2.2.17 Problems 1601 to 1700

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

#

ODE

CAS classification

Solved?

time (sec)

1601

\[ {}y^{\prime } \sqrt {-x^{2}+1}+\sqrt {1-y^{2}} = 0 \]

[_separable]

17.322

1602

\[ {}y^{\prime } = \frac {\cos \left (x \right )}{\sin \left (y\right )} \]
i.c.

[_separable]

2.488

1603

\[ {}y^{\prime } = a y-b y^{2} \]
i.c.

[_quadrature]

1.786

1604

\[ {}y^{\prime }+y = \frac {2 x \,{\mathrm e}^{-x}}{1+y \,{\mathrm e}^{x}} \]

[[_Abel, ‘2nd type‘, ‘class B‘]]

1.973

1605

\[ {}y^{\prime } x -2 y = \frac {x^{6}}{y+x^{2}} \]

[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]

4.198

1606

\[ {}y^{\prime }-y = \frac {\left (x +1\right ) {\mathrm e}^{4 x}}{\left (y+{\mathrm e}^{x}\right )^{2}} \]

[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]

2.612

1607

\[ {}y^{\prime }-2 y = \frac {x \,{\mathrm e}^{2 x}}{1-y \,{\mathrm e}^{-2 x}} \]

[[_Abel, ‘2nd type‘, ‘class A‘]]

2.013

1608

\[ {}y^{\prime } = \frac {x^{2}+y^{2}}{\sin \left (x \right )} \]

[_Riccati]

8.149

1609

\[ {}y^{\prime } = \frac {y+{\mathrm e}^{x}}{x^{2}+y^{2}} \]

[‘y=_G(x,y’)‘]

1.813

1610

\[ {}y^{\prime } = \tan \left (x y\right ) \]

[‘y=_G(x,y’)‘]

1.283

1611

\[ {}y^{\prime } = \frac {x^{2}+y^{2}}{\ln \left (x y\right )} \]

[‘y=_G(x,y’)‘]

1.636

1612

\[ {}y^{\prime } = \left (x^{2}+y^{2}\right ) y^{{1}/{3}} \]

[‘y=_G(x,y’)‘]

1.150

1613

\[ {}y^{\prime } = 2 x y \]

[_separable]

1.596

1614

\[ {}y^{\prime } = \ln \left (1+x^{2}+y^{2}\right ) \]

[‘y=_G(x,y’)‘]

1.067

1615

\[ {}y^{\prime } = \frac {2 x +3 y}{x -4 y} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

4.988

1616

\[ {}y^{\prime } = \sqrt {x^{2}+y^{2}} \]

[‘y=_G(x,y’)‘]

1.110

1617

\[ {}y^{\prime } = x \left (y^{2}-1\right )^{{2}/{3}} \]

[_separable]

1.440

1618

\[ {}y^{\prime } = \left (x^{2}+y^{2}\right )^{2} \]

[‘y=_G(x,y’)‘]

0.843

1619

\[ {}y^{\prime } = \sqrt {x +y} \]

[[_homogeneous, ‘class C‘], _dAlembert]

2.191

1620

\[ {}y^{\prime } = \frac {\tan \left (y\right )}{x -1} \]

[_separable]

2.106

1621

\[ {}y^{\prime } = y^{{2}/{5}} \]
i.c.

[_quadrature]

2.054

1622

\[ {}y^{\prime } = 3 x \left (-1+y\right )^{{1}/{3}} \]
i.c.

[_separable]

6.934

1623

\[ {}y^{\prime } = 3 x \left (-1+y\right )^{{1}/{3}} \]
i.c.

[_separable]

22.347

1624

\[ {}y^{\prime } = 3 x \left (-1+y\right )^{{1}/{3}} \]
i.c.

[_separable]

7.372

1625

\[ {}y^{\prime }-y = x y^{2} \]

[_Bernoulli]

1.563

1626

\[ {}y^{\prime } = \frac {y+x \,{\mathrm e}^{-\frac {y}{x}}}{x} \]

[[_homogeneous, ‘class A‘], _dAlembert]

12.276

1627

\[ {}x^{2} y^{\prime } = y^{2}+x y-x^{2} \]

[[_homogeneous, ‘class A‘], _rational, _Riccati]

0.272

1628

\[ {}x^{2} y^{\prime } = y^{2}+x y-x^{2} \]
i.c.

