2.3.10 first order ode bernoulli

Table 2.413: first order ode bernoulli

#

ODE

CAS classification

Solved?

27

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

[_separable]

29

\[ {}y^{\prime } = y^{{1}/{3}} \]
i.c.

[_quadrature]

30

\[ {}y^{\prime } = y^{{1}/{3}} \]
i.c.

[_quadrature]

33

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

[_separable]

34

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

[_separable]

42

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

[_separable]

51

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

[_separable]

52

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

[_separable]

53

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

[_separable]

61

\[ {}2 y y^{\prime } = \frac {x}{\sqrt {x^{2}-16}} \]
i.c.

[_separable]

66

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

[_separable]

69

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

[_quadrature]

71

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

[_quadrature]

106

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

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

111

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

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

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]

123

\[ {}x^{2} y^{\prime }+2 x y = 5 y^{3} \]

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

124

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

[_separable]

125

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

[_quadrature]

126

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

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

127

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

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

128

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

[_Bernoulli]

129

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

[_Bernoulli]

130

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

[[_1st_order, _with_linear_symmetries], _Bernoulli]

131

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

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

160

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

[_Bernoulli]

171

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

[_quadrature]

172

\[ {}x^{\prime } = 10 x-x^{2} \]
i.c.

[_quadrature]

175

\[ {}x^{\prime } = 3 x \left (5-x\right ) \]
i.c.

[_quadrature]

176

\[ {}x^{\prime } = 3 x \left (5-x\right ) \]
i.c.

[_quadrature]

177

\[ {}x^{\prime } = 4 x \left (7-x\right ) \]
i.c.

[_quadrature]

180

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

[_separable]

181

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

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

184

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

[_separable]

186

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

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

187

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

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

189

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

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

191

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

[_separable]

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]

197

\[ {}3 x^{5} y^{2}+x^{3} y^{\prime } = 2 y^{2} \]

[_separable]

200

\[ {}x y^{\prime } = 6 y+12 x^{4} y^{{2}/{3}} \]

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

202

\[ {}9 y^{2} x^{2}+x^{{3}/{2}} y^{\prime } = y^{2} \]

[_separable]

205

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

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

210

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

[_separable]

211

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

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

214

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

[_separable]

231

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

[_quadrature]

669

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

[_separable]

671

\[ {}y^{\prime } = y^{{1}/{3}} \]
i.c.

[_quadrature]

672

\[ {}y^{\prime } = y^{{1}/{3}} \]
i.c.

[_quadrature]

673

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

[_separable]

674

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

[_separable]

678

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

[_separable]

687

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

[_separable]

688

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

[_separable]

696

\[ {}2 y y^{\prime } = \frac {x}{\sqrt {x^{2}-16}} \]
i.c.

[_separable]

701

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

[_separable]

730

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

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

735

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

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

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]

747

\[ {}x^{2} y^{\prime }+2 x y = 5 y^{3} \]

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

748

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

[_separable]

749

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

[_quadrature]

750

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

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

751

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

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

752

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

[_Bernoulli]

753

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

[_Bernoulli]

754

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

[[_1st_order, _with_linear_symmetries], _Bernoulli]

755

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

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

772

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

[_separable]

773

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

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

776

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

[_separable]

778

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

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

779

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

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

781

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

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

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]

789

\[ {}3 x^{5} y^{2}+x^{3} y^{\prime } = 2 y^{2} \]

[_separable]

792

\[ {}x y^{\prime } = 6 y+12 x^{4} y^{{2}/{3}} \]

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

794

\[ {}9 y^{2} x^{2}+x^{{3}/{2}} y^{\prime } = y^{2} \]

[_separable]

797

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

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

802

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

[_separable]

803

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

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

806

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

[_separable]

1129

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

[_separable]

1130

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

[_separable]

1131

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

[_separable]

1137

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

[_separable]

1138

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

[_separable]

1139

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

[_separable]

1140

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

[_separable]

1141

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

[_separable]

1142

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

[_separable]

1144

\[ {}y^{\prime } = \frac {x \left (x^{2}+1\right )}{4 y^{3}} \]
i.c.

[_separable]

1148

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

[_separable]

1151

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

[_separable]

1155

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

[_separable]

1156

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

[_separable]

1159

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

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

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]

1175

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

[_separable]

1176

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

[_quadrature]

1177

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

[_separable]

1178

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

[_separable]

1179

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

[_Bernoulli]

1180

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

[_Bernoulli]

1182

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

[_quadrature]

1189

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

[_quadrature]

1190

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

[_quadrature]

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]

1533

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

[_separable]

1534

\[ {}y^{\prime } = a y^{\frac {a -1}{a}} \]

[_quadrature]

1580

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

[_separable]

1588

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

[_separable]

1592

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

[_separable]

1596

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

[_quadrature]

1597

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

[_separable]

1603

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

[_quadrature]

1621

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

[_quadrature]

1625

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

[_Bernoulli]

1629

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

[_quadrature]

1630

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

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

1631

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

[_Bernoulli]

1632

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

[_rational, _Bernoulli]

1633

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

[_Bernoulli]

1634

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

[_rational, _Bernoulli]

1635

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

[_Bernoulli]

1636

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

[_separable]

1637

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

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

1638

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

[_quadrature]

1639

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

[_rational, _Bernoulli]

1640

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

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

1641

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

[_Bernoulli]

1643

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

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

1644

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

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

1647

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

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

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]

1654

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

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

1669

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

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

1670

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

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

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]

1699

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

[_separable]

1703

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

[_exact, _Bernoulli]

1707

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

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

1712

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

[_separable]

1736

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

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

2323

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

[_separable]

2324

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

[_separable]

2325

\[ {}\sqrt {t^{2}+1}\, y^{\prime } = \frac {t y^{3}}{\sqrt {t^{2}+1}} \]
i.c.

