2.2.18 Problems 1701 to 1800

Table 2.37: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

time (sec)

1701

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

[_separable]

2.134

1702

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

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

4.325

1703

\[ {}{\mathrm e}^{x} \left (x^{4} y^{2}+4 x^{3} y^{2}+1\right )+\left (2 x^{4} y \,{\mathrm e}^{x}+2 y\right ) y^{\prime } = 0 \]

[_exact, _Bernoulli]

2.912

1704

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

[_exact, _rational]

2.704

1705

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

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

1.276

1706

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

[_exact, _rational]

2.710

1707

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

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

58.696

1708

\[ {}y^{\prime }+\frac {2 y}{x} = -\frac {2 x y}{x^{2}+2 x^{2} y+1} \]
i.c.

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

4.224

1709

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

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

2.141

1710

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

[[_Abel, ‘2nd type‘, ‘class B‘]]

52.544

1711

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

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

2.300

1712

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

[_separable]

2.891

1713

\[ {}y-x y^{\prime } = 0 \]

[_separable]

1.606

1714

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

[_separable]

2.236

1715

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

[_quadrature]

1.629

1716

\[ {}5 x y+2 y+5+2 x y^{\prime } = 0 \]

[_linear]

1.312

1717

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

[_linear]

1.526

1718

\[ {}27 x y^{2}+8 y^{3}+\left (18 x^{2} y+12 x y^{2}\right ) y^{\prime } = 0 \]

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

100.640

1719

\[ {}6 x y^{2}+2 y+\left (12 x^{2} y+6 x +3\right ) y^{\prime } = 0 \]

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

1.512

1720

\[ {}y^{2}+\left (x y^{2}+6 x y+\frac {1}{y}\right ) y^{\prime } = 0 \]

[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]

1.437

1721

\[ {}12 x^{3} y+24 y^{2} x^{2}+\left (9 x^{4}+32 x^{3} y+4 y\right ) y^{\prime } = 0 \]

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

1.560

1722

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

[_separable]

2.049

1723

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

[_separable]

1.852

1724

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

[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]

38.332

1725

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

[_rational]

1.639

1726

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

[_separable]

4.184

1727

\[ {}a y+b x y+\left (c x +d x y\right ) y^{\prime } = 0 \]

[_separable]

1.814

1728

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

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

2.563

1729

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

[_separable]

2.294

1730

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

[_linear]

3.726

1731

\[ {}x^{4} y^{4}+x^{5} y^{3} y^{\prime } = 0 \]

[_separable]

2.181

1732

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

[_separable]

3.325

1733

\[ {}x^{4} y^{3}+y+\left (x^{5} y^{2}-x \right ) y^{\prime } = 0 \]

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

2.309

1734

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

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

1.992

1735

\[ {}12 x y+6 y^{3}+\left (9 x^{2}+10 x y^{2}\right ) y^{\prime } = 0 \]

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

2.523

1736

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

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

2.204

1737

\[ {}y^{\prime \prime }-7 y^{\prime }+10 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1.405

1738

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

[[_2nd_order, _missing_x]]

2.325

1739

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

[[_2nd_order, _missing_x]]

2.356

1740

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

[[_2nd_order, _missing_x]]

1.304

1741

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

[[_2nd_order, _missing_x]]

1.008

1742

\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 0 \]
i.c.

[[_2nd_order, _exact, _linear, _homogeneous]]

1.380

1743

\[ {}y^{\prime \prime }-2 y^{\prime }-3 y = 0 \]

[[_2nd_order, _missing_x]]

0.880

1744

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 0 \]

[[_2nd_order, _missing_x]]

0.967

1745

\[ {}y^{\prime \prime }-2 a y^{\prime }+a^{2} y = 0 \]

[[_2nd_order, _missing_x]]

0.417

1746

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

[[_2nd_order, _exact, _linear, _homogeneous]]

1.203

1747

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

[[_Emden, _Fowler]]

0.948

1748

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

[[_Emden, _Fowler]]

0.894

1749

\[ {}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

1.112

1750

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

[[_2nd_order, _with_linear_symmetries]]

1.179

1751

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

[[_2nd_order, _with_linear_symmetries]]

1.263

1752

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

[[_2nd_order, _with_linear_symmetries]]

