2.3.4 first order ode homogA

Table 2.401: first order ode homogA

#

ODE

CAS classification

Solved?

77

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

[_linear]

80

\[ {}3 x y^{\prime }+y = 12 x \]

[_linear]

105

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

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

106

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

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

107

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

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

108

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

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

109

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

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

110

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

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

111

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

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

112

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

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

113

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

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

114

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

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

115

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

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

116

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

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

117

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

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

118

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

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

119

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

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

135

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

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

136

\[ {}4 x -y+\left (6 y-x \right ) y^{\prime } = 0 \]

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

137

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

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

146

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

[[_1st_order, _with_linear_symmetries], _exact, _rational]

166

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

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

181

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

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

186

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

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

189

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

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

190

\[ {}6 x y^{3}+2 y^{4}+\left (9 y^{2} x^{2}+8 x y^{3}\right ) y^{\prime } = 0 \]

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

192

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

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

196

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

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

211

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

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

212

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

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

708

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

[_linear]

711

\[ {}3 x y^{\prime }+y = 12 x \]

[_linear]

729

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

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

730

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

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

731

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

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

732

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

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

733

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

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

734

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

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

735

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

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

736

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

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

737

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

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

738

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

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

739

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

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

740

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

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

741

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

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

742

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

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

743

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

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

759

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

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

760

\[ {}4 x -y+\left (6 y-x \right ) y^{\prime } = 0 \]

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

761

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

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

770

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

[[_1st_order, _with_linear_symmetries], _exact, _rational]

773

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

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

778

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

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

781

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

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

782

\[ {}6 x y^{3}+2 y^{4}+\left (9 y^{2} x^{2}+8 x y^{3}\right ) y^{\prime } = 0 \]

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

784

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

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

788

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

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

803

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

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

804

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

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

1158

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

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

1159

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

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

1160

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

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

1161

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

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

1162

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

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

1163

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

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

1164

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

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

1165

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

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

1174

\[ {}y^{\prime } = -\frac {4 t}{y} \]

[_separable]

1194

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

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

1196

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

[_separable]

1197

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

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

1198

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

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

1204

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

[_separable]

1205

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

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

1217

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

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

1231

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

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

1243

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

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

1245

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

[_linear]

1246

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

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

1247

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

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

1540

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

[_separable]

1546

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

[_separable]

1597

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

[_separable]

1615

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

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

1626

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

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

1628

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

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

1643

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

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

1644

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

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

1645

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

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

1646

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

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

1647

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

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

1648

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

[[_homogeneous, ‘class A‘]]

1649

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

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

1650

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

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

1651

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

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

1652

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

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

1653

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

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

1654

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

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

1655

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

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

1656

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

[[_homogeneous, ‘class A‘]]

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]

1658

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

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

1659

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

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

1660

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

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

1661

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

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

1662

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

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

1663

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

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

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‘]]

1665

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

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

1680

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

[_separable]

1685

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

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

1687

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

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

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]

1702

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

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

1707

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

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

1712

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

[_separable]

1714

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

[_separable]

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‘]]

1731

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

[_separable]

2330

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

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

2331

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

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

2332

\[ {}\left (t -\sqrt {t y}\right ) y^{\prime } = y \]

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

2333

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

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

2334

\[ {}{\mathrm e}^{\frac {t}{y}} \left (-t +y\right ) y^{\prime }+y \left (1+{\mathrm e}^{\frac {t}{y}}\right ) = 0 \]

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

2342

\[ {}2 t y^{3}+3 t^{2} y^{2} y^{\prime } = 0 \]
i.c.

[_separable]

2346

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

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

2501

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

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

2502

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

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

2503

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

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

2504

\[ {}\left (t -\sqrt {t y}\right ) y^{\prime } = y \]

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

2505

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

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

2506

\[ {}{\mathrm e}^{\frac {t}{y}} \left (-t +y\right ) y^{\prime }+y \left (1+{\mathrm e}^{\frac {t}{y}}\right ) = 0 \]

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

2514

\[ {}2 t y^{3}+3 t^{2} y^{2} y^{\prime } = 0 \]
i.c.

[_separable]

2518

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

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

2844

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

[_separable]

2851

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

[_separable]

2862

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

[_separable]

2864

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

[_separable]

2872

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

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

2873

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

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

2874

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

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

2875

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

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

2876

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

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

2877

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

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

2878

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

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

2879

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

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

2881

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

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

2882

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

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

2883

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

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

2884

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

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

2885

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

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

2886

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

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

2887

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

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

2888

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

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

2889

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

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

2890

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

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

2891

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

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

2892

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

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

2893

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

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

2914

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

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

2915

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

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

2919

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

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

2934

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

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

2935

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

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

2964

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

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

2986

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

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

2989

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

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

3005

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

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

3006

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

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

3014

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

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

3019

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

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

3021

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

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

3023

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

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

3026

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

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

3032

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

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

3036

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

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

3041

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

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

3045

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

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

3049

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

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

3050

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

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

3056

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

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

3285

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

[_separable]

3288

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

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

3291

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

[_separable]

3292

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

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

3295

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

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

3298

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

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

3300

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

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

3301

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

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

3303

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

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

3306

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

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

3308

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

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

3311

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

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

3312

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

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

3314

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

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

3315

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

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

3317

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

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

3318

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

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

3432

\[ {}y^{\prime } = -\frac {t}{y} \]

[_separable]

3461

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

[_linear]

3467

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

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

3476

\[ {}y^{\prime }-\frac {y^{2}}{x^{2}} = {\frac {1}{4}} \]
i.c.

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

3477

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

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

3544

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

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

3545

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

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

3546

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

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

3547

\[ {}x y^{\prime } = \sqrt {16 x^{2}-y^{2}}+y \]

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

3548

\[ {}-y+x y^{\prime } = \sqrt {9 x^{2}+y^{2}} \]

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

3549

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

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

3550

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

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

3551

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

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

3552

\[ {}2 x y y^{\prime }-2 y^{2}-x^{2} {\mathrm e}^{-\frac {y^{2}}{x^{2}}} = 0 \]

[[_homogeneous, ‘class A‘]]

3553

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

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

3554

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

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

3555

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

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

3556

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

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

3557

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

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

3562

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

[_separable]

3636

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

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

3637

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

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

3638

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

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

3639

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

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

3640

\[ {}x y^{\prime } = \sqrt {16 x^{2}-y^{2}}+y \]

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

3641

\[ {}-y+x y^{\prime } = \sqrt {9 x^{2}+y^{2}} \]

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

3643

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

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

3644

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

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

3645

\[ {}2 x y y^{\prime }-2 y^{2}-x^{2} {\mathrm e}^{-\frac {y^{2}}{x^{2}}} = 0 \]

[[_homogeneous, ‘class A‘]]

3646

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

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

3647

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

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

3648

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

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

3649

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

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

3650

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

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

3651

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

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

3652

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

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

3653

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

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

3654

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

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

3655

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

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

3656

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

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

3682

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

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

4098

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

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

4103

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

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

4112

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

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

4190

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

[_separable]

4196

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

[_linear]

4223

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

[_separable]

4240

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

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

4241

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

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

4242

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

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

4243

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

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

4244

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

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

4254

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

[_separable]

4261

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

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

4267

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

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

4277

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

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

4281

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

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

4290

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

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

4295

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

[_separable]

4300

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

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

4314

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

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

4315

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

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

4316

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

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

4317

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

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

4318

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

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

4319

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

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

4320

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

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

4333

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

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

4347

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

[[_homogeneous, ‘class G‘], _dAlembert]

4386

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

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

4399

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

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

4402

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

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

4405

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

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

4413

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

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

4416

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

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

4422

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

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

4441

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

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

4743

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

[_linear]

4752

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

[_separable]

4754

\[ {}x y^{\prime } = a x +b y \]

[_linear]

4794

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

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

4795

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

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

4800

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

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

4801

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

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

4805

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

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

4806

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

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

4808

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

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

4811

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

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

4813

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

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

4814

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

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

4816

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

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

4818

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

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

4857

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

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

4860

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

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

4861

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

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

4862

\[ {}x^{2} y^{\prime }+a \,x^{2}+b x y+c y^{2} = 0 \]

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

4938

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

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

4951

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

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

4965

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

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

4966

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

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

5015

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

[_separable]

5018

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

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

5032

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

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

5033

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

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

5034

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

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

5035

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

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

5039

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

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

5044

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

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

5051

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

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

5060

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

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

5061

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

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

5062

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

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

5081

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

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

5088

\[ {}\left (7 x +5 y\right ) y^{\prime }+10 x +8 y = 0 \]

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

5097

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

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

5098

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

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

5099

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

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

5100

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

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

5103

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

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

5106

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

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

5107

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

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

5111

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

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

5112

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

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

5122

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

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

5123

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

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

5124

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

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

5125

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

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

5126

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

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

5128

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

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

5129

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

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

5138

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

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

5139

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

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

5143

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

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

5144

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

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

5145

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

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

5150

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

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

5151

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

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

5154

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

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

5155

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

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

5157

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

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

5173

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

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

5176

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

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

5181

\[ {}8 x^{3} y y^{\prime }+3 x^{4}-6 y^{2} x^{2}-y^{4} = 0 \]

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

5192

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

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

5193

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

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

5194

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

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

5195

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

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

5196

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

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

5201

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

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

5210

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

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

5211

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

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

5213

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

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

5214

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

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

5219

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

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

5221

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

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

5225

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

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

5226

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

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

5227

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

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

5228

\[ {}\left (a \,x^{2}+2 b x y+c y^{2}\right ) y^{\prime }+k \,x^{2}+2 y a x +b y^{2} = 0 \]

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

5234

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

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

5237

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

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

5238

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

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

5239

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

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

5240

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

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

5241

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

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

5242

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

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

5243

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

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

5251

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

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

5267

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

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

5268

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

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

5272

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

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

5274

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

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

5276

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

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

5277

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

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

5279

\[ {}\left (3 x^{3}+6 x^{2} y-3 x y^{2}+20 y^{3}\right ) y^{\prime }+4 x^{3}+9 x^{2} y+6 x y^{2}-y^{3} = 0 \]

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

5280

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

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

5283

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

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

5284

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

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

5285

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

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

5286

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

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

5301

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

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

5313

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

[_separable]

5315

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

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

5316

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

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

5319

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

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

5321

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

[[_homogeneous, ‘class G‘], _dAlembert]

5322

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

[[_1st_order, _with_linear_symmetries], _dAlembert]