[_separable]

2331

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

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

2358

\[ {}y^{\prime } = \frac {\left (1+\cos \left (4 t \right )\right ) y}{4}-\frac {\left (1-\cos \left (4 t \right )\right ) y^{2}}{800} \]
i.c.

[_Bernoulli]

2494

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

[_separable]

2495

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

[_separable]

2501

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

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

2503

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

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

2533

\[ {}y^{\prime } = \frac {\left (1+\cos \left (4 t \right )\right ) y}{4}-\frac {\left (1-\cos \left (4 t \right )\right ) y^{2}}{800} \]
i.c.

[_Bernoulli]

2536

\[ {}y^{\prime } = t y^{a} \]
i.c.

[_separable]

2541

\[ {}y^{\prime } = {\mathrm e}^{t} y^{2}-2 y \]
i.c.

[[_1st_order, _with_linear_symmetries], _Bernoulli]

2542

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

[_Bernoulli]

2809

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

[_quadrature]

2810

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

[_quadrature]

2811

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

[_quadrature]

2842

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

[_separable]

2846

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

[_separable]

2851

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

[_separable]

2853

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

[_separable]

2860

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

[_separable]

2864

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

[_separable]

2878

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

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

2885

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

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

2940

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

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

2941

\[ {}x y^{3}-1+x^{2} y^{2} y^{\prime } = 0 \]

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

2943

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

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

2948

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

[_Bernoulli]

2951

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

[[_homogeneous, ‘class D‘], _Bernoulli]

2952

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

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

2982

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

[_Bernoulli]

2983

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

[_Bernoulli]

2986

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

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

2987

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

[_Bernoulli]

2988

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

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

2989

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

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

2991

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

[_separable]

2992

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

[_Bernoulli]

2993

\[ {}r^{\prime }+\left (r-\frac {1}{r}\right ) \theta = 0 \]

[_separable]

2994

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

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

2995

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

[_rational, _Bernoulli]

2998

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

[_Bernoulli]

2999

\[ {}y^{\prime }+y = y^{2} {\mathrm e}^{-t} \]
i.c.

[[_1st_order, _with_linear_symmetries], _Bernoulli]

3015

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

[_separable]

3022

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

[_rational, _Bernoulli]

3028

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

[_separable]

3030

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

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

3031

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

[_separable]

3039

\[ {}x y^{\prime }-5 y-x \sqrt {y} = 0 \]

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

3041

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

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

3044

\[ {}x y^{\prime }-2 y-2 x^{4} y^{3} = 0 \]
i.c.

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

3047

\[ {}x y^{\prime }+y = x^{3} y^{6} \]
i.c.

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

3048

\[ {}x^{\prime } = x+x^{2} {\mathrm e}^{\theta } \]
i.c.

[[_1st_order, _with_linear_symmetries], _Bernoulli]

3049

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

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

3052

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

[_separable]

3057

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

[_separable]

3294

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

[_quadrature]

3410

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

[_separable]

3426

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

[_quadrature]

3427

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

[_separable]

3432

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

[_separable]

3433

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

[_quadrature]

3457

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

[_separable]

3459

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

[_separable]

3466

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

[_rational, _Bernoulli]

3473

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

[_separable]

3480

\[ {}x y^{\prime }+y-\frac {y^{2}}{x^{{3}/{2}}} = 0 \]
i.c.

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

3516

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

[_separable]

3529

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

[_separable]

3561

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

[_quadrature]

3581

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

[_Bernoulli]

3594

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

[_separable]

3607

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

[_separable]

3657

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

[[_homogeneous, ‘class D‘], _Bernoulli]

3658

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

[_Bernoulli]

3659

\[ {}y^{\prime }-\frac {3 y}{2 x} = 6 y^{{1}/{3}} x^{2} \ln \left (x \right ) \]

[_Bernoulli]

3660

\[ {}y^{\prime }+\frac {2 y}{x} = 6 \sqrt {x^{2}+1}\, \sqrt {y} \]

[_Bernoulli]

3661

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

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

3662

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

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

3663

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

[_rational, _Bernoulli]

3664

\[ {}y^{\prime }+\frac {6 y}{x} = \frac {3 y^{{2}/{3}} \cos \left (x \right )}{x} \]

[_Bernoulli]

3665

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

[_Bernoulli]

3666

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

[_Bernoulli]

3667

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

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

3668

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

[_Bernoulli]

3669

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

[_separable]

3670

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

[_rational, _Bernoulli]

3671

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

[_Bernoulli]

4094

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

[_separable]

4096

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

[_separable]

4098

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

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

4190

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

[_separable]

4213

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

[_separable]

4214

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

[_separable]

4223

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

[_separable]

4231

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

[_separable]

4237

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

4305

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

[_separable]

4311

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

[_separable]

4342

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

[_rational, _Bernoulli]

4361

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

[_separable]

4375

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

[_Bernoulli]

4377

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

[_rational, _Bernoulli]

4378

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

[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli]

4379

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

[_Bernoulli]

4380

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

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

4381

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

[_Bernoulli]

4396

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

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

4400

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

[_exact, _Bernoulli]

4411

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

[_Bernoulli]

4421

\[ {}2 x^{3} y y^{\prime }+3 y^{2} x^{2}+7 = 0 \]