[[_homogeneous, ‘class A‘], _rational, _Riccati]

3.702

1629

\[ {}y^{\prime }+y = y^{2} \]

[_quadrature]

0.295

1630

\[ {}7 y^{\prime } x -2 y = -\frac {x^{2}}{y^{6}} \]

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

0.366

1631

\[ {}x^{2} y^{\prime }+2 y = 2 \,{\mathrm e}^{\frac {1}{x}} \sqrt {y} \]

[_Bernoulli]

0.511

1632

\[ {}\left (x^{2}+1\right ) y^{\prime }+2 x y = \frac {1}{\left (x^{2}+1\right ) y} \]

[_rational, _Bernoulli]

0.506

1633

\[ {}y^{\prime }-x y = x^{3} y^{3} \]

[_Bernoulli]

0.510

1634

\[ {}y^{\prime }-\frac {\left (x +1\right ) y}{3 x} = y^{4} \]

[_rational, _Bernoulli]

0.777

1635

\[ {}y^{\prime }-2 y = x y^{3} \]
i.c.

[_Bernoulli]

0.737

1636

\[ {}y^{\prime }-x y = x y^{{3}/{2}} \]
i.c.

[_separable]

7.531

1637

\[ {}y^{\prime } x +y = x^{4} y^{4} \]
i.c.

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

0.757

1638

\[ {}y^{\prime }-2 y = 2 \sqrt {y} \]
i.c.

[_quadrature]

3.056

1639

\[ {}y^{\prime }-4 y = \frac {48 x}{y^{2}} \]
i.c.

[_rational, _Bernoulli]

1.096

1640

\[ {}x^{2} y^{\prime }+2 x y = y^{3} \]
i.c.

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

0.986

1641

\[ {}y^{\prime }-y = x \sqrt {y} \]
i.c.

[_Bernoulli]

0.838

1642

\[ {}y^{\prime } = \frac {x +y}{x} \]

[_linear]

1.490

1643

\[ {}y^{\prime } = \frac {y^{2}+2 x y}{x^{2}} \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

2.711

1644

\[ {}x y^{3} y^{\prime } = y^{4}+x^{4} \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

5.765

1645

\[ {}y^{\prime } = \frac {y}{x}+\sec \left (\frac {y}{x}\right ) \]

[[_homogeneous, ‘class A‘], _dAlembert]

4.971

1646

\[ {}x^{2} y^{\prime } = x^{2}+x y+y^{2} \]

[[_homogeneous, ‘class A‘], _rational, _Riccati]

2.569

1647

\[ {}x y y^{\prime } = x^{2}+2 y^{2} \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

10.416

1648

\[ {}y^{\prime } = \frac {2 y^{2}+x^{2} {\mathrm e}^{-\frac {y^{2}}{x^{2}}}}{2 x y} \]

[[_homogeneous, ‘class A‘]]

3.207

1649

\[ {}y^{\prime } = \frac {x y+y^{2}}{x^{2}} \]
i.c.

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

2.658

1650

\[ {}y^{\prime } = \frac {x^{3}+y^{3}}{x y^{2}} \]
i.c.

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

95.211

1651

\[ {}x y y^{\prime }+x^{2}+y^{2} = 0 \]
i.c.

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

6.483

1652

\[ {}y^{\prime } = \frac {y^{2}-3 x y-5 x^{2}}{x^{2}} \]
i.c.

[[_homogeneous, ‘class A‘], _rational, _Riccati]

3.766

1653

\[ {}x^{2} y^{\prime } = 2 x^{2}+y^{2}+4 x y \]
i.c.

[[_homogeneous, ‘class A‘], _rational, _Riccati]

3.441

1654

\[ {}x y y^{\prime } = 3 x^{2}+4 y^{2} \]
i.c.

