$ i.c.	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	0.596

1638	$y^{'} - 2 y = 2 \sqrt{y}$ i.c.	[_quadrature]	✓	1.597

1639	$y^{'} - 4 y = \frac{48 x}{y^{2}}$ i.c.	[_rational, _Bernoulli]	✓	0.932

1640	$x^{2} y^{'} + 2 x y = y^{3}$ i.c.	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	1.044

1641	$y^{'} - y = x \sqrt{y}$ i.c.	[_Bernoulli]	✗	0.806

1642	$y^{'} = \frac{x + y}{x}$	[_linear]	✓	1.408

1643	$y^{'} = \frac{y^{2} + 2 x y}{x^{2}}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	2.260

1644	$x y^{3} y^{'} = y^{4} + x^{4}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	6.309

1645	$y^{'} = \frac{y}{x} + \sec (\frac{y}{x})$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	6.351

1646	$x^{2} y^{'} = x^{2} + x y + y^{2}$	[[_homogeneous, ‘class A‘], _rational, _Riccati]	✓	2.001

1647	$x y^{'} y = x^{2} + 2 y^{2}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	4.506

1648	$y^{'} = \frac{2 y^{2} + x^{2} e^{- \frac{y^{2}}{x^{2}}}}{2 x y}$	[[_homogeneous, ‘class A‘]]	✓	4.530

1649	$y^{'} = \frac{x y + y^{2}}{x^{2}}$ i.c.	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	2.037

1650	$y^{'} = \frac{x^{3} + y^{3}}{x y^{2}}$ i.c.	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	82.111

1651	$x y^{'} y + x^{2} + y^{2} = 0$ i.c.	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	4.626

1652	$y^{'} = \frac{y^{2} - 3 x y - 5 x^{2}}{x^{2}}$ i.c.	[[_homogeneous, ‘class A‘], _rational, _Riccati]	✓	4.945

1653	$x^{2} y^{'} = 2 x^{2} + y^{2} + 4 x y$ i.c.	[[_homogeneous, ‘class A‘], _rational, _Riccati]	✓	2.779

1654	$x y^{'} y = 3 x^{2} + 4 y^{2}$ i.c.	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	4.835

1655	$y^{'} = \frac{x + y}{x - y}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.439

1656	$(y^{'} x - y) (\ln (y) - \ln (x)) = x$	[[_homogeneous, ‘class A‘]]	✓	5.511

1657	$y^{'} = \frac{y^{3} + 2 x y^{2} + x^{2} y + x^{3}}{x {(x + y)}^{2}}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	166.686

1658	$y^{'} = \frac{x + 2 y}{2 x + y}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	5.510

1659	$y^{'} = \frac{y}{y - 2 x}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	4.727

1660	$y^{'} = \frac{x y^{2} + 2 y^{3}}{x^{3} + x^{2} y + x y^{2}}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	226.384

1661	$y^{'} = \frac{x^{3} + x^{2} y + 3 y^{3}}{x^{3} + 3 x y^{2}}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	164.886

1662	$x^{2} y^{'} = y^{2} + x y - 4 x^{2}$ i.c.	[[_homogeneous, ‘class A‘], _rational, _Riccati]	✓	4.597

1663	$x y^{'} y = x^{2} - x y + y^{2}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	8.493

1664	$y^{'} = \frac{2 y^{2} - x y + 2 x^{2}}{x y + 2 x^{2}}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	123.408

1665	$y^{'} = \frac{x^{2} + x y + y^{2}}{x y}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	88.012

1666	$y^{'} = \frac{- 6 x + y - 3}{2 x - y - 1}$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.448

1667	$y^{'} = \frac{2 x + y + 1}{x + 2 y - 4}$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	9.261

1668	$y^{'} = \frac{- x + 3 y - 14}{x + y - 2}$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	2.475

1669	$3 x y^{2} y^{'} = y^{3} + x$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	2.231

1670	$x y^{'} y = 3 x^{6} + 6 y^{2}$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	2.309

1671	$x^{3} y^{'} = 2 y^{2} + 2 x^{2} y - 2 x^{4}$	[[_homogeneous, ‘class G‘], _rational, _Riccati]	✓	2.054

1672	$y^{'} = y^{2} e^{- x} + 4 y + 2 e^{x}$	[[_1st_order, _with_linear_symmetries], _Riccati]	✓	2.294

1673	$y^{'} = \frac{y^{2} + y \tan (x) + \tan {(x)}^{2}}{\sin {(x)}^{2}}$	[_Riccati]	✓	54.443