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

4423

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

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

4430

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

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

4438

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

[_rational, _Bernoulli]

4443

\[ {}x y^{3}-1+x^{2} y^{2} y^{\prime } = 0 \]

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

4671

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

[_separable]

4675

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

[_separable]

4678

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

[_Bernoulli]

4688

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

[_quadrature]

4690

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

[_separable]

4691

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

[_Bernoulli]

4693

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

[_Bernoulli]

4694

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

[_Bernoulli]

4695

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

[_separable]

4698

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

[_Bernoulli]

4704

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

[_Bernoulli]

4772

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

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

4773

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

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

4774

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

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

4775

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

[_Bernoulli]

4777

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

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

4782

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

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

4785

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

[_Bernoulli]

4787

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

[_separable]

4788

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

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

4789

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

[_rational, _Bernoulli]

4790

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

[_rational, _Bernoulli]

4791

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

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

4792

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

[_separable]

4824

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

[_rational, _Bernoulli]

4825

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

[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli]

4826

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

[_rational, _Bernoulli]

4834

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

[_separable]

4835

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

[_rational, _Bernoulli]

4838

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

[_separable]

4839

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

[_separable]

4840

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

[_rational, _Bernoulli]

4845

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

[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli]

4847

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

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

4848

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

[_Bernoulli]

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]

4870

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

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

4871

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

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

4874

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

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

4875

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

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

4899

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

[_separable]

4900

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

[_separable]

4904

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

[_rational, _Bernoulli]

4907

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

[_rational, _Bernoulli]

4909

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

[_separable]

4919

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

[_separable]

4924

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

[_separable]

4946

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

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

4948

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

[_separable]

4951

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

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

4964

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

[[_homogeneous, ‘class D‘], _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]

4967

\[ {}6 x^{3} y^{\prime } = 4 x^{2} y+\left (1-3 x \right ) y^{4} \]

[_rational, _Bernoulli]

4969

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

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

4975

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

[_rational, _Bernoulli]

5008

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

[_Bernoulli]

5015

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

[_separable]

5016

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

[_separable]

5021

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

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

5022

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

[_rational, _Bernoulli]

5023

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

[_Bernoulli]

5025

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

[_separable]

5026

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

[_Bernoulli]

5058

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

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

5059

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

[_rational, _Bernoulli]

5101

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

[_separable]

5102

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

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

5103

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

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

5104

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

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

5105

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

[[_homogeneous, ‘class D‘], _Bernoulli]

5108

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

[_separable]

5109

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

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

5110

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

[_separable]

5135

\[ {}2 x y y^{\prime }+1-2 x^{3}-y^{2} = 0 \]

[_rational, _Bernoulli]

5136

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

[_separable]

5137

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

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

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]

5140

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

[_rational, _Bernoulli]

5141

\[ {}2 x y y^{\prime }+x^{2} \left (a \,x^{3}+1\right ) = 6 y^{2} \]

[_rational, _Bernoulli]

5149

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

[_exact, _rational, _Bernoulli]

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]

5167

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

[_separable]

5168

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

[_rational, _Bernoulli]

5169

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

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

5174

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

[_separable]

5175

\[ {}3 x^{2} y y^{\prime }+1+2 x y^{2} = 0 \]

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

5178

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

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

5182

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

[_separable]

5183

\[ {}3 x^{4} y y^{\prime } = 1-2 x^{3} y^{2} \]

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

5217

\[ {}3 y^{2} y^{\prime } = 1+x +a y^{3} \]

[_rational, _Bernoulli]

5244

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

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

5249

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

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

5253

\[ {}x^{2} y^{2} y^{\prime }+1-x +x^{3} = 0 \]

[_separable]

5313

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

[_separable]

5693

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

[_Bernoulli]

5695

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

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

5701

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

[_separable]

5717

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

[_separable]

5718

\[ {}3 z^{2} z^{\prime }-a z^{3} = x +1 \]

[_rational, _Bernoulli]

5719

\[ {}z^{\prime }+2 x z = 2 a \,x^{3} z^{3} \]

[_Bernoulli]

5720

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

[_Bernoulli]

5721

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

[_Bernoulli]

5763

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

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

5781

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

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

5784

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

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

5841

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

[_Bernoulli]

5845

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

[_Bernoulli]

5846

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

[_rational, _Bernoulli]

5855

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

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

5856

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

[_Bernoulli]

5857

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

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

5859

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

[_separable]

5860

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

[_Bernoulli]

5866

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

[_Bernoulli]

5876

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

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

5879

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

[_Bernoulli]

5883

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

[_Bernoulli]

5891

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

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

5899

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

[_separable]

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]

5911

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

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

6032

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

[_separable]

6034

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

[_separable]

6096

\[ {}x y y^{\prime }+1+y^{2} = 0 \]
i.c.

[_separable]

6098

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

[_separable]

6099

\[ {}y y^{\prime }+x y^{2}-8 x = 0 \]
i.c.

[_separable]

6100

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

[_separable]

6119

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

[_Bernoulli]

6120

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

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

6121

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

[_separable]

6125

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

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

6214

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

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

6216

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

[[_1st_order, _with_linear_symmetries], _Bernoulli]

6228

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

[_separable]

6260

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

[_separable]

6262

\[ {}x y^{\prime } = \frac {1}{y^{3}} \]

[_separable]

6265

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

[_separable]

6266

\[ {}v^{\prime } x = \frac {1-4 v^{2}}{3 v} \]

[_separable]

6269

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

[_quadrature]

6270

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

[_separable]

6271

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

[_separable]

6277

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

[_separable]

6281

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

[_separable]

6283

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

[_separable]

6286

\[ {}y^{\prime } = y^{{1}/{3}} \]

[_quadrature]

6287

\[ {}y^{\prime } = y^{{1}/{3}} \]
i.c.