5328

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

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

5428

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

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

5429

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

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

5434

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

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

5438

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

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

5440

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

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

5445

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

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

5448

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

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

5449

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

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

5453

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

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

5461

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

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

5465

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

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

5472

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

[_separable]

5473

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

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

5474

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

[_linear]

5482

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

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

5485

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

[_separable]

5487

\[ {}{y^{\prime }}^{2} x^{2}+4 x y y^{\prime }-5 y^{2} = 0 \]

[_separable]

5489

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

[_separable]

5491

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

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

5492

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

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

5504

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

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

5505

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

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

5520

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

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

5522

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

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

5523

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

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

5524

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

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

5528

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

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

5532

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

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

5539

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

[_separable]

5540

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

[_separable]

5541

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

[_separable]

5544

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

[_separable]

5545

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

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

5546

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

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

5553

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

[_separable]

5555

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

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

5561

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

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

5562

\[ {}\left (\left (-4 a^{2}+1\right ) x^{2}+y^{2}\right ) {y^{\prime }}^{2}-8 a^{2} x y y^{\prime }+x^{2}+\left (-4 a^{2}+1\right ) y^{2} = 0 \]

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

5563

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

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

5564

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

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

5565

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

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

5568

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

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

5570

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

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

5573

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

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

5579

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

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

5689

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

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

5694

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

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

5705

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

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

5706

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

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

5707

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

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

5708

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

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

5709

\[ {}\left (7 x +5 y\right ) y^{\prime }+10 x +8 y = 0 \]

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

5733

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

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

5734

\[ {}\left (7 x +5 y\right ) y^{\prime }+10 x +8 y = 0 \]

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

5735

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

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

5736

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

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

5753

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

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

5763

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

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

5769

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

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

5771

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

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

5772

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

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

5773

\[ {}x +y-y^{\prime } \left (x -y\right ) = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5774

\[ {}x y^{\prime }-y-x \sin \left (\frac {y}{x}\right ) = 0 \]

[[_homogeneous, ‘class A‘], _dAlembert]

5775

\[ {}2 x^{2} y+y^{3}+\left (x y^{2}-2 x^{3}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

5776

\[ {}y^{2}+\left (x \sqrt {y^{2}-x^{2}}-x y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _dAlembert]

5777

\[ {}\frac {y \cos \left (\frac {y}{x}\right )}{x}-\left (\frac {x \sin \left (\frac {y}{x}\right )}{y}+\cos \left (\frac {y}{x}\right )\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _dAlembert]

5778

\[ {}y+x \ln \left (\frac {y}{x}\right ) y^{\prime }-2 x y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _dAlembert]

5779

\[ {}2 y \,{\mathrm e}^{\frac {x}{y}}+\left (y-2 x \,{\mathrm e}^{\frac {x}{y}}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _dAlembert]

5780

\[ {}{\mathrm e}^{\frac {y}{x}} x -y \sin \left (\frac {y}{x}\right )+x \sin \left (\frac {y}{x}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _dAlembert]

5781

\[ {}x^{2}+y^{2} = 2 x y y^{\prime } \]
i.c.

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

5782

\[ {}{\mathrm e}^{\frac {y}{x}} x +y = x y^{\prime } \]
i.c.

[[_homogeneous, ‘class A‘], _dAlembert]

5783

\[ {}y^{\prime }-\frac {y}{x}+\csc \left (\frac {y}{x}\right ) = 0 \]
i.c.

[[_homogeneous, ‘class A‘], _dAlembert]

5784

\[ {}x y-y^{2}-x^{2} y^{\prime } = 0 \]
i.c.

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

5865

\[ {}y^{\prime } = 1+\frac {y}{x}-\frac {y^{2}}{x^{2}} \]

[[_homogeneous, ‘class A‘], _rational, _Riccati]

5872

\[ {}-y+x y^{\prime } = \sqrt {x^{2}+y^{2}} \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

5874

\[ {}\left (x^{2}-y^{2}\right ) y^{\prime } = 2 x y \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

5888

\[ {}x y^{\prime } = x +y+{\mathrm e}^{\frac {y}{x}} x \]

[[_homogeneous, ‘class A‘], _dAlembert]

5893

\[ {}x y^{\prime }-y-x \sin \left (\frac {y}{x}\right ) = 0 \]

[[_homogeneous, ‘class A‘], _dAlembert]

5894

\[ {}\left (x y-x^{2}\right ) y^{\prime }+y^{2}-3 x y-2 x^{2} = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

5896

\[ {}x^{2} y^{\prime }+x^{2}+x y+y^{2} = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Riccati]

5906

\[ {}x y y^{\prime }+x^{2}+y^{2} = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

5907

\[ {}2 x y y^{\prime }+3 x^{2}-y^{2} = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

5908

\[ {}\left (2 x y^{3}-x^{4}\right ) y^{\prime }+2 x^{3} y-y^{4} = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

5910

\[ {}\left (x^{2}+y^{2}\right ) y^{\prime }+2 x \left (2 x +y\right ) = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]

5912

\[ {}2 y^{3} y^{\prime }+x y^{2}-x^{3} = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

6027

\[ {}{y^{\prime }}^{2} y+2 x y^{\prime }-y = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

6125

\[ {}x^{2} y^{\prime }+y^{2}-x y = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

6126

\[ {}y y^{\prime } = -x +\sqrt {x^{2}+y^{2}} \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

6127

\[ {}x y+\left (y^{2}-x^{2}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

6128

\[ {}y^{2}-x y+\left (x^{2}+x y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

6130

\[ {}y^{\prime } = \frac {y}{x}-\tan \left (\frac {y}{x}\right ) \]

[[_homogeneous, ‘class A‘], _dAlembert]

6224

\[ {}\left (2 x +y\right ) y^{\prime }-x +2 y = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

6232

\[ {}3 x^{2} y+x^{3} y^{\prime } = 0 \]
i.c.

[_separable]

6424

\[ {}\left (x^{3}+x y^{2}\right ) y^{\prime } = 2 y^{3} \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

6435

\[ {}\left (-x +2 y\right ) y^{\prime } = 2 x +y \]

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

6436

\[ {}x y+y^{2}+\left (x^{2}-x y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

6437

\[ {}x^{3}+y^{3} = 3 x y^{2} y^{\prime } \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

6438

\[ {}y-3 x +\left (3 x +4 y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

6439

\[ {}\left (x^{3}+3 x y^{2}\right ) y^{\prime } = y^{3}+3 x^{2} y \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

6457

\[ {}x^{2}-2 x y+5 y^{2} = \left (x^{2}+2 x y+y^{2}\right ) y^{\prime } \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

6461

\[ {}y^{\prime } = \frac {2 x y+y^{2}}{x^{2}+2 x y} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

6464

\[ {}x^{2} y^{\prime } = y^{2}-x y y^{\prime } \]
i.c.

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

6467

\[ {}x^{2} y^{\prime }+y^{2} = x y y^{\prime } \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

6468

\[ {}2 x y y^{\prime } = x^{2}-y^{2} \]

[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli]

6569

\[ {}x y^{\prime } = 2 y \]

[_separable]

6570

\[ {}x +y y^{\prime } = 0 \]

[_separable]

6572

\[ {}2 x^{3} y^{\prime } = y \left (3 x^{2}+y^{2}\right ) \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

6579

\[ {}4 y+x y^{\prime } = 0 \]

[_separable]

6581

\[ {}y^{2}-x^{2} y^{\prime } = 0 \]

[_separable]

6584

\[ {}x \sin \left (\frac {y}{x}\right )-y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _dAlembert]

6586

\[ {}y \sqrt {x^{2}+y^{2}}-x \left (x +\sqrt {x^{2}+y^{2}}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _dAlembert]

6590

\[ {}x +2 y+\left (2 x +3 y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

6591

\[ {}2 x y^{\prime }-2 y = \sqrt {4 y^{2}+x^{2}} \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

6594

\[ {}y^{2}-x^{2}+x y y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

6597

\[ {}x^{3}+y^{3}+3 x y^{2} y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli]

6599

\[ {}x y^{\prime }+2 y = 0 \]
i.c.

[_separable]

6600

\[ {}x y y^{\prime }+x^{2}+y^{2} = 0 \]
i.c.

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

6615

\[ {}y \left (x -2 y\right )-x^{2} y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

6616

\[ {}x y y^{\prime }+x^{2}+y^{2} = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

6617

\[ {}x^{2}+y^{2}+2 x y y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli]

6666

\[ {}{y^{\prime }}^{2} x^{2}+x y y^{\prime }-6 y^{2} = 0 \]

[_separable]

6668

\[ {}{y^{\prime }}^{2} x -2 y y^{\prime }+4 x = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

6670

\[ {}8 {y^{\prime }}^{2} y-2 x y^{\prime }+y = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

6675

\[ {}{y^{\prime }}^{2} x -y y^{\prime }-y = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

6680

\[ {}{y^{\prime }}^{2} y-x y^{\prime }+3 y = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

6683

\[ {}{y^{\prime }}^{2} x -2 y y^{\prime }+4 x = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

6684

\[ {}{y^{\prime }}^{2} x -2 y y^{\prime }+x +2 y = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

6690

\[ {}\left (1+{y^{\prime }}^{2}\right ) \left (x -y\right )^{2} = \left (x +y y^{\prime }\right )^{2} \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

6904

\[ {}x y^{\prime }-2 y = 0 \]

[_separable]

6905

\[ {}y^{\prime } = -\frac {x}{y} \]

[_separable]

6948

\[ {}x y^{\prime } = 2 y \]
i.c.

[_separable]

6955

\[ {}\left (x^{2}+y^{2}\right ) y^{\prime } = y^{2} \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

6956

\[ {}\left (y-x \right ) y^{\prime } = x +y \]

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

6968

\[ {}y y^{\prime } = 3 x \]
i.c.

[_separable]

6969

\[ {}y y^{\prime } = 3 x \]
i.c.

[_separable]

6970

\[ {}y y^{\prime } = 3 x \]
i.c.

[_separable]

6990

\[ {}3 x y^{\prime }-2 y = 0 \]

[_separable]

6992

\[ {}x y^{\prime }+y = 2 x \]
i.c.

[_linear]

7034

\[ {}y y^{\prime } = -x \]
i.c.

[_separable]

7035

\[ {}y y^{\prime } = -x \]
i.c.

[_separable]

7044

\[ {}y^{\prime } = 1-\frac {y}{x} \]
i.c.

[_linear]

7045

\[ {}y^{\prime } = 1-\frac {y}{x} \]
i.c.

[_linear]

7067

\[ {}x y^{\prime } = 4 y \]

[_separable]

7127

\[ {}y^{\prime } = -\frac {x}{y} \]
i.c.