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

9.417

1655

\[ {}y^{\prime } = \frac {x +y}{x -y} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

3.571

1656

\[ {}\left (y^{\prime } x -y\right ) \left (\ln \left (y\right )-\ln \left (x \right )\right ) = x \]

[[_homogeneous, ‘class A‘]]

10.110

1657

\[ {}y^{\prime } = \frac {y^{3}+2 x y^{2}+x^{2} y+x^{3}}{x \left (x +y\right )^{2}} \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

44.052

1658

\[ {}y^{\prime } = \frac {x +2 y}{2 x +y} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7.148

1659

\[ {}y^{\prime } = \frac {y}{y-2 x} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

6.112

1660

\[ {}y^{\prime } = \frac {x y^{2}+2 y^{3}}{x^{3}+x^{2} y+x y^{2}} \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

110.847

1661

\[ {}y^{\prime } = \frac {x^{3}+x^{2} y+3 y^{3}}{x^{3}+3 x y^{2}} \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

39.280

1662

\[ {}x^{2} y^{\prime } = y^{2}+x y-4 x^{2} \]
i.c.

[[_homogeneous, ‘class A‘], _rational, _Riccati]

3.608

1663

\[ {}x y y^{\prime } = x^{2}-x y+y^{2} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

4.782

1664

\[ {}y^{\prime } = \frac {2 y^{2}-x y+2 x^{2}}{x y+2 x^{2}} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

49.143

1665

\[ {}y^{\prime } = \frac {x^{2}+x y+y^{2}}{x y} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

37.280

1666

\[ {}y^{\prime } = \frac {-6 x +y-3}{2 x -y-1} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

4.340

1667

\[ {}y^{\prime } = \frac {2 x +y+1}{x +2 y-4} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

16.713

1668

\[ {}y^{\prime } = \frac {-x +3 y-14}{x +y-2} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

2.597

1669

\[ {}3 x y^{2} y^{\prime } = y^{3}+x \]

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

2.323

1670

\[ {}x y y^{\prime } = 3 x^{6}+6 y^{2} \]

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

2.349

1671

\[ {}x^{3} y^{\prime } = 2 y^{2}+2 x^{2} y-2 x^{4} \]

[[_homogeneous, ‘class G‘], _rational, _Riccati]

1.960

1672

\[ {}y^{\prime } = y^{2} {\mathrm e}^{-x}+4 y+2 \,{\mathrm e}^{x} \]

[[_1st_order, _with_linear_symmetries], _Riccati]

1.531

1673

\[ {}y^{\prime } = \frac {y^{2}+y \tan \left (x \right )+\tan \left (x \right )^{2}}{\sin \left (x \right )^{2}} \]

[_Riccati]

45.109

1674

\[ {}x \ln \left (x \right )^{2} y^{\prime } = -4 \ln \left (x \right )^{2}+y \ln \left (x \right )+y^{2} \]

[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], _Riccati]

1.952

1675

\[ {}2 x \left (y+2 \sqrt {x}\right ) y^{\prime } = \left (y+\sqrt {x}\right )^{2} \]

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

2.334

1676

\[ {}\left (y+{\mathrm e}^{x^{2}}\right ) y^{\prime } = 2 x \left (y^{2}+y \,{\mathrm e}^{x^{2}}+{\mathrm e}^{2 x^{2}}\right ) \]

[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], [_Abel, ‘2nd type‘, ‘class A‘]]

2.439

1677

\[ {}y^{\prime }+\frac {2 y}{x} = \frac {3 x^{2} y^{2}+6 x y+2}{x^{2} \left (2 x y+3\right )} \]
i.c.

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

8.059

1678

\[ {}y^{\prime }+\frac {3 y}{x} = \frac {3 x^{4} y^{2}+10 x^{2} y+6}{x^{3} \left (2 x^{2} y+5\right )} \]
i.c.