[_quadrature]

6289

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

[_separable]

6290

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

[_separable]

6291

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

[_separable]

6292

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

[_separable]

6318

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

[_rational, _Bernoulli]

6343

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

[_separable]

6344

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

[_separable]

6405

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

[_separable]

6406

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

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

6428

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

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

6429

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

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

6437

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

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

6450

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

[_Bernoulli]

6451

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

[[_1st_order, _with_linear_symmetries], _Bernoulli]

6452

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

[_Bernoulli]

6453

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

[_Bernoulli]

6454

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

[_Bernoulli]

6458

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

[_Bernoulli]

6468

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

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

6475

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

[_separable]

6476

\[ {}\frac {r \tan \left (\theta \right ) r^{\prime }}{a^{2}-r^{2}} = 1 \]
i.c.

[_separable]

6478

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

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

6570

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

[_separable]

6572

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

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

6581

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

[_separable]

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]

6600

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

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

6602

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

[_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]

6645

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

[[_1st_order, _with_linear_symmetries], _Bernoulli]

6648

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

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

6651

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

[_separable]

6653

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

[_Bernoulli]

6657

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

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

6663

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

[_Bernoulli]

6892

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

[_separable]

6893

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

[_separable]

6896

\[ {}p^{\prime } = p \left (1-p\right ) \]

[_quadrature]

6905

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

[_separable]

6933

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

[_quadrature]

6934

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

[_quadrature]

6935

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

[_separable]

6936

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

[_separable]

6937

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

[_separable]

6938

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

[_separable]

6947

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

[_quadrature]

6949

\[ {}y^{\prime } = y^{{2}/{3}} \]

[_quadrature]

6963

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

[_quadrature]

6964

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

[_quadrature]

6965

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

[_quadrature]

6966

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

[_quadrature]

6967

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

[_quadrature]

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]

6981

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

[_separable]

6989

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

[_quadrature]

7004

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

[_separable]

7034

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

[_separable]

7035

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

[_separable]

7036

\[ {}y^{\prime } = \frac {1}{y} \]
i.c.

[_quadrature]

7037

\[ {}y^{\prime } = \frac {1}{y} \]
i.c.

[_quadrature]

7050

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

[_quadrature]

7052

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

[_quadrature]

7068

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

[_separable]

7074

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

[_separable]

7079

\[ {}p^{\prime } = p-p^{2} \]

[_quadrature]

7084

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

[_separable]

7094

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

[_separable]

7097

\[ {}y^{\prime } = \frac {3 x +1}{2 y} \]
i.c.

[_separable]

7100

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

[_separable]

7104

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

[_separable]

7105

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

[_separable]

7106

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

[_separable]

7107

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

[_separable]

7113

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

[_quadrature]

7114

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

[_quadrature]

7115

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

[_quadrature]

7116

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

[_quadrature]

7122

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

[_separable]

7123

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

[_separable]

7124

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

[_quadrature]

7125

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

[_separable]

7126

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

[_separable]

7127

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

[_separable]

7128

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

[_separable]

7134

\[ {}m^{\prime } = -\frac {k}{m^{2}} \]
i.c.

[_quadrature]

7172

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

[_rational, _Bernoulli]

7382

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

[_separable]

7383

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

[_separable]

7388

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

[_separable]

7389

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

[_quadrature]

7390

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

[_separable]

7391

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

[_separable]

7392

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

[_separable]

7395

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

[_separable]

7396

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

[_separable]

7398

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

[_separable]

7403

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

[_separable]

7404

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

[_separable]

7419

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

[_rational, _Bernoulli]

7435

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

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

7460

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

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

7509

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

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

7511

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

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

7550

\[ {}\phi ^{\prime }-\frac {\phi ^{2}}{2}-\phi \cot \left (\theta \right ) = 0 \]

[_Bernoulli]

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]

7732

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

[_separable]

7736

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

[_quadrature]

7737

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

[_quadrature]

7738

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

[_quadrature]

7775

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

[_separable]

7782

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

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

7807

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

[_separable]

7816

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

[_separable]

7817

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

[_separable]

7819

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

[_separable]

7820

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

[_separable]

7821

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

[_separable]

7841

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

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

7842

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

[_Bernoulli]

7843

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

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

7844

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

[_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]

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]

7886

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

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

7887

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

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

7927

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

[_separable]

8702

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

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

8732

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

[_Bernoulli]

8745

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

[_quadrature]

8746

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

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

8758

\[ {}f^{\prime } = \frac {1}{f} \]

[_quadrature]

8794

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

[_quadrature]

8798

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

[_Bernoulli]

8889

\[ {}v v^{\prime } = \frac {2 v^{2}}{r^{3}}+\frac {\lambda r}{3} \]

[_rational, _Bernoulli]

8952

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

[_quadrature]

9007

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

[_rational, _Bernoulli]

9171

\[ {}y^{\prime } = y^{{1}/{3}} \]
i.c.