[_separable]

7417

\[ {}\left (x +y\right ) y^{\prime }+x -y = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7420

\[ {}x^{2} y^{\prime }+y^{2} = x y y^{\prime } \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

7421

\[ {}\left (x^{2}+y^{2}\right ) y^{\prime } = 2 x y \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

7422

\[ {}-y+x y^{\prime } = x \tan \left (\frac {y}{x}\right ) \]

[[_homogeneous, ‘class A‘], _dAlembert]

7423

\[ {}x y^{\prime } = y-{\mathrm e}^{\frac {y}{x}} x \]

[[_homogeneous, ‘class A‘], _dAlembert]

7424

\[ {}-y+x y^{\prime } = \left (x +y\right ) \ln \left (\frac {x +y}{x}\right ) \]

[[_homogeneous, ‘class A‘], _dAlembert]

7425

\[ {}x y^{\prime } = y \cos \left (\frac {y}{x}\right ) \]

[[_homogeneous, ‘class A‘], _dAlembert]

7426

\[ {}y+\sqrt {x y}-x y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

7427

\[ {}x y^{\prime }-\sqrt {x^{2}-y^{2}}-y = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

7428

\[ {}x +y-y^{\prime } \left (x -y\right ) = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7429

\[ {}x^{2}+2 x y-y^{2}+\left (y^{2}+2 x y-x^{2}\right ) y^{\prime } = 0 \]
i.c.

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

7430

\[ {}-y+x y^{\prime } = y y^{\prime } \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7431

\[ {}y^{2}+\left (x^{2}-x y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

7432

\[ {}y^{2}+x y+x^{2} = x^{2} y^{\prime } \]

[[_homogeneous, ‘class A‘], _rational, _Riccati]

7433

\[ {}\frac {1}{x^{2}-x y+y^{2}} = \frac {y^{\prime }}{2 y^{2}-x y} \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

7434

\[ {}y^{\prime } = \frac {2 x y}{3 x^{2}-y^{2}} \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

7435

\[ {}y^{\prime } = \frac {x}{y}+\frac {y}{x} \]
i.c.

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

7437

\[ {}\left (2 \sqrt {x y}-x \right ) y^{\prime }+y = 0 \]

[[_homogeneous, ‘class A‘], _dAlembert]

7438

\[ {}x y^{\prime } = y \ln \left (\frac {y}{x}\right ) \]

[[_homogeneous, ‘class A‘], _dAlembert]

7440

\[ {}\left (x y^{\prime }+y\right )^{2} = y^{2} y^{\prime } \]

[[_homogeneous, ‘class A‘], _dAlembert]

7441

\[ {}{y^{\prime }}^{2} x^{2}-3 x y y^{\prime }+2 y^{2} = 0 \]

[_separable]

7442

\[ {}-y+x y^{\prime } = \sqrt {x^{2}+y^{2}} \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

7443

\[ {}{y^{\prime }}^{2} y+2 x y^{\prime }-y = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

7444

\[ {}y^{\prime }+\frac {x +2 y}{x} = 0 \]

[_linear]

7445

\[ {}y^{\prime } = \frac {y}{x +y} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7446

\[ {}x y^{\prime } = x +\frac {y}{2} \]
i.c.

[_linear]

7477

\[ {}2 x +4 y+\left (2 x -2 y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7505

\[ {}x y^{\prime }-2 \sqrt {x y} = y \]

[[_homogeneous, ‘class A‘], _dAlembert]

7509

\[ {}x^{2} y^{\prime }+y^{2}-x y = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

7510

\[ {}x +y-y^{\prime } \left (x -y\right ) = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7543

\[ {}y+\sqrt {x^{2}+y^{2}}-x y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

7555

\[ {}y \,{\mathrm e}^{x y}+x \,{\mathrm e}^{x y} y^{\prime } = 0 \]

[_separable]

7560

\[ {}x^{2}+y^{2}-2 x y y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

7561

\[ {}x^{2}-y^{2}+2 x y y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

7564

\[ {}x +y y^{\prime }+y-x y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7732

\[ {}y y^{\prime } = x \]

[_separable]

7739

\[ {}y^{\prime } = \frac {x +y}{x -y} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7740

\[ {}y^{\prime } = \frac {y^{2}}{x^{2}+x y} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

7741

\[ {}y^{\prime } = \frac {y^{2}+x y+x^{2}}{x^{2}} \]

[[_homogeneous, ‘class A‘], _rational, _Riccati]

7742

\[ {}y^{\prime } = \frac {y+x \,{\mathrm e}^{-\frac {2 y}{x}}}{x} \]

[[_homogeneous, ‘class A‘], _dAlembert]

7774

\[ {}x y^{\prime } = 2 y \]

[_separable]

7781

\[ {}y^{\prime } = \frac {x y}{x^{2}+y^{2}} \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

7782

\[ {}2 x y y^{\prime } = x^{2}+y^{2} \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

7784

\[ {}y^{\prime } = \frac {y^{2}}{x y-x^{2}} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

7807

\[ {}x^{5} y^{\prime }+y^{5} = 0 \]

[_separable]

7854

\[ {}y+y \cos \left (x y\right )+\left (x +x \cos \left (x y\right )\right ) y^{\prime } = 0 \]

[_separable]

7871

\[ {}x^{2}-2 y^{2}+x y y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

7872

\[ {}x^{2} y^{\prime }-3 x y-2 y^{2} = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

7873

\[ {}x^{2} y^{\prime } = 3 \left (x^{2}+y^{2}\right ) \arctan \left (\frac {y}{x}\right )+x y \]

[[_homogeneous, ‘class A‘], _dAlembert]

7874

\[ {}x \sin \left (\frac {y}{x}\right ) y^{\prime } = y \sin \left (\frac {y}{x}\right )+x \]

[[_homogeneous, ‘class A‘], _dAlembert]

7875

\[ {}x y^{\prime } = y+2 x \,{\mathrm e}^{-\frac {y}{x}} \]

[[_homogeneous, ‘class A‘], _dAlembert]

7876

\[ {}x -y-\left (x +y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7877

\[ {}x y^{\prime } = 2 x -6 y \]

[_linear]

7878

\[ {}x y^{\prime } = \sqrt {x^{2}+y^{2}} \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

7879

\[ {}x^{2} y^{\prime } = 2 x y+y^{2} \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

7880

\[ {}x^{3}+y^{3}-x y^{2} y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

7889

\[ {}y^{\prime } = \sin \left (\frac {y}{x}\right )-\cos \left (\frac {y}{x}\right ) \]

[[_homogeneous, ‘class A‘], _dAlembert]

7890

\[ {}{\mathrm e}^{\frac {x}{y}}-\frac {y y^{\prime }}{x} = 0 \]

[[_homogeneous, ‘class A‘], _dAlembert]

7891

\[ {}y^{\prime } = \frac {x^{2}-x y}{y^{2} \cos \left (\frac {x}{y}\right )} \]

[[_homogeneous, ‘class A‘], _dAlembert]

7892

\[ {}y^{\prime } = \frac {y \tan \left (\frac {y}{x}\right )}{x} \]

[[_homogeneous, ‘class A‘], _dAlembert]

7917

\[ {}x y^{\prime }+y = x \]

[_linear]

7921

\[ {}y^{\prime } = \frac {x^{2}+y^{2}}{x^{2}-y^{2}} \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

7922

\[ {}y^{\prime } = \frac {x +2 y}{2 x -y} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7923

\[ {}2 x y+x^{2} y^{\prime } = 0 \]

[_separable]

7929

\[ {}y^{\prime } = \frac {x +y}{x -y} \]
i.c.

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7930

\[ {}y^{\prime } = \frac {x^{2}+2 y^{2}}{x^{2}-2 y^{2}} \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

8435

\[ {}{y^{\prime }}^{2} x^{2}-y^{2} = 0 \]

[_separable]

8437

\[ {}{y^{\prime }}^{2} x^{2}-5 x y y^{\prime }+6 y^{2} = 0 \]

[_separable]

8443

\[ {}\left (x +y\right )^{2} {y^{\prime }}^{2} = y^{2} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

8447

\[ {}\left (x -y\right )^{2} {y^{\prime }}^{2} = y^{2} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

8449

\[ {}\left (x^{2}+y^{2}\right )^{2} {y^{\prime }}^{2} = 4 y^{2} x^{2} \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

8450

\[ {}\left (x +y\right )^{2} {y^{\prime }}^{2}+\left (2 y^{2}+x y-x^{2}\right ) y^{\prime }+y \left (y-x \right ) = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

8451

\[ {}x y \left (x^{2}+y^{2}\right ) \left ({y^{\prime }}^{2}-1\right ) = y^{\prime } \left (x^{4}+y^{2} x^{2}+y^{4}\right ) \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

8454

\[ {}{y^{\prime }}^{2} x -2 y y^{\prime }+4 x = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

8470

\[ {}{y^{\prime }}^{2} x -2 y y^{\prime }+4 x = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

8550

\[ {}{y^{\prime }}^{2} x^{2} = \left (x -y\right )^{2} \]

[_linear]

8554

\[ {}{y^{\prime }}^{2} y-\left (x +y\right ) y^{\prime }+y = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

8701

\[ {}y^{\prime } = \frac {2 x -y}{x +4 y} \]
i.c.

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

8724

\[ {}y^{\prime } = \frac {2 y}{x} \]
i.c.