1674	$x \ln {(x)}^{2} y^{'} = - 4 \ln {(x)}^{2} + y \ln (x) + y^{2}$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], _Riccati]	✓	2.266

1675	$2 x (y + 2 \sqrt{x}) y^{'} = {(y + \sqrt{x})}^{2}$	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	2.795

1676	$(y + e^{x^{2}}) y^{'} = 2 x (y^{2} + y e^{x^{2}} + e^{2 x^{2}})$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], [_Abel, ‘2nd type‘, ‘class A‘]]	✓	2.922

1677	$y^{'} + \frac{2 y}{x} = \frac{3 x^{2} y^{2} + 6 x y + 2}{x^{2} (2 x y + 3)}$ i.c.	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	6.772

1678	$y^{'} + \frac{3 y}{x} = \frac{3 x^{4} y^{2} + 10 x^{2} y + 6}{x^{3} (2 x^{2} y + 5)}$ i.c.	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	5.153

1679	$y^{'} = 1 + x - (2 x + 1) y + x y^{2}$	[_Riccati]	✓	2.332

1680	$6 x^{2} y^{2} + 4 x^{3} y y^{'} = 0$	[_separable]	✓	2.025

1681	$3 \cos (x) y + 4 x e^{x} + 2 x^{3} y + (3 \sin (x) + 3) y^{'} = 0$	[_linear]	✓	165.939

1682	$14 x^{2} y^{3} + 21 x^{2} y^{2} y^{'} = 0$	[_quadrature]	✓	1.441

1683	$2 x - 2 y^{2} + (12 y^{2} - 4 x y) y^{'} = 0$	[_exact, _rational]	✓	1.309

1684	${(x + y)}^{2} + {(x + y)}^{2} y^{'} = 0$	[_quadrature]	✓	0.903

1685	$4 x + 7 y + (3 x + 4 y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	65.103

1686	$- 2 \sin (x) y^{2} + 3 y^{3} - 2 x + (4 \cos (x) y + 9 x y^{2}) y^{'} = 0$	[_exact]	✓	35.036

1687	$2 x + y + (2 y + 2 x) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	5.869

1688	$3 x^{2} + 2 x y + 4 y^{2} + (x^{2} + 8 x y + 18 y) y^{'} = 0$	[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	1.712

1689	$2 x^{2} + 8 x y + y^{2} + (2 x^{2} + \frac{x y^{3}}{3}) y^{'} = 0$	[_rational]	✗	1.749

1690	$\frac{1}{x} + 2 x + (\frac{1}{y} + 2 y) y^{'} = 0$	[_separable]	✓	2.460

1691	$y \sin (x y) + x y^{2} \cos (x y) + (x \sin (x y) + x y^{2} \cos (x y)) y^{'} = 0$	[‘y=_G(x,y’)‘]	✗	79.877

1692	$\frac{x}{{(x^{2} + y^{2})}^{3 / 2}} + \frac{y y^{'}}{{(x^{2} + y^{2})}^{3 / 2}} = 0$	[_separable]	✓	8.445

1693	$e^{x} (x^{2} y^{2} + 2 x y^{2}) + 6 x + (2 x^{2} y e^{x} + 2) y^{'} = 0$	[_exact, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	2.366

1694	$x^{2} e^{y + x^{2}} (2 x^{2} + 3) + 4 x + (x^{3} e^{y + x^{2}} - 12 y^{2}) y^{'} = 0$	[_exact]	✓	3.143

1695	$e^{x y} (y x^{4} + 4 x^{3}) + 3 y + (x^{5} e^{x y} + 3 x) y^{'} = 0$	[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	7.364

1696	$3 x^{2} \cos (x) y - x^{3} y \sin (x) + 4 x + (8 y - x^{4} \sin (x) y) y^{'} = 0$	[[_Abel, ‘2nd type‘, ‘class B‘]]	✗	57.543

1697	$4 x^{3} y^{2} - 6 x^{2} y - 2 x - 3 + (2 y x^{4} - 2 x^{3}) y^{'} = 0$ i.c.	[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	2.381

1698	$- 4 \cos (x) y + 4 \sin (x) \cos (x) + \sec {(x)}^{2} + (4 y - 4 \sin (x)) y^{'} = 0$ i.c.	[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]]	✓	8.777

1699	$(y^{3} - 1) e^{x} + 3 y^{2} (e^{x} + 1) y^{'} = 0$ i.c.	[_separable]	✓	3.304

1700	$\sin (x) - y \sin (x) - 2 \cos (x) + \cos (x) y^{'} = 0$ i.c.	[_linear]	✓	2.401

2.2.17 Problems 1601 to 1700