[_quadrature]

10043

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

[_separable]

10048

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

[_Bernoulli]

10058

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

[_Bernoulli]

10113

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

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

10120

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

[_Bernoulli]

10121

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

[_Bernoulli]

10140

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

[_rational, _Bernoulli]

10143

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

[_Bernoulli]

10148

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

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

10167

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

[_rational, _Bernoulli]

10169

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

[_separable]

10171

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

[_rational, _Bernoulli]

10182

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

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

10188

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

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

10208

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

[_Bernoulli]

10217

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

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

10218

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

[_Bernoulli]

10220

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

[_separable]

10229

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

[_rational, _Bernoulli]

10239

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

[_Bernoulli]

10241

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

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

10242

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

[[_homogeneous, ‘class D‘], _Bernoulli]

10249

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

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

10250

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

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

10251

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

[_separable]

10267

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

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

10268

\[ {}2 x^{2} y y^{\prime }-y^{2}-x^{2} {\mathrm e}^{x -\frac {1}{x}} = 0 \]

[_Bernoulli]

10272

\[ {}2 x^{3}+y y^{\prime }+3 y^{2} x^{2}+7 = 0 \]

[_rational, _Bernoulli]

10276

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

[_exact, _Bernoulli]

10277

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

[_Bernoulli]

10306

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

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

10308

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

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

10316

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

[_separable]

10322

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

[_Bernoulli]

10558

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

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

10681

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

[_Bernoulli]

10701

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

[_Bernoulli]

10712

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

[_Bernoulli]

10717

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

[_Bernoulli]

10745

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

[_Bernoulli]

10763

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

[_Bernoulli]

10764

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

[_Bernoulli]

10774

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

[_Bernoulli]

10780

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

[_Bernoulli]

10781

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

[_Bernoulli]

10786

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

[_Bernoulli]

10790

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

[_Bernoulli]

10795

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

[_Bernoulli]

10797

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

[_Bernoulli]

11926

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

[_Bernoulli]

12725

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

[_separable]

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]

12745

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

[_rational, _Bernoulli]

12746

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

[_separable]

12748

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

[_Bernoulli]

12753

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

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

12756

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

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

12757

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

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

12772

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

[_Bernoulli]

12780

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

[_separable]

12785

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

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

12794

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

[_Bernoulli]

12947

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

[_separable]

12948

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

[_quadrature]

12955

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

[_quadrature]

12965

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

[_quadrature]

12977

\[ {}y^{\prime }+y+\frac {1}{y} = 0 \]

[_quadrature]

12978

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

[_separable]

12981

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

[_separable]

12983

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

[_quadrature]

12988

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

[_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]

12995

\[ {}y^{\prime } = -y^{2} {\mathrm e}^{-t^{2}} \]
i.c.

[_separable]

13021

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

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

13022

\[ {}x^{\prime } = x \left (1+x \,{\mathrm e}^{t}\right ) \]

[[_1st_order, _with_linear_symmetries], _Bernoulli]

13023

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

[_separable]

13024

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

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

13025

\[ {}x^{\prime } = a x+b x^{3} \]

[_quadrature]

13026

\[ {}w^{\prime } = t w+t^{3} w^{3} \]

[_Bernoulli]

13030

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

[_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]

13172

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

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

13191

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

[_separable]

13192

\[ {}y^{\prime } = y^{{1}/{3}} \]
i.c.

[_quadrature]

13208

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

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

13209

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

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

13217

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

[_separable]

13227

\[ {}\left (3 x +8\right ) \left (y^{2}+4\right )-4 y \left (x^{2}+5 x +6\right ) y^{\prime } = 0 \]
i.c.

[_separable]

13228

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

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

13249

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

[_separable]

13250

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

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

13251

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

[_separable]

13252

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

[_separable]

13259

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

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

13283

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

[_separable]

13286

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

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

13287

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

[_separable]

13288

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

[_exact, _Bernoulli]

13290

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

[_separable]

13295

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

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

13636

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

[_quadrature]

13643

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

[_quadrature]

13644

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

[_separable]

13650

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

[_quadrature]

13651

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

[_quadrature]

13666

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

[_separable]

13670

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

[_quadrature]

13783

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

[_separable]

13789

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

[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli]

13798

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

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

13800

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

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

13806

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

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

13810

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

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

13812

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

[_Bernoulli]

13817

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

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

13874

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

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

13887

\[ {}y y^{\prime } = 1 \]

[_quadrature]

14095

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

[_separable]

14103

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

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

14121

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

[_Bernoulli]

14122

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

[_separable]

14123

\[ {}3 y^{2} y^{\prime }-a y^{3}-x -1 = 0 \]

[_rational, _Bernoulli]

14125

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

[_Bernoulli]

14126

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

[_Bernoulli]

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]

14197

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

[_separable]

14203

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

[_Bernoulli]

14236

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

[_quadrature]

14257

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

[_separable]

14259

\[ {}y^{\prime } = 3 y^{{2}/{3}} \]

[_quadrature]

14284

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

[_separable]

14287

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

[_quadrature]

14296

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

[_separable]

14300

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

[_separable]

14301

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

[_separable]

14305

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

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

14333

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

[_separable]

14334

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

[_quadrature]

14338

\[ {}2 y y^{\prime } = 1 \]

[_quadrature]

14339

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

[_separable]

14350

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

[_separable]

14353

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

[_separable]

14354

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

[_separable]

14363

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

[_quadrature]

14364

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

[_quadrature]

14365

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

[_quadrature]

14366

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

[_quadrature]

14367

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

[_quadrature]

14368

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

[_quadrature]

14369

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

[_separable]

14370

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

[_separable]

14371

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

[_separable]

14372

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

[_separable]

14373

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

[_separable]

14374

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

[_separable]

14375

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

[_separable]

14376

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

[_separable]

14377

\[ {}y^{\prime } = 3 x y^{{1}/{3}} \]
i.c.