[_separable]

8725

\[ {}y^{\prime } = \frac {2 y}{x} \]

[_separable]

8734

\[ {}x^{2} y^{\prime }+y^{2} = x y y^{\prime } \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

8742

\[ {}y^{\prime } = \frac {5 x^{2}-x y+y^{2}}{x^{2}} \]

[[_homogeneous, ‘class A‘], _rational, _Riccati]

8751

\[ {}y y^{\prime }-y = x \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

8756

\[ {}y = {y^{\prime }}^{2} x \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

8886

\[ {}y^{\prime } = {\mathrm e}^{-\frac {y}{x}} \]

[[_homogeneous, ‘class A‘], _dAlembert]

9035

\[ {}{y^{\prime }}^{2} = \frac {y}{x} \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

10124

\[ {}x y^{\prime }-y-\sqrt {x^{2}+y^{2}} = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

10125

\[ {}x y^{\prime }+a \sqrt {x^{2}+y^{2}}-y = 0 \]

[[_homogeneous, ‘class A‘], _dAlembert]

10128

\[ {}x y^{\prime }-{\mathrm e}^{\frac {y}{x}} x -y-x = 0 \]

[[_homogeneous, ‘class A‘], _dAlembert]

10134

\[ {}x y^{\prime }-y-x \sin \left (\frac {y}{x}\right ) = 0 \]

[[_homogeneous, ‘class A‘], _dAlembert]

10135

\[ {}x y^{\prime }+x -y+x \cos \left (\frac {y}{x}\right ) = 0 \]

[[_homogeneous, ‘class A‘], _dAlembert]

10136

\[ {}x y^{\prime }+x \tan \left (\frac {y}{x}\right )-y = 0 \]

[[_homogeneous, ‘class A‘], _dAlembert]

10147

\[ {}x^{2} y^{\prime }+x^{2}+x y+y^{2} = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Riccati]

10148

\[ {}x^{2} y^{\prime }-y^{2}-x y = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

10149

\[ {}x^{2} y^{\prime }-y^{2}-x y-x^{2} = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Riccati]

10178

\[ {}3 x^{2} y^{\prime }-7 y^{2}-3 x y-x^{2} = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Riccati]

10214

\[ {}y y^{\prime }+a y+x = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

10221

\[ {}y y^{\prime }-x \,{\mathrm e}^{\frac {x}{y}} = 0 \]

[[_homogeneous, ‘class A‘], _dAlembert]

10232

\[ {}\left (-x +2 y\right ) y^{\prime }-y-2 x = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

10241

\[ {}x y y^{\prime }+x^{2}+y^{2} = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

10248

\[ {}\left (x y-x^{2}\right ) y^{\prime }+y^{2}-3 x y-2 x^{2} = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

10250

\[ {}2 x y y^{\prime }-y^{2}+a \,x^{2} = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

10255

\[ {}x \left (2 x +3 y\right ) y^{\prime }+3 \left (x +y\right )^{2} = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

10271

\[ {}\left (2 x^{2} y-x^{3}\right ) y^{\prime }+y^{3}-4 x y^{2}+2 x^{3} = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]

10279

\[ {}\left (x^{2}+y^{2}\right ) y^{\prime }+2 x \left (2 x +y\right ) = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]

10280

\[ {}\left (x^{2}+y^{2}\right ) y^{\prime }-y^{2} = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

10284

\[ {}\left (y^{2}-x^{2}\right ) y^{\prime }+2 x y = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

10289

\[ {}x^{2}+2 x y-y^{2}+\left (y^{2}+2 x y-x^{2}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

10292

\[ {}\left (4 y^{2}+x^{2}\right ) y^{\prime }-x y = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

10293

\[ {}\left (3 x^{2}+2 x y+4 y^{2}\right ) y^{\prime }+2 x^{2}+6 x y+y^{2} = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]

10298

\[ {}\left (a y^{2}+2 b x y+c \,x^{2}\right ) y^{\prime }+b y^{2}+2 c x y+d \,x^{2} = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]

10303

\[ {}x \left (y^{2}+x y-x^{2}\right ) y^{\prime }-y^{3}+x y^{2}+x^{2} y = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

10305

\[ {}2 x \left (5 x^{2}+y^{2}\right ) y^{\prime }+y^{3}-x^{2} y = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

10314

\[ {}\left (y^{3}-x^{3}\right ) y^{\prime }-x^{2} y = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

10316

\[ {}2 y^{3} y^{\prime }+x y^{2} = 0 \]

[_separable]

10318

\[ {}\left (2 y^{3}+5 x^{2} y\right ) y^{\prime }+5 x y^{2}+x^{3} = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]

10319

\[ {}\left (3 x^{3}+6 x^{2} y-3 x y^{2}+20 y^{3}\right ) y^{\prime }+4 x^{3}+9 x^{2} y+6 x y^{2}-y^{3} = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]

10323

\[ {}\left (2 x y^{3}-x^{4}\right ) y^{\prime }+2 x^{3} y-y^{4} = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

10333

\[ {}y \left (y^{3}-2 x^{3}\right ) y^{\prime }+\left (2 y^{3}-x^{3}\right ) x = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

10334

\[ {}y \left (\left (b x +a y\right )^{3}+b \,x^{3}\right ) y^{\prime }+x \left (\left (b x +a y\right )^{3}+a y^{3}\right ) = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

10344

\[ {}\left (x +\sqrt {x^{2}+y^{2}}\right ) y^{\prime }-y = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

10345

\[ {}\left (y \sqrt {x^{2}+y^{2}}+\left (y^{2}-x^{2}\right ) \sin \left (\alpha \right )-2 x y \cos \left (\alpha \right )\right ) y^{\prime }+x \sqrt {x^{2}+y^{2}}+2 x y \sin \left (\alpha \right )+\left (y^{2}-x^{2}\right ) \cos \left (\alpha \right ) = 0 \]

[[_homogeneous, ‘class A‘], _dAlembert]

10356

\[ {}x y^{\prime } \cot \left (\frac {y}{x}\right )+2 x \sin \left (\frac {y}{x}\right )-y \cot \left (\frac {y}{x}\right ) = 0 \]

[[_homogeneous, ‘class A‘]]

10370

\[ {}\left (-y+x y^{\prime }\right ) \cos \left (\frac {y}{x}\right )^{2}+x = 0 \]

[[_homogeneous, ‘class A‘], _dAlembert]

10371

\[ {}\left (y \sin \left (\frac {y}{x}\right )-x \cos \left (\frac {y}{x}\right )\right ) x y^{\prime }-\left (x \cos \left (\frac {y}{x}\right )+y \sin \left (\frac {y}{x}\right )\right ) y = 0 \]

[[_homogeneous, ‘class A‘], _dAlembert]

10410

\[ {}{y^{\prime }}^{2} x -y = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

10411

\[ {}{y^{\prime }}^{2} x -2 y+x = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

10414

\[ {}{y^{\prime }}^{2} x +x y^{\prime }-y = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

10419

\[ {}{y^{\prime }}^{2} x +\left (y-3 x \right ) y^{\prime }+y = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

10421

\[ {}{y^{\prime }}^{2} x -y y^{\prime }+a y = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

10422

\[ {}{y^{\prime }}^{2} x +2 y y^{\prime }-x = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

10424

\[ {}{y^{\prime }}^{2} x -2 y y^{\prime }-x = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

10425

\[ {}{y^{\prime }}^{2} x -2 y y^{\prime }+4 x = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

10426

\[ {}{y^{\prime }}^{2} x -2 y y^{\prime }+x +2 y = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

10427

\[ {}{y^{\prime }}^{2} x +a y y^{\prime }+b x = 0 \]

[[_homogeneous, ‘class A‘], _dAlembert]

10441

\[ {}{y^{\prime }}^{2} x^{2}+3 x y y^{\prime }+2 y^{2} = 0 \]

[_separable]

10443

\[ {}{y^{\prime }}^{2} x^{2}+4 x y y^{\prime }-5 y^{2} = 0 \]

[_separable]

10446

\[ {}{y^{\prime }}^{2} x^{2}-y \left (-2 x +y\right ) y^{\prime }+y^{2} = 0 \]

[[_homogeneous, ‘class A‘], _dAlembert]

10455

\[ {}\left (a^{2}-1\right ) x^{2} {y^{\prime }}^{2}+2 x y y^{\prime }-y^{2}+a^{2} x^{2} = 0 \]

[[_homogeneous, ‘class A‘], _dAlembert]

10456

\[ {}a \,x^{2} {y^{\prime }}^{2}-2 a x y y^{\prime }+y^{2}-a \left (a -1\right ) x^{2} = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

10465

\[ {}{y^{\prime }}^{2} y+2 x y^{\prime }-y = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

10466

\[ {}{y^{\prime }}^{2} y+2 x y^{\prime }-9 y = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

10467

\[ {}{y^{\prime }}^{2} y-2 x y^{\prime }+y = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

10468

\[ {}{y^{\prime }}^{2} y-4 x y^{\prime }+y = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

10469

\[ {}{y^{\prime }}^{2} y-4 a^{2} x y^{\prime }+a^{2} y = 0 \]

[[_homogeneous, ‘class A‘], _dAlembert]

10470

\[ {}{y^{\prime }}^{2} y+a x y^{\prime }+b y = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

10473

\[ {}\left (x +y\right ) {y^{\prime }}^{2}+2 x y^{\prime }-y = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

10476

\[ {}4 {y^{\prime }}^{2} y+2 x y^{\prime }-y = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

10482

\[ {}x y {y^{\prime }}^{2}+\left (x^{2}+y^{2}\right ) y^{\prime }+x y = 0 \]

[_separable]

10484

\[ {}\left (2 x y-x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+2 x y-y^{2} = 0 \]

[[_homogeneous, ‘class A‘], _dAlembert]

10485

\[ {}\left (2 x y-x^{2}\right ) {y^{\prime }}^{2}-6 x y y^{\prime }-y^{2}+2 x y = 0 \]

[[_homogeneous, ‘class A‘], _dAlembert]

10495

\[ {}\left (y^{2}-a^{2} x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+\left (-a^{2}+1\right ) x^{2} = 0 \]

[[_homogeneous, ‘class A‘], _dAlembert]

10496

\[ {}\left (\left (1-a \right ) x^{2}+y^{2}\right ) {y^{\prime }}^{2}+2 a x y y^{\prime }+\left (1-a \right ) y^{2}+x^{2} = 0 \]

[[_homogeneous, ‘class A‘], _dAlembert]

10498

\[ {}3 y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+4 y^{2}-x^{2} = 0 \]

[[_homogeneous, ‘class A‘], _dAlembert]

10500

\[ {}\left (-a^{2}+1\right ) y^{2} {y^{\prime }}^{2}-2 a^{2} x y y^{\prime }+y^{2}-a^{2} x^{2} = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

10506

\[ {}x y^{2} {y^{\prime }}^{2}-2 y^{3} y^{\prime }+2 x y^{2}-x^{3} = 0 \]

[_separable]

10517

\[ {}\left (x^{2}+y^{2}\right ) f \left (\frac {x}{\sqrt {x^{2}+y^{2}}}\right ) \left (1+{y^{\prime }}^{2}\right )-\left (-y+x y^{\prime }\right )^{2} = 0 \]

[[_homogeneous, ‘class A‘]]

10518

\[ {}\left (x^{2}+y^{2}\right ) f \left (\frac {y}{\sqrt {x^{2}+y^{2}}}\right ) \left (1+{y^{\prime }}^{2}\right )-\left (-y+x y^{\prime }\right )^{2} = 0 \]

[[_homogeneous, ‘class A‘]]

10558

\[ {}x \left (\sqrt {1+{y^{\prime }}^{2}}+y^{\prime }\right )-y = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