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

6.766

1679

\[ {}y^{\prime } = 1+x -\left (2 x +1\right ) y+x y^{2} \]

[_Riccati]

2.038

1680

\[ {}6 x^{2} y^{2}+4 x^{3} y y^{\prime } = 0 \]

[_separable]

2.299

1681

\[ {}3 \cos \left (x \right ) y+4 x \,{\mathrm e}^{x}+2 x^{3} y+\left (3 \sin \left (x \right )+3\right ) y^{\prime } = 0 \]

[_linear]

104.227

1682

\[ {}14 x^{2} y^{3}+21 x^{2} y^{2} y^{\prime } = 0 \]

[_quadrature]

1.375

1683

\[ {}2 x -2 y^{2}+\left (12 y^{2}-4 x y\right ) y^{\prime } = 0 \]

[_exact, _rational]

1.212

1684

\[ {}\left (x +y\right )^{2}+\left (x +y\right )^{2} y^{\prime } = 0 \]

[_quadrature]

0.789

1685

\[ {}4 x +7 y+\left (3 x +4 y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7.323

1686

\[ {}-2 \sin \left (x \right ) y^{2}+3 y^{3}-2 x +\left (4 \cos \left (x \right ) y+9 x y^{2}\right ) y^{\prime } = 0 \]

[_exact]

33.800

1687

\[ {}2 x +y+\left (2 y+2 x \right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5.361

1688

\[ {}3 x^{2}+2 x y+4 y^{2}+\left (x^{2}+8 x y+18 y\right ) y^{\prime } = 0 \]

[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

1.468

1689

\[ {}2 x^{2}+8 x y+y^{2}+\left (2 x^{2}+\frac {x y^{3}}{3}\right ) y^{\prime } = 0 \]

[_rational]

1.579

1690

\[ {}\frac {1}{x}+2 x +\left (\frac {1}{y}+2 y\right ) y^{\prime } = 0 \]

[_separable]

1.961

1691

\[ {}y \sin \left (x y\right )+x y^{2} \cos \left (x y\right )+\left (x \sin \left (x y\right )+x y^{2} \cos \left (x y\right )\right ) y^{\prime } = 0 \]

[‘y=_G(x,y’)‘]

82.443

1692

\[ {}\frac {x}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{{3}/{2}}} = 0 \]

[_separable]

4.739

1693

\[ {}{\mathrm e}^{x} \left (x^{2} y^{2}+2 x y^{2}\right )+6 x +\left (2 x^{2} y \,{\mathrm e}^{x}+2\right ) y^{\prime } = 0 \]

[_exact, [_Abel, ‘2nd type‘, ‘class B‘]]

1.927

1694

\[ {}x^{2} {\mathrm e}^{y+x^{2}} \left (2 x^{2}+3\right )+4 x +\left (x^{3} {\mathrm e}^{y+x^{2}}-12 y^{2}\right ) y^{\prime } = 0 \]

[_exact]

2.789

1695

\[ {}{\mathrm e}^{x y} \left (x^{4} y+4 x^{3}\right )+3 y+\left (x^{5} {\mathrm e}^{x y}+3 x \right ) y^{\prime } = 0 \]

[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]

6.786

1696

\[ {}3 x^{2} \cos \left (x \right ) y-x^{3} y \sin \left (x \right )+4 x +\left (8 y-x^{4} \sin \left (x \right ) y\right ) y^{\prime } = 0 \]

[[_Abel, ‘2nd type‘, ‘class B‘]]

52.655

1697

\[ {}4 x^{3} y^{2}-6 x^{2} y-2 x -3+\left (2 x^{4} y-2 x^{3}\right ) y^{\prime } = 0 \]
i.c.

[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

2.237

1698

\[ {}-4 \cos \left (x \right ) y+4 \sin \left (x \right ) \cos \left (x \right )+\sec \left (x \right )^{2}+\left (4 y-4 \sin \left (x \right )\right ) y^{\prime } = 0 \]
i.c.

[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]]

6.608

1699

\[ {}\left (y^{3}-1\right ) {\mathrm e}^{x}+3 y^{2} \left (1+{\mathrm e}^{x}\right ) y^{\prime } = 0 \]
i.c.

[_separable]

3.120

1700

\[ {}\sin \left (x \right )-\sin \left (x \right ) y-2 \cos \left (x \right )+\cos \left (x \right ) y^{\prime } = 0 \]
i.c.

[_linear]

2.533