[_separable]

14378

\[ {}y^{\prime } = 3 x y^{{1}/{3}} \]
i.c.

[_separable]

14379

\[ {}y^{\prime } = 3 x y^{{1}/{3}} \]
i.c.

[_separable]

14380

\[ {}y^{\prime } = 3 x y^{{1}/{3}} \]
i.c.

[_separable]

14381

\[ {}y^{\prime } = 3 x y^{{1}/{3}} \]
i.c.

[_separable]

14523

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

[_separable]

14529

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

[_separable]

14530

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

[_separable]

14531

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

[_separable]

14532

\[ {}y^{\prime } = t y^{{1}/{3}} \]

[_separable]

14535

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

[_quadrature]

14545

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

[_quadrature]

14546

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

[_separable]

14547

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

[_quadrature]

14548

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

[_separable]

14550

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

[_separable]

14551

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

[_separable]

14552

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

[_quadrature]

14555

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

[_separable]

14556

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

[_quadrature]

14560

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

[_quadrature]

14561

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

[_quadrature]

14563

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

[_quadrature]

14572

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

[_quadrature]

14573

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

[_quadrature]

14576

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

[_separable]

14596

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

[_quadrature]

14603

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

[_quadrature]

14604

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

[_quadrature]

14611

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

[_quadrature]

14640

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

[_quadrature]

14644

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

[_quadrature]

14700

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

[_quadrature]

14705

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

[_separable]

14709

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

[_separable]

14711

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

[_separable]

14904

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

[_separable]

14950

\[ {}y^{3}-25 y+y^{\prime } = 0 \]

[_quadrature]

14955

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

[_quadrature]

14956

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

[_separable]

14966

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

[_separable]

14968

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

[_separable]

14972

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

[_separable]

14974

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

[_separable]

14978

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

[_separable]

14981

\[ {}y^{\prime } = 200 y-2 y^{2} \]

[_quadrature]

14984

\[ {}y^{\prime } = 3 y^{2}-y^{2} \sin \left (x \right ) \]

[_separable]

14992

\[ {}y^{\prime } = 3 x y^{3} \]

[_separable]

14996

\[ {}y^{\prime } = 200 y-2 y^{2} \]

[_quadrature]

14998

\[ {}y y^{\prime } = \sin \left (x \right ) \]
i.c.

[_separable]

15000

\[ {}x y^{\prime } = y^{2}-y \]
i.c.

[_separable]

15001

\[ {}x y^{\prime } = y^{2}-y \]
i.c.

[_separable]

15002

\[ {}y^{\prime } = \frac {y^{2}-1}{x y} \]
i.c.

[_separable]

15012

\[ {}y^{\prime }+4 y = y^{3} \]

[_quadrature]

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]

15041

\[ {}y^{\prime }+3 y = 3 y^{3} \]

[_quadrature]

15042

\[ {}y^{\prime }-\frac {3 y}{x} = \frac {y^{2}}{x^{2}} \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

15043

\[ {}y^{\prime }+3 y \cot \left (x \right ) = 6 \cos \left (x \right ) y^{{2}/{3}} \]

[_Bernoulli]

15044

\[ {}y^{\prime }-\frac {y}{x} = \frac {1}{y} \]
i.c.

[[_homogeneous, ‘class D‘], _rational, _Bernoulli]

15045

\[ {}y^{\prime } = \frac {y}{x}+\frac {x^{2}}{y^{2}} \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

15047

\[ {}3 y^{\prime }+\frac {2 y}{x} = 4 \sqrt {y} \]

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

15052

\[ {}y^{\prime }+\frac {y}{x} = y^{3} x^{2} \]

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

15056

\[ {}y^{\prime }+3 y = \frac {28 \,{\mathrm e}^{2 x}}{y^{3}} \]

[[_1st_order, _with_linear_symmetries], _Bernoulli]

15061

\[ {}y^{\prime } = \frac {1}{y}-\frac {y}{2 x} \]

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

15062

\[ {}{\mathrm e}^{x y^{2}-x^{2}} \left (y^{2}-2 x \right )+2 \,{\mathrm e}^{x y^{2}-x^{2}} x y y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli]

15064

\[ {}2 x y^{3}+4 x^{3}+3 x^{2} y^{2} y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli]

15065

\[ {}2-2 x +3 y^{2} y^{\prime } = 0 \]

[_separable]

15066

\[ {}1+3 y^{2} x^{2}+\left (2 x^{3} y+6 y\right ) y^{\prime } = 0 \]

[_exact, _rational, _Bernoulli]

15071

\[ {}1+y^{4}+x y^{3} y^{\prime } = 0 \]

[_separable]

15081

\[ {}x y^{\prime } = 2 y^{2}-6 y \]

[_separable]

15082

\[ {}4 y^{2}-y^{2} x^{2}+y^{\prime } = 0 \]

[_separable]

15088

\[ {}x y^{2}-6+x^{2} y y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli]

15089

\[ {}x^{3}+y^{3}+x y^{2} y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

15091

\[ {}1+2 x y^{2}+\left (2 x^{2} y+2 y\right ) y^{\prime } = 0 \]

[_exact, _rational, _Bernoulli]

15092

\[ {}3 x y^{3}-y+x y^{\prime } = 0 \]

[[_homogeneous, ‘class D‘], _rational, _Bernoulli]

15097

\[ {}y^{\prime } = \frac {3 y}{x +1}-y^{2} \]

[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli]

15101

\[ {}x y y^{\prime } = 2 x^{2}+2 y^{2} \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

15112

\[ {}x y^{3} y^{\prime } = y^{4}-x^{2} \]