10560

\[ {}y \sqrt {1+{y^{\prime }}^{2}}-a y y^{\prime }-a x = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

11927

\[ {}y^{\prime } = f \left (\frac {y}{x}\right ) \]

[[_homogeneous, ‘class A‘], _dAlembert]

12720

\[ {}\frac {-2 x^{2}+y^{2}}{x y^{2}-x^{3}}+\frac {\left (2 y^{2}-x^{2}\right ) y^{\prime }}{y^{3}-x^{2} y} = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]

12721

\[ {}\frac {1}{\sqrt {x^{2}+y^{2}}}+\left (\frac {1}{y}-\frac {x}{y \sqrt {x^{2}+y^{2}}}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]

12722

\[ {}y+x +x y^{\prime } = 0 \]

[_linear]

12728

\[ {}{\mathrm e}^{\frac {y}{x}} x +y-x y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _dAlembert]

12729

\[ {}2 x^{2} y+3 y^{3}-\left (x^{3}+2 x y^{2}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

12730

\[ {}x^{2} y^{\prime }+y^{2}-x y = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

12731

\[ {}2 x^{2} y+y^{3}-x^{3} y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

12732

\[ {}y^{3}+x^{3} y^{\prime } = 0 \]

[_separable]

12733

\[ {}x +y \cos \left (\frac {y}{x}\right )-x \cos \left (\frac {y}{x}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _dAlembert]

12751

\[ {}y^{2} \left (3 y-6 x y^{\prime }\right )-x \left (y-2 x y^{\prime }\right ) = 0 \]

[_separable]

12753

\[ {}x^{2} y^{\prime }+y^{2}-x y = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

12755

\[ {}x +y-y^{\prime } \left (x -y\right ) = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

12756

\[ {}x^{2}+y^{2}-2 x y y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

12759

\[ {}3 x^{2}+6 x y+3 y^{2}+\left (2 x^{2}+3 x y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

12763

\[ {}y^{2}-x^{2}+2 m x y+\left (m y^{2}-m \,x^{2}-2 x y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

12766

\[ {}x +y y^{\prime }+y-x y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

12774

\[ {}\left (y-x \right ) y^{\prime }+y = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

12775

\[ {}-y+x y^{\prime } = \sqrt {x^{2}+y^{2}} \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

12776

\[ {}-y+x y^{\prime } = \sqrt {x^{2}-y^{2}} \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

12777

\[ {}x \sin \left (\frac {y}{x}\right )-y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _dAlembert]

12790

\[ {}y^{3}-2 x^{2} y+\left (2 x y^{2}-x^{3}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

12793

\[ {}1+{\mathrm e}^{\frac {y}{x}}+{\mathrm e}^{\frac {x}{y}} \left (1-\frac {x}{y}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _dAlembert]

12796

\[ {}\left (2 \sqrt {x y}-x \right ) y^{\prime }+y = 0 \]

[[_homogeneous, ‘class A‘], _dAlembert]

12798

\[ {}{y^{\prime }}^{2} x -2 y y^{\prime }-x = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

12804

\[ {}4 {y^{\prime }}^{2} x +2 x y^{\prime }-y = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

12805

\[ {}{y^{\prime }}^{2} x -2 y y^{\prime }-x = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

12809

\[ {}x +y^{\prime } y \left (2 {y^{\prime }}^{2}+3\right ) = 0 \]

[[_homogeneous, ‘class A‘], _dAlembert]

12810

\[ {}a^{2} y {y^{\prime }}^{2}-2 x y^{\prime }+y = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

12811

\[ {}{y^{\prime }}^{2} x -2 y y^{\prime }-x = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

12818

\[ {}\left (x^{2}+y^{2}\right ) \left (1+y^{\prime }\right )^{2}-2 \left (x +y\right ) \left (1+y^{\prime }\right ) \left (x +y y^{\prime }\right )+\left (x +y y^{\prime }\right )^{2} = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

12820

\[ {}a^{2} y {y^{\prime }}^{2}-2 x y^{\prime }+y = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

12825

\[ {}3 {y^{\prime }}^{2} x -6 y y^{\prime }+x +2 y = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

12834

\[ {}{y^{\prime }}^{2} x -2 y y^{\prime }-x = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

12946

\[ {}x^{\prime } = \frac {2 x}{t} \]

[_separable]

12947

\[ {}x^{\prime } = -\frac {t}{x} \]

[_separable]

12952

\[ {}2 t x^{\prime } = x \]

[_separable]

12991

\[ {}x^{\prime } = \frac {4 t^{2}+3 x^{2}}{2 t x} \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

12994

\[ {}y^{\prime } = \frac {y^{2}+2 t y}{t^{2}} \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

13021

\[ {}x^{\prime } = \frac {2 x}{3 t}+\frac {2 t}{x} \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

13024

\[ {}t^{2} y^{\prime }+2 t y-y^{2} = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

13027

\[ {}x^{3}+3 t x^{2} x^{\prime } = 0 \]

[_separable]

13031

\[ {}x^{2}-t^{2} x^{\prime } = 0 \]

[_separable]

13171

\[ {}x^{2}+y^{2}+2 x y y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli]

13193

\[ {}3 x +2 y+\left (2 x +y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

13209

\[ {}y^{2}+2 x y-x^{2} y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

13219

\[ {}2 x y+3 y^{2}-\left (x^{2}+2 x y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

13220

\[ {}v^{3}+\left (u^{3}-u v^{2}\right ) v^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

13221

\[ {}x \tan \left (\frac {y}{x}\right )+y-x y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _dAlembert]

13222

\[ {}\left (2 s^{2}+2 s t +t^{2}\right ) s^{\prime }+s^{2}+2 s t -t^{2} = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]

13223

\[ {}x^{3}+y^{2} \sqrt {x^{2}+y^{2}}-x y \sqrt {x^{2}+y^{2}}\, y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _dAlembert]

13224

\[ {}\sqrt {x +y}+\sqrt {x -y}+\left (\sqrt {x -y}-\sqrt {x +y}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _dAlembert]

13228

\[ {}x^{2}+3 y^{2}-2 x y y^{\prime } = 0 \]
i.c.

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

13229

\[ {}2 x -5 y+\left (4 x -y\right ) y^{\prime } = 0 \]
i.c.

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

13230

\[ {}3 x^{2}+9 x y+5 y^{2}-\left (6 x^{2}+4 x y\right ) y^{\prime } = 0 \]
i.c.

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

13231

\[ {}x +2 y+\left (2 x -y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

13232

\[ {}3 x -y-\left (x +y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

13233

\[ {}x^{2}+2 y^{2}+\left (4 x y-y^{2}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]

13234

\[ {}2 x^{2}+2 x y+y^{2}+\left (x^{2}+2 x y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

13276

\[ {}3 x -5 y+\left (x +y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

13279

\[ {}2 x^{2}+x y+y^{2}+2 x^{2} y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Riccati]

13282

\[ {}y^{\prime } = \frac {2 x -7 y}{3 y-8 x} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

13285

\[ {}y^{\prime } = \frac {2 x^{2}+y^{2}}{2 x y-x^{2}} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

13286

\[ {}x^{2}+y^{2}-2 x y y^{\prime } = 0 \]
i.c.

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

13291

\[ {}y^{\prime } = \frac {2 x +7 y}{2 x -2 y} \]
i.c.

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

13295

\[ {}x^{2} y^{\prime }+x y = \frac {y^{3}}{x} \]
i.c.

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

13646

\[ {}x y^{\prime } = k y \]

[_separable]

13668

\[ {}x y+y^{2}+x^{2}-x^{2} y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Riccati]

13669

\[ {}x^{\prime } = \frac {x^{2}+t \sqrt {t^{2}+x^{2}}}{t x} \]

[[_homogeneous, ‘class A‘], _dAlembert]

13771

\[ {}x y^{\prime } = y+\sqrt {x^{2}+y^{2}} \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

13778

\[ {}x \left (\ln \left (x \right )-\ln \left (y\right )\right ) y^{\prime }-y = 0 \]

[[_homogeneous, ‘class A‘], _dAlembert]

13779

\[ {}x y {y^{\prime }}^{2}-\left (x^{2}+y^{2}\right ) y^{\prime }+x y = 0 \]

[_separable]

13781

\[ {}x^{\prime } = {\mathrm e}^{\frac {x}{t}}+\frac {x}{t} \]

[[_homogeneous, ‘class A‘], _dAlembert]

13798

\[ {}y \left (x -y\right )-x^{2} y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

13810

\[ {}y \left (x -y\right )-x^{2} y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

13816

\[ {}\left (y^{2}-x^{2}\right ) y^{\prime }+2 x y = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

14077

\[ {}{y^{\prime }}^{2} y+2 x y^{\prime }-y = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

14096

\[ {}y-x +\left (x +y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

14097

\[ {}y+x +x y^{\prime } = 0 \]

[_linear]

14098

\[ {}x +y+\left (y-x \right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

14099

\[ {}-y+x y^{\prime } = \sqrt {x^{2}+y^{2}} \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

14100

\[ {}8 y+10 x +\left (7 x +5 y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

14101

\[ {}2 \sqrt {s t}-s+t s^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _dAlembert]

14103

\[ {}x y^{2} y^{\prime } = x^{3}+y^{3} \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

14104

\[ {}x \cos \left (\frac {y}{x}\right ) \left (x y^{\prime }+y\right ) = y \sin \left (\frac {y}{x}\right ) \left (-y+x y^{\prime }\right ) \]

[[_homogeneous, ‘class A‘], _dAlembert]

14108

\[ {}\frac {y-x y^{\prime }}{\sqrt {x^{2}+y^{2}}} = m \]

[[_homogeneous, ‘class A‘], _dAlembert]

14109

\[ {}\frac {x +y y^{\prime }}{\sqrt {x^{2}+y^{2}}} = m \]

[[_homogeneous, ‘class A‘], _exact, _dAlembert]

14110

\[ {}y+\frac {x}{y^{\prime }} = \sqrt {x^{2}+y^{2}} \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

14111

\[ {}y y^{\prime } = -x +\sqrt {x^{2}+y^{2}} \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

14132

\[ {}\frac {x}{\left (x +y\right )^{2}}+\frac {\left (2 x +y\right ) y^{\prime }}{\left (x +y\right )^{2}} = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]

14133

\[ {}\frac {1}{x^{2}}+\frac {3 y^{2}}{x^{4}} = \frac {2 y y^{\prime }}{x^{3}} \]

[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli]

14134

\[ {}\frac {x^{2} y^{\prime }}{\left (x -y\right )^{2}}-\frac {y^{2}}{\left (x -y\right )^{2}} = 0 \]

[_separable]

14139

\[ {}y = {y^{\prime }}^{2} y+2 x y^{\prime } \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

14145

\[ {}y^{\prime } = \frac {2 y}{x}-\sqrt {3} \]

[_linear]

14197

\[ {}\frac {x^{2} y^{\prime }}{\left (x -y\right )^{2}}-\frac {y^{2}}{\left (x -y\right )^{2}} = 0 \]

[_separable]

14201

\[ {}x \cos \left (\frac {y}{x}\right ) y^{\prime } = y \cos \left (\frac {y}{x}\right )-x \]

[[_homogeneous, ‘class A‘], _dAlembert]

14239

\[ {}2 x y+x^{2} y^{\prime } = 0 \]

[_separable]

14247

\[ {}2 x y^{\prime }-y = 0 \]

[_separable]

14284

\[ {}y^{\prime } = \frac {x}{y} \]

[_separable]

14292

\[ {}y^{\prime } = \frac {2 x -y}{x +3 y} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

14295

\[ {}y^{\prime } = \frac {x y}{x^{2}+y^{2}} \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

14299

\[ {}y^{\prime } = \frac {y}{y-x} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

14333

\[ {}y^{\prime } = \frac {2 x}{y} \]
i.c.