2.399

1753

\[ {}\left (3 x -1\right ) y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }+\left (6 x -8\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.851

1754

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

[[_2nd_order, _exact, _linear, _homogeneous]]

0.863

1755

\[ {}\left (2 x +1\right ) y^{\prime \prime }-2 \left (2 x^{2}-1\right ) y^{\prime }-4 \left (x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.835

1756

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

[[_2nd_order, _with_linear_symmetries]]

1.326

1757

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

[[_2nd_order, _with_linear_symmetries]]

0.217

1758

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

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

0.158

1759

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

[[_2nd_order, _with_linear_symmetries]]

0.165

1760

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.313

1761

\[ {}y^{\prime \prime }-2 y^{\prime }+y = 7 x^{{3}/{2}} {\mathrm e}^{x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.366

1762

\[ {}4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 4 \sqrt {x}\, {\mathrm e}^{x} \left (1+4 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.322

1763

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.518

1764

\[ {}y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y = 8 \,{\mathrm e}^{-x \left (x +2\right )} \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.284

1765

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

[[_2nd_order, _with_linear_symmetries]]

0.178

1766

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.295

1767

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.276

1768

\[ {}\left (1-2 x \right ) y^{\prime \prime }+2 y^{\prime }+\left (2 x -3\right ) y = \left (4 x^{2}-4 x +1\right ) {\mathrm e}^{x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.219

1769

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

[[_2nd_order, _with_linear_symmetries]]

0.187

1770

\[ {}2 x y^{\prime \prime }+\left (1+4 x \right ) y^{\prime }+\left (2 x +1\right ) y = 3 \sqrt {x}\, {\mathrm e}^{-x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.245

1771

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.307

1772

\[ {}4 x^{2} y^{\prime \prime }-4 x \left (x +1\right ) y^{\prime }+\left (2 x +3\right ) y = 4 x^{{5}/{2}} {\mathrm e}^{2 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.223

1773

\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y = 4 x^{2} \]

[[_2nd_order, _with_linear_symmetries]]

0.176

1774

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

[[_2nd_order, _with_linear_symmetries]]

0.095

1775

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

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

0.080

1776

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

[[_2nd_order, _with_linear_symmetries]]

0.090

1777

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

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

0.157

1778

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

[[_2nd_order, _with_linear_symmetries]]

0.098

1779

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

[[_Emden, _Fowler]]

0.113

1780

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

[[_2nd_order, _with_linear_symmetries]]

0.147

1781

\[ {}x y^{\prime \prime }-\left (1+4 x \right ) y^{\prime }+\left (4 x +2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.106

1782

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

[[_2nd_order, _with_linear_symmetries]]

0.155

1783

\[ {}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.102

1784

\[ {}\left (2 x +1\right ) x y^{\prime \prime }-2 \left (2 x^{2}-1\right ) y^{\prime }-4 \left (x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.112

1785

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

[[_2nd_order, _with_linear_symmetries]]

0.115

1786

\[ {}x y^{\prime \prime }-\left (1+4 x \right ) y^{\prime }+\left (4 x +2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.096

1787

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

[[_2nd_order, _with_linear_symmetries]]

0.205

1788

\[ {}\left (3 x -1\right ) y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }-\left (6 x -8\right ) y = 0 \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

0.173

1789

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.381

1790

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

[[_2nd_order, _with_linear_symmetries]]

0.204

1791

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

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

0.356

1792

\[ {}y^{\prime }+y^{2}+k^{2} = 0 \]

[_quadrature]

2.820

1793

\[ {}y^{\prime }+y^{2}-3 y+2 = 0 \]

[_quadrature]

2.070

1794

\[ {}y^{\prime }+y^{2}+5 y-6 = 0 \]

[_quadrature]

1.943

1795

\[ {}y^{\prime }+y^{2}+8 y+7 = 0 \]

[_quadrature]

1.928

1796

\[ {}y^{\prime }+y^{2}+14 y+50 = 0 \]

[_quadrature]

1.319

1797

\[ {}6 y^{\prime }+6 y^{2}-y-1 = 0 \]

[_quadrature]

1.901

1798

\[ {}36 y^{\prime }+36 y^{2}-12 y+1 = 0 \]

[_quadrature]

1.199

1799

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

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

1.666

1800

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

[[_homogeneous, ‘class C‘], _Riccati]

1.904