[[_homogeneous, ‘class D‘], _rational, _Bernoulli]

15113

\[ {}y^{\prime } = 4 y-\frac {16 \,{\mathrm e}^{4 x}}{y^{2}} \]

[[_1st_order, _with_linear_symmetries], _Bernoulli]

15116

\[ {}y y^{\prime }-x y^{2} = 6 x \,{\mathrm e}^{4 x^{2}} \]

[_Bernoulli]

15119

\[ {}y^{2}-y^{2} \cos \left (x \right )+y^{\prime } = 0 \]

[_separable]

15122

\[ {}y^{\prime } = y^{3}-y^{3} \cos \left (x \right ) \]

[_separable]

15723

\[ {}y^{\prime } = -\frac {x}{y} \]

[_separable]

15754

\[ {}y^{\prime } = \frac {2 x y+y^{2}}{x^{2}} \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

15785

\[ {}y^{\prime } = y^{{1}/{5}} \]
i.c.

[_quadrature]

15786

\[ {}\frac {y^{\prime }}{t} = \sqrt {y} \]
i.c.

[_separable]

15789

\[ {}y^{\prime } = 6 y^{{2}/{3}} \]
i.c.

[_quadrature]

15811

\[ {}y^{\prime } = y^{2} \]
i.c.

[_quadrature]

15812

\[ {}y^{\prime } = t y^{2} \]
i.c.

[_separable]

15813

\[ {}y^{\prime } = -\frac {t}{y} \]
i.c.

[_separable]

15814

\[ {}y^{\prime } = -y^{3} \]
i.c.

[_quadrature]

15815

\[ {}y^{\prime } = \frac {x}{y^{2}} \]

[_separable]

15816

\[ {}\frac {1}{2 \sqrt {t}}+y^{2} y^{\prime } = 0 \]

[_separable]

15817

\[ {}y^{\prime } = \frac {\sqrt {y}}{x^{2}} \]

[_separable]

15818

\[ {}y^{\prime } = \frac {1+y^{2}}{y} \]

[_quadrature]

15844

\[ {}y^{\prime } = \frac {5^{-t}}{y^{2}} \]

[_separable]

15851

\[ {}y^{\prime } = y^{3}+y \]

[_quadrature]

15853

\[ {}y^{\prime } = y^{3}-y \]

[_quadrature]

15854

\[ {}y^{\prime } = y^{3}+y \]

[_quadrature]

15859

\[ {}y^{\prime } = \frac {\sqrt {t}}{y} \]
i.c.

[_separable]

15872

\[ {}y^{\prime } = y^{2} \cos \left (t \right ) \]
i.c.

[_separable]

15873

\[ {}y^{\prime } = \sqrt {y}\, \cos \left (t \right ) \]
i.c.

[_separable]

15882

\[ {}y^{\prime } = y^{2}-y \]

[_quadrature]

15883

\[ {}y^{\prime } = 16 y-8 y^{2} \]

[_quadrature]

15946

\[ {}\frac {t}{\sqrt {t^{2}+y^{2}}}+\frac {y y^{\prime }}{\sqrt {t^{2}+y^{2}}} = 0 \]

[_separable]

15949

\[ {}3 t y^{2}+y^{3} y^{\prime } = 0 \]

[_separable]

15955

\[ {}-1+3 y^{2} y^{\prime } = 0 \]

[_quadrature]

15963

\[ {}3 t^{2}+3 y^{2}+6 t y y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli]

15989

\[ {}2 t y+y^{2}-t^{2} y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

15992

\[ {}5 t y^{2}+y+\left (2 t^{3}-t \right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class D‘], _rational, _Bernoulli]

15999

\[ {}y^{\prime }-\frac {y}{2} = \frac {t}{y} \]

[_rational, _Bernoulli]

16000

\[ {}y^{\prime }+y = t y^{2} \]

[_Bernoulli]

16001

\[ {}2 t y^{\prime }-y = 2 t y^{3} \cos \left (t \right ) \]

[_Bernoulli]

16002

\[ {}t y^{\prime }-y = t y^{3} \sin \left (t \right ) \]

[[_homogeneous, ‘class D‘], _Bernoulli]

16003

\[ {}y^{\prime }-2 y = \frac {\cos \left (t \right )}{\sqrt {y}} \]

[_Bernoulli]

16004

\[ {}y^{\prime }+3 y = \sqrt {y}\, \sin \left (t \right ) \]

[_Bernoulli]

16005

\[ {}y^{\prime }-\frac {y}{t} = t y^{2} \]

[[_homogeneous, ‘class D‘], _rational, _Bernoulli]

16006

\[ {}y^{\prime }-\frac {y}{t} = \frac {y^{2}}{t^{2}} \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

16007

\[ {}y^{\prime }-\frac {y}{t} = \frac {y^{2}}{t} \]

[_separable]

16008

\[ {}y^{\prime }-\frac {y}{t} = t^{2} y^{{3}/{2}} \]

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

16012

\[ {}\frac {2}{t}+\frac {1}{y}+\frac {t y^{\prime }}{y^{2}} = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

16014

\[ {}\sqrt {t^{2}+1}+y y^{\prime } = 0 \]

[_separable]

16019

\[ {}t^{3}+y^{3}-t y^{2} y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

16031

\[ {}y^{\prime }+2 y = t^{2} \sqrt {y} \]
i.c.

[_Bernoulli]

16032

\[ {}y^{\prime }-2 y = t^{2} \sqrt {y} \]
i.c.