[_separable]

14341

\[ {}y^{\prime } = -\frac {y \left (2 x +y\right )}{x \left (x +2 y\right )} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

14350

\[ {}x -y y^{\prime } = 0 \]

[_separable]

14385

\[ {}y^{\prime } = \frac {y}{y-x} \]
i.c.

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

14386

\[ {}y^{\prime } = \frac {y}{y-x} \]
i.c.

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

14387

\[ {}y^{\prime } = \frac {y}{y-x} \]
i.c.

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

14388

\[ {}y^{\prime } = \frac {y}{y-x} \]
i.c.

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

14390

\[ {}y^{\prime } = \frac {x y}{x^{2}+y^{2}} \]
i.c.

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

14530

\[ {}y^{\prime } = \frac {t}{y} \]

[_separable]

14663

\[ {}y^{\prime } = -\frac {y}{t}+2 \]

[_linear]

14671

\[ {}y^{\prime } = -\frac {y}{t}+2 \]
i.c.

[_linear]

14904

\[ {}y y^{\prime } = 2 x \]

[_separable]

14966

\[ {}y^{\prime } = \frac {x}{y} \]

[_separable]

14972

\[ {}y^{\prime } = \frac {x}{y} \]
i.c.

[_separable]

15037

\[ {}x^{2} y^{\prime }-x y = y^{2} \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

15038

\[ {}y^{\prime } = \frac {x}{y}+\frac {y}{x} \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

15039

\[ {}\cos \left (\frac {y}{x}\right ) \left (y^{\prime }-\frac {y}{x}\right ) = 1+\sin \left (\frac {y}{x}\right ) \]

[[_homogeneous, ‘class A‘], _dAlembert]

15040

\[ {}y^{\prime } = \frac {x -y}{x +y} \]
i.c.

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

15042

\[ {}y^{\prime }-\frac {3 y}{x} = \frac {y^{2}}{x^{2}} \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

15045

\[ {}y^{\prime } = \frac {y}{x}+\frac {x^{2}}{y^{2}} \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

15050

\[ {}\left (x +y\right ) y^{\prime } = y \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

15051

\[ {}\left (2 x y+2 x^{2}\right ) y^{\prime } = x^{2}+2 x y+2 y^{2} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

15055

\[ {}-y+x y^{\prime } = \sqrt {x^{2}+x y} \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

15063

\[ {}2 x y+y^{2}+\left (x^{2}+2 x y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

15067

\[ {}4 x^{3} y+\left (x^{4}-y^{4}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]

15085

\[ {}x y y^{\prime }-y^{2} = \sqrt {x^{4}+y^{2} x^{2}} \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

15089

\[ {}x^{3}+y^{3}+x y^{2} y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

15101

\[ {}x y y^{\prime } = 2 x^{2}+2 y^{2} \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

15103

\[ {}y^{\prime } = \frac {x +2 y}{2 x -y} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

15104

\[ {}y^{\prime } = \frac {y}{x}+\tan \left (\frac {y}{x}\right ) \]

[[_homogeneous, ‘class A‘], _dAlembert]

15110

\[ {}x y y^{\prime } = y^{2}+x y+x^{2} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

15710

\[ {}2 x -y-y y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

15723

\[ {}y^{\prime } = -\frac {x}{y} \]

[_separable]

15725

\[ {}y^{\prime } = -\frac {2 y}{x}-3 \]

[_linear]

15754

\[ {}y^{\prime } = \frac {2 x y+y^{2}}{x^{2}} \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

15771

\[ {}2 x -3 y+\left (2 y-3 x \right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

15813

\[ {}y^{\prime } = -\frac {t}{y} \]
i.c.

[_separable]

15860

\[ {}y^{\prime } = \sqrt {\frac {y}{t}} \]
i.c.

[[_homogeneous, ‘class A‘], _dAlembert]

15892

\[ {}t y^{\prime }+y = t \]

[_linear]

15946

\[ {}\frac {t}{\sqrt {t^{2}+y^{2}}}+\frac {y y^{\prime }}{\sqrt {t^{2}+y^{2}}} = 0 \]

[_separable]

15947

\[ {}y \cos \left (t y\right )+t \cos \left (t y\right ) y^{\prime } = 0 \]

[_separable]

15949

\[ {}3 t y^{2}+y^{3} y^{\prime } = 0 \]

[_separable]

15953

\[ {}{\mathrm e}^{t y}+\frac {t \,{\mathrm e}^{t y} y^{\prime }}{y} = 0 \]

[_separable]

15956

\[ {}y^{2}+2 t y y^{\prime } = 0 \]

[_separable]

15957

\[ {}\frac {3 t^{2}}{y}-\frac {t^{3} y^{\prime }}{y^{2}} = 0 \]

[_separable]

15960

\[ {}2 t y+\left (t^{2}+y^{2}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]

15963

\[ {}3 t^{2}+3 y^{2}+6 t y y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli]

15972

\[ {}-\frac {y^{2} {\mathrm e}^{\frac {y}{t}}}{t^{2}}+1+{\mathrm e}^{\frac {y}{t}} \left (1+\frac {y}{t}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _dAlembert]

15973

\[ {}2 t \sin \left (\frac {y}{t}\right )-y \cos \left (\frac {y}{t}\right )+t \cos \left (\frac {y}{t}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _dAlembert]

15974

\[ {}2 t y^{2}+2 t^{2} y y^{\prime } = 0 \]
i.c.

[_separable]

15986

\[ {}t^{2} y+t^{3} y^{\prime } = 0 \]

[_separable]

15989

\[ {}2 t y+y^{2}-t^{2} y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

15997

\[ {}\frac {9 t}{5}+2 y+\left (2 t +2 y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

15998

\[ {}2 t +\frac {19 y}{10}+\left (\frac {19 t}{10}+2 y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

16006

\[ {}y^{\prime }-\frac {y}{t} = \frac {y^{2}}{t^{2}} \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

16009

\[ {}\cos \left (\frac {t}{y+t}\right )+{\mathrm e}^{\frac {2 y}{t}} y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _dAlembert]

16010

\[ {}y \ln \left (\frac {t}{y}\right )+\frac {t^{2} y^{\prime }}{y+t} = 0 \]

[[_homogeneous, ‘class A‘], _dAlembert]

16012

\[ {}\frac {2}{t}+\frac {1}{y}+\frac {t y^{\prime }}{y^{2}} = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

16015

\[ {}2 t +\left (y-3 t \right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]

16016

\[ {}2 y-3 t +t y^{\prime } = 0 \]

[_linear]

16017

\[ {}t y-y^{2}+t \left (t -3 y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

16018

\[ {}t^{2}+t y+y^{2}-t y y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

16019

\[ {}t^{3}+y^{3}-t y^{2} y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

16020

\[ {}y^{\prime } = \frac {t +4 y}{4 t +y} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

16022

\[ {}y+\left (y+t \right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

16023

\[ {}2 t^{2}-7 t y+5 y^{2}+t y y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

16024

\[ {}y+2 \sqrt {t^{2}+y^{2}}-t y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _dAlembert]

16025

\[ {}y^{2} = \left (t y-4 t^{2}\right ) y^{\prime } \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

16026

\[ {}y-\left (3 \sqrt {t y}+t \right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _dAlembert]

16027

\[ {}\left (t^{2}-y^{2}\right ) y^{\prime }+y^{2}+t y = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

16028

\[ {}t y y^{\prime }-t^{2} {\mathrm e}^{-\frac {y}{t}}-y^{2} = 0 \]

[[_homogeneous, ‘class A‘], _dAlembert]

16029

\[ {}y^{\prime } = \frac {1}{\frac {2 y \,{\mathrm e}^{-\frac {t}{y}}}{t}+\frac {t}{y}} \]

[[_homogeneous, ‘class A‘], _dAlembert]

16030

\[ {}t \left (\ln \left (t \right )-\ln \left (y\right )\right ) y^{\prime } = y \]

[[_homogeneous, ‘class A‘], _dAlembert]

16033

\[ {}y^{\prime } = \frac {4 y^{2}-t^{2}}{2 t y} \]
i.c.

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

16035

\[ {}t y^{\prime }-y-\sqrt {t^{2}+y^{2}} = 0 \]
i.c.

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

16036

\[ {}t^{3}+y^{2} \sqrt {t^{2}+y^{2}}-t y \sqrt {t^{2}+y^{2}}\, y^{\prime } = 0 \]
i.c.

[[_homogeneous, ‘class A‘], _dAlembert]

16037

\[ {}y^{3}-t^{3}-t y^{2} y^{\prime } = 0 \]
i.c.

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

16038

\[ {}t y^{3}-\left (t^{4}+y^{4}\right ) y^{\prime } = 0 \]
i.c.

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

16039

\[ {}y^{4}+\left (t^{4}-t y^{3}\right ) y^{\prime } = 0 \]
i.c.

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

16055

\[ {}t^{{1}/{3}} y^{{2}/{3}}+t +\left (t^{{2}/{3}} y^{{1}/{3}}+y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _rational]

16056

\[ {}y^{\prime } = \frac {y^{2}-t^{2}}{t y} \]
i.c.

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

16057

\[ {}y \sin \left (\frac {t}{y}\right )-\left (t +t \sin \left (\frac {t}{y}\right )\right ) y^{\prime } = 0 \]
i.c.

[[_homogeneous, ‘class A‘], _dAlembert]

16067

\[ {}3 t +\left (t -4 y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]

16068

\[ {}y-t +\left (y+t \right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

16070

\[ {}y^{2}+\left (t^{2}+t y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

16071

\[ {}r^{\prime } = \frac {r^{2}+t^{2}}{r t} \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

16072

\[ {}x^{\prime } = \frac {5 t x}{t^{2}+x^{2}} \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

16586

\[ {}y^{\prime } = \frac {x}{y} \]

[_separable]

16610

\[ {}y^{\prime } = \frac {x +y}{x -y} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

16614

\[ {}y^{\prime } = -\frac {y}{x} \]

[_separable]

16623

\[ {}x y^{\prime } = 2 x -y \]
i.c.

[_linear]

16658

\[ {}x y^{\prime } = y+x \cos \left (\frac {y}{x}\right )^{2} \]

[[_homogeneous, ‘class A‘], _dAlembert]

16660

\[ {}x y^{\prime } = y \left (\ln \left (y\right )-\ln \left (x \right )\right ) \]

[[_homogeneous, ‘class A‘], _dAlembert]

16661

\[ {}x^{2} y^{\prime } = x^{2}-x y+y^{2} \]

[[_homogeneous, ‘class A‘], _rational, _Riccati]

16663

\[ {}2 x^{2} y^{\prime } = x^{2}+y^{2} \]

[[_homogeneous, ‘class A‘], _rational, _Riccati]

16664

\[ {}4 x -3 y+\left (2 y-3 x \right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

16665

\[ {}y-x +\left (x +y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

16698

\[ {}x y^{\prime }+y = 2 x \]

[_linear]

16702

\[ {}3 x y^{2} y^{\prime }-2 y^{3} = x^{3} \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

16715

\[ {}x \left (2 x^{2}+y^{2}\right )+y \left (x^{2}+2 y^{2}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]

16725

\[ {}\frac {2 x}{y^{3}}+\frac {\left (y^{2}-3 x^{2}\right ) y^{\prime }}{y^{4}} = 0 \]
i.c.

[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]

16727

\[ {}3 x^{2} y+y^{3}+\left (x^{3}+3 x y^{2}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]

16741

\[ {}{y^{\prime }}^{2} x^{2}+3 x y y^{\prime }+2 y^{2} = 0 \]

[_separable]

16783

\[ {}\left (x y^{\prime }+y\right )^{2} = y^{2} y^{\prime } \]

[[_homogeneous, ‘class A‘], _dAlembert]

16786

\[ {}3 {y^{\prime }}^{2} x -6 y y^{\prime }+x +2 y = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

16791

\[ {}x^{3}-3 x y^{2}+\left (y^{3}-3 x^{2} y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]

16792

\[ {}5 x y-4 y^{2}-6 x^{2}+\left (y^{2}-8 x y+\frac {5 x^{2}}{2}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]

16799

\[ {}\frac {1}{x^{2}-x y+y^{2}} = \frac {y^{\prime }}{2 y^{2}-x y} \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

16805

\[ {}1+{\mathrm e}^{\frac {x}{y}}+{\mathrm e}^{\frac {x}{y}} \left (1-\frac {x}{y}\right ) y^{\prime } = 0 \]
i.c.

[[_homogeneous, ‘class A‘], _exact, _dAlembert]

16806

\[ {}x^{2}+y^{2}-x y y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

17299

\[ {}y^{\prime } = \frac {-y+t}{2 t +5 y} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

17307

\[ {}y^{\prime } = -\frac {4 t}{y} \]
i.c.

[_separable]

17317

\[ {}2 x +4 y+\left (2 x -2 y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

17319

\[ {}2 x y^{2}+2 y+\left (2 x^{2} y+2 x \right ) y^{\prime } = 0 \]

[_separable]

17320

\[ {}y^{\prime } = -\frac {4 x +2 y}{2 x +3 y} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

17321

\[ {}y^{\prime } = -\frac {4 x -2 y}{2 x -3 y} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

17327

\[ {}\frac {x}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{{3}/{2}}} = 0 \]

[_separable]

17328

\[ {}2 x -y+\left (-x +2 y\right ) y^{\prime } = 0 \]
i.c.

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

17341

\[ {}3 x y+y^{2}+\left (x^{2}+x y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

17344

\[ {}\frac {\left (3 x^{3}-x y^{2}\right ) y^{\prime }}{3 x^{2} y+y^{3}} = 1 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

17346

\[ {}\sqrt {x^{2}-y^{2}}+y = x y^{\prime } \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

17347

\[ {}x y y^{\prime } = \left (x +y\right )^{2} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

17348

\[ {}y^{\prime } = \frac {4 y-7 x}{5 x -y} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

17350

\[ {}y^{\prime } = \frac {y^{4}+2 x y^{3}-3 y^{2} x^{2}-2 x^{3} y}{2 y^{2} x^{2}-2 x^{3} y-2 x^{4}} \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

17351

\[ {}\left (y+x \,{\mathrm e}^{\frac {x}{y}}\right ) y^{\prime } = y \,{\mathrm e}^{\frac {x}{y}} \]

[[_homogeneous, ‘class A‘], _dAlembert]

17352

\[ {}x y y^{\prime } = x^{2}+y^{2} \]
i.c.

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

17364

\[ {}\left (3 x-y \right ) x^{\prime }+9 y -2 x = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

17370

\[ {}5 x y^{2}+5 y+\left (5 x^{2} y+5 x \right ) y^{\prime } = 0 \]

[_separable]

17374

\[ {}x^{\prime } = \frac {2 x y +x^{2}}{3 y^{2}+2 x y} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

17375

\[ {}4 x y y^{\prime } = 8 x^{2}+5 y^{2} \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

17818

\[ {}y^{\prime } = \frac {2 x y}{x^{2}+y^{2}} \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

17819

\[ {}y^{\prime } = \frac {y \left (1+\ln \left (y\right )-\ln \left (x \right )\right )}{x} \]

[[_homogeneous, ‘class A‘], _dAlembert]

17820

\[ {}x^{2} y^{\prime }+y^{2} = x y y^{\prime } \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

17821

\[ {}\left (x +y\right ) y^{\prime } = y-x \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

17822

\[ {}x -y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _dAlembert]

17847

\[ {}\frac {2 x}{y^{3}}+\frac {\left (y^{2}-3 x^{2}\right ) y^{\prime }}{y^{4}} = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]

17860

\[ {}{y^{\prime }}^{2} x +2 x y^{\prime }-y = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

17869

\[ {}y = \frac {k \left (x +y y^{\prime }\right )}{\sqrt {1+{y^{\prime }}^{2}}} \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

17883

\[ {}{y^{\prime }}^{2} x -2 y y^{\prime }+4 x = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

17884

\[ {}{y^{\prime }}^{2} x +2 x y^{\prime }-y = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

17887

\[ {}{y^{\prime }}^{2} x^{2}-2 x y y^{\prime }+2 x y = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

17978

\[ {}x y^{\prime } = 2 y \]

[_separable]

17985

\[ {}y^{\prime } = \frac {x y}{x^{2}+y^{2}} \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

17986

\[ {}2 x y y^{\prime } = x^{2}+y^{2} \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

17988

\[ {}y^{\prime } = \frac {y^{2}}{x y-x^{2}} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

18000

\[ {}x^{5} y^{\prime }+y^{5} = 0 \]

[_separable]

18025

\[ {}x^{2}-2 y^{2}+x y y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

18026

\[ {}x^{2} y^{\prime }-3 x y-2 y^{2} = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

18027

\[ {}x^{2} y^{\prime } = 3 \left (x^{2}+y^{2}\right ) \arctan \left (\frac {y}{x}\right )+x y \]

[[_homogeneous, ‘class A‘], _dAlembert]

18028

\[ {}x \sin \left (\frac {y}{x}\right ) y^{\prime } = y \sin \left (\frac {y}{x}\right )+x \]

[[_homogeneous, ‘class A‘], _dAlembert]

18029

\[ {}x y^{\prime } = y+2 x \,{\mathrm e}^{-\frac {y}{x}} \]

[[_homogeneous, ‘class A‘], _dAlembert]

18030

\[ {}x -y-\left (x +y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18031

\[ {}x y^{\prime } = 2 x +3 y \]

[_linear]

18032

\[ {}x y^{\prime } = \sqrt {x^{2}+y^{2}} \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

18033

\[ {}x^{2} y^{\prime } = 2 x y+y^{2} \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

18034

\[ {}x^{3}+y^{3}-x y^{2} y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

18048

\[ {}y+y \cos \left (x y\right )+\left (x +x \cos \left (x y\right )\right ) y^{\prime } = 0 \]

[_separable]

18061

\[ {}\frac {x}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{{3}/{2}}} = 0 \]

[_separable]

18064

\[ {}\frac {4 y^{2}-2 x^{2}}{4 x y^{2}-x^{3}}+\frac {\left (8 y^{2}-x^{2}\right ) y^{\prime }}{4 y^{3}-x^{2} y} = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]

18065

\[ {}\left (3 x^{2}-y^{2}\right ) y^{\prime }-2 x y = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

18079

\[ {}\left (x +y\right ) y^{\prime } = y-x \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18083

\[ {}x y^{\prime }+y = \sqrt {x y}\, y^{\prime } \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

18123

\[ {}x y^{\prime } = \sqrt {x^{2}+y^{2}} \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

18128

\[ {}x y y^{\prime } = x^{2} y^{\prime }+y^{2} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

18139

\[ {}y^{2}-3 x y-2 x^{2} = \left (x^{2}-x y\right ) y^{\prime } \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

18145

\[ {}x^{2} y^{4}+x^{6}-x^{3} y^{3} y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

18147

\[ {}y^{\prime } = 1+\frac {y}{x}-\frac {y^{2}}{x^{2}} \]

[[_homogeneous, ‘class A‘], _rational, _Riccati]

18148

\[ {}y^{\prime } = \frac {2 x y \,{\mathrm e}^{\frac {x^{2}}{y^{2}}}}{y^{2}+y^{2} {\mathrm e}^{\frac {x^{2}}{y^{2}}}+2 x^{2} {\mathrm e}^{\frac {x^{2}}{y^{2}}}} \]

[[_homogeneous, ‘class A‘], _dAlembert]

18152

\[ {}\frac {y-x}{\left (x +y\right )^{3}}-\frac {2 x y^{\prime }}{\left (x +y\right )^{3}} = 0 \]

[_linear]

18155

\[ {}3 x^{2} y-y^{3}-\left (3 x y^{2}-x^{3}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]

18161

\[ {}3 x y+y^{2}+\left (3 x y+x^{2}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

18162

\[ {}x^{2} y^{\prime } = y^{2}+x y+x^{2} \]

[[_homogeneous, ‘class A‘], _rational, _Riccati]

18167

\[ {}x^{2} y^{\prime }-y^{2} = 2 x y \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

18423

\[ {}x^{\prime } = \cos \left (\frac {x}{t}\right ) \]

[[_homogeneous, ‘class A‘], _dAlembert]

18424

\[ {}\left (t^{2}-x^{2}\right ) x^{\prime } = t x \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

18460

\[ {}v^{\prime }+\frac {2 v}{u} = 3 \]

[_linear]

18466

\[ {}y^{2} = x \left (y-x \right ) y^{\prime } \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

18467

\[ {}2 x^{2} y+y^{3}-x^{3} y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

18470

\[ {}x +y y^{\prime } = m y \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18471

\[ {}\frac {2 x}{y^{3}}+\left (\frac {1}{y^{2}}-\frac {3 x^{2}}{y^{4}}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]

18496

\[ {}y^{\prime } = 1+\frac {2 y}{x -y} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18524

\[ {}y-2 x y^{\prime }-{y^{\prime }}^{2} y = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

18561

\[ {}x \left (x -2 y\right ) y^{\prime }+x^{2}+2 y^{2} = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

18562

\[ {}5 x y y^{\prime }-x^{2}-y^{2} = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

18563

\[ {}\left (x^{2}+3 x y-y^{2}\right ) y^{\prime }-3 y^{2} = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

18564

\[ {}\left (x^{2}+2 x y\right ) y^{\prime }-3 x^{2}+2 x y-y^{2} = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

18565

\[ {}5 x y y^{\prime }-4 x^{2}-y^{2} = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

18567

\[ {}3 x^{2} y^{\prime }+2 x^{2}-3 y^{2} = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Riccati]

18652

\[ {}x^{2}+y^{2}-2 x y y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

18653

\[ {}y^{2}+\left (x^{2}+x y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

18654

\[ {}x^{2} y-\left (x^{3}+y^{3}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

18655

\[ {}\left (4 y+3 x \right ) y^{\prime }+y-2 x = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18658

\[ {}x^{2}-4 x y-2 y^{2}+\left (y^{2}-4 x y-2 x^{2}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]

18668

\[ {}x^{2} y-2 x y^{2}-\left (x^{3}-3 x^{2} y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

18674

\[ {}y^{3}-2 x^{2} y+\left (2 x y^{2}-x^{3}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

18688

\[ {}-y+x y^{\prime } = \sqrt {x^{2}+y^{2}} \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

18696

\[ {}x y^{\prime }+\frac {y^{2}}{x} = y \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

18699

\[ {}x^{2} y-\left (x^{3}+y^{3}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

18702

\[ {}x +y y^{\prime } = m \left (-y+x y^{\prime }\right ) \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18710

\[ {}y y^{\prime } = a x \]

[_separable]

18712

\[ {}\left (x +y\right ) y^{\prime }+x -y = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18714

\[ {}\left (y^{2}-x^{2}\right ) y^{\prime }+2 x y = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

18719

\[ {}x^{2} y^{\prime }+y^{2} = x y y^{\prime } \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

18731

\[ {}{y^{\prime }}^{2} x -2 y y^{\prime }+a x = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

18736

\[ {}y^{2}+x y y^{\prime }-{y^{\prime }}^{2} x^{2} = 0 \]

[_separable]

18737

\[ {}y = {y^{\prime }}^{2} y+2 x y^{\prime } \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

18744

\[ {}{y^{\prime }}^{2} x^{2}-2 x y y^{\prime }+2 y^{2}-x^{2} = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

18746

\[ {}x y^{2} \left ({y^{\prime }}^{2}+2\right ) = 2 y^{3} y^{\prime }+x^{3} \]

[_separable]

18752

\[ {}3 y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+4 y^{2}-x^{2} = 0 \]

[[_homogeneous, ‘class A‘], _dAlembert]

18753

\[ {}\left (x^{2}+y^{2}\right ) \left (1+y^{\prime }\right )^{2}-2 \left (x +y\right ) \left (1+y^{\prime }\right ) \left (x +y y^{\prime }\right )+\left (x +y y^{\prime }\right )^{2} = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

18754

\[ {}\left (y y^{\prime }+n x \right )^{2} = \left (y^{2}+n \,x^{2}\right ) \left (1+{y^{\prime }}^{2}\right ) \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

18760

\[ {}x y {y^{\prime }}^{2}+\left (3 x^{2}-2 y^{2}\right ) y^{\prime }-6 x y = 0 \]

[_separable]

18778

\[ {}{y^{\prime }}^{2} x -2 y y^{\prime }+a x = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

18968

\[ {}y+x +x y^{\prime } = 0 \]

[_linear]

18971

\[ {}y-x +\left (x +y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18973

\[ {}x^{3}+3 x y^{2}+\left (3 x^{2} y+y^{3}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]

18977

\[ {}x +y y^{\prime } = m \left (-y+x y^{\prime }\right ) \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18997

\[ {}\left (x^{2}+y^{2}\right ) y^{\prime } = x^{2}+x y \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

18998

\[ {}\left (x \cos \left (\frac {y}{x}\right )+y \sin \left (\frac {y}{x}\right )\right ) y-\left (y \sin \left (\frac {y}{x}\right )-x \cos \left (\frac {y}{x}\right )\right ) x y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _dAlembert]

18999

\[ {}x^{2}-y^{2}+2 x y y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

19000

\[ {}y^{\prime } = \frac {y}{x}+\tan \left (\frac {y}{x}\right ) \]

[[_homogeneous, ‘class A‘], _dAlembert]

19003

\[ {}y^{2} = \left (x y-x^{2}\right ) y^{\prime } \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

19004

\[ {}x \sin \left (\frac {y}{x}\right ) y^{\prime } = y \sin \left (\frac {y}{x}\right )-x \]

[[_homogeneous, ‘class A‘], _dAlembert]

19005

\[ {}\left (x^{2}+y^{2}\right ) y^{\prime } = x y \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

19006

\[ {}x^{2} y^{\prime }+y \left (x +y\right ) = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

19007

\[ {}2 y^{\prime } = \frac {y}{x}+\frac {y^{2}}{x^{2}} \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

19011

\[ {}-y+x y^{\prime } = \sqrt {x^{2}+y^{2}} \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

19012

\[ {}\left (3 x^{2}+y^{2}\right ) y y^{\prime }+x \left (x^{2}+3 y^{2}\right ) = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]

19013

\[ {}x^{2}+3 y^{2}-2 x y y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

19040

\[ {}x^{2} y-2 x y^{2}-\left (x^{3}-3 x^{2} y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

19044

\[ {}x^{2}+y^{2}-2 x y y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

19055

\[ {}-y+x y^{\prime } = \sqrt {x^{2}+y^{2}} \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

19058

\[ {}x +y y^{\prime } = m \left (-y+x y^{\prime }\right ) \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

19075

\[ {}x^{2} y^{\prime }+y^{2} = x y y^{\prime } \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

19147

\[ {}{y^{\prime }}^{2} x^{2}+x y y^{\prime }-6 y^{2} = 0 \]

[_separable]

19155

\[ {}{y^{\prime }}^{2} x +a x = 2 y y^{\prime } \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

19163

\[ {}{y^{\prime }}^{2} y+2 x y^{\prime } = y \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

19175

\[ {}4 {y^{\prime }}^{2} y+2 x y^{\prime }-y = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

19176

\[ {}{y^{\prime }}^{2} y+2 x y^{\prime }-y = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

19178

\[ {}{y^{\prime }}^{2} x^{2}-2 x y y^{\prime }+2 y^{2} = x^{2} \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

19179

\[ {}y = x y^{\prime }+x \sqrt {1+{y^{\prime }}^{2}} \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

19180

\[ {}x +y^{\prime } y \left (2 {y^{\prime }}^{2}+3\right ) = 0 \]

[[_homogeneous, ‘class A‘], _dAlembert]

19186

\[ {}y-x y^{\prime } = x +y y^{\prime } \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

19187

\[ {}a^{2} y {y^{\prime }}^{2}-4 x y^{\prime }+y = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

19192

\[ {}x y {y^{\prime }}^{2}+\left (3 x^{2}-2 y^{2}\right ) y^{\prime }-6 x y = 0 \]

[_separable]

19201

\[ {}\left (x \cos \left (\frac {y}{x}\right )+y \sin \left (\frac {y}{x}\right )\right ) y = \left (y \sin \left (\frac {y}{x}\right )-x \cos \left (\frac {y}{x}\right )\right ) x y^{\prime } \]

[[_homogeneous, ‘class A‘], _dAlembert]

19204

\[ {}{y^{\prime }}^{2} x -2 y y^{\prime }+a x = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

19215

\[ {}{y^{\prime }}^{2} y-2 x y^{\prime }+y = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

19216

\[ {}3 {y^{\prime }}^{2} x -6 y y^{\prime }+x +2 y = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

19436

\[ {}y^{2}+\left (x^{2}+x y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

19445

\[ {}x^{2} y-\left (x^{3}+y^{3}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

19449

\[ {}y^{3}-2 x^{2} y+\left (2 x y^{2}-x^{3}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

19479

\[ {}y-2 x y^{\prime }+a y {y^{\prime }}^{2} = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

19482

\[ {}x y^{2} \left ({y^{\prime }}^{2}+2\right ) = 2 y^{3} y^{\prime }+x^{3} \]

[_separable]

19484

\[ {}\left (y y^{\prime }+n x \right )^{2} = \left (y^{2}+n \,x^{2}\right ) \left (1+{y^{\prime }}^{2}\right ) \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

19486

\[ {}\left (x^{2}+y^{2}\right ) \left (1+y^{\prime }\right )^{2}-2 \left (x +y\right ) \left (1+y^{\prime }\right ) \left (x +y y^{\prime }\right )+\left (x +y y^{\prime }\right )^{2} = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

19496

\[ {}{y^{\prime }}^{2} x -2 y y^{\prime }+x +2 y = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

19497

\[ {}{y^{\prime }}^{2} y^{2} \cos \left (a \right )^{2}-2 y^{\prime } x y \sin \left (a \right )^{2}+y^{2}-x^{2} \sin \left (a \right )^{2} = 0 \]

[[_homogeneous, ‘class A‘], _dAlembert]