[_Bernoulli]

16033

\[ {}y^{\prime } = \frac {4 y^{2}-t^{2}}{2 t y} \]
i.c.

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

16037

\[ {}y^{3}-t^{3}-t y^{2} y^{\prime } = 0 \]
i.c.

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

16045

\[ {}y^{\prime }+y \cot \left (x \right ) = y^{4} \]
i.c.

[_Bernoulli]

16056

\[ {}y^{\prime } = \frac {y^{2}-t^{2}}{t y} \]
i.c.

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

16058

\[ {}y^{\prime } = \frac {2 t^{5}}{5 y^{2}} \]

[_separable]

16060

\[ {}y^{\prime }-\frac {y}{t} = \frac {y^{2}}{t} \]

[_separable]

16062

\[ {}y^{\prime } = \frac {{\mathrm e}^{5 t}}{y^{4}} \]

[_separable]

16071

\[ {}r^{\prime } = \frac {r^{2}+t^{2}}{r t} \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

16081

\[ {}y^{\prime }-y = t y^{3} \]

[_Bernoulli]

16082

\[ {}y^{\prime }+y = \frac {{\mathrm e}^{t}}{y^{2}} \]

[[_1st_order, _with_linear_symmetries], _Bernoulli]

16084

\[ {}y-t y^{\prime } = 2 y^{2} \ln \left (t \right ) \]

[[_homogeneous, ‘class D‘], _Bernoulli]

16095

\[ {}y^{\prime } = t y^{3} \]
i.c.

[_separable]

16096

\[ {}y^{\prime } = \frac {t}{y^{3}} \]
i.c.

[_separable]

16586

\[ {}y^{\prime } = \frac {x}{y} \]

[_separable]

16587

\[ {}y^{\prime } = y+3 y^{{1}/{3}} \]

[_quadrature]

16618

\[ {}y^{\prime } = y^{2} \]

[_quadrature]

16625

\[ {}x y y^{\prime }+1+y^{2} = 0 \]

[_separable]

16675

\[ {}4 y^{6}+x^{3} = 6 x y^{5} y^{\prime } \]

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

16701

\[ {}y^{\prime }+2 x y = 2 x y^{2} \]

[_separable]

16702

\[ {}3 x y^{2} y^{\prime }-2 y^{3} = x^{3} \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

16706

\[ {}2 y^{\prime } \ln \left (x \right )+\frac {y}{x} = \frac {\cos \left (x \right )}{y} \]

[_Bernoulli]

16707

\[ {}2 y^{\prime } \sin \left (x \right )+y \cos \left (x \right ) = y^{3} \sin \left (x \right )^{2} \]

[_Bernoulli]

16709

\[ {}y^{\prime }-y \cos \left (x \right ) = y^{2} \cos \left (x \right ) \]

[_separable]

16730

\[ {}x +y^{2}-2 x y y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

16732

\[ {}x^{4} \ln \left (x \right )-2 x y^{3}+3 x^{2} y^{2} y^{\prime } = 0 \]

[_Bernoulli]

16736

\[ {}x^{2}+y^{2}+1-2 x y y^{\prime } = 0 \]

[_rational, _Bernoulli]

16790

\[ {}y^{\prime }+y \cos \left (x \right ) = y^{n} \sin \left (2 x \right ) \]

[_Bernoulli]

16794

\[ {}y-x y^{2} \ln \left (x \right )+x y^{\prime } = 0 \]

[_Bernoulli]

16798

\[ {}x y y^{\prime }-y^{2} = x^{4} \]

[[_homogeneous, ‘class D‘], _rational, _Bernoulli]

16804

\[ {}x y^{2} y^{\prime }-y^{3} = \frac {x^{4}}{3} \]

[[_homogeneous, ‘class D‘], _rational, _Bernoulli]

16806

\[ {}x^{2}+y^{2}-x y y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

16808

\[ {}x y^{2}+y-x y^{\prime } = 0 \]

[[_homogeneous, ‘class D‘], _rational, _Bernoulli]

16809

\[ {}2 y y^{\prime }+2 x +x^{2}+y^{2} = 0 \]

[[_homogeneous, ‘class D‘], _rational, _Bernoulli]

16817

\[ {}x -y^{2}+2 x y y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

16818

\[ {}x y^{\prime }+y = y^{2} \ln \left (x \right ) \]
i.c.

[_Bernoulli]

17221

\[ {}y^{\prime } = \frac {x^{4}}{y} \]

[_separable]

17222

\[ {}y^{\prime } = \frac {x^{2} \left (x^{3}+1\right )}{y} \]

[_separable]

17223

\[ {}y^{\prime }+y^{3} \sin \left (x \right ) = 0 \]

[_separable]

17227

\[ {}y y^{\prime } = \left (x y^{2}+x \right ) {\mathrm e}^{x^{2}} \]

[_separable]

17232

\[ {}y^{\prime } = x \left (y-y^{2}\right ) \]

[_separable]

17233

\[ {}y^{\prime } = \left (1-12 x \right ) y^{2} \]
i.c.

[_separable]

17234

\[ {}y^{\prime } = \frac {3-2 x}{y} \]
i.c.

[_separable]

17235

\[ {}x +y \,{\mathrm e}^{-x} y^{\prime } = 0 \]
i.c.

[_separable]

17236

\[ {}r^{\prime } = \frac {r^{2}}{\theta } \]
i.c.

[_separable]

17237

\[ {}y^{\prime } = \frac {3 x}{y+x^{2} y} \]
i.c.

[_separable]

17239

\[ {}y^{\prime } = 2 x y^{2}+4 x^{3} y^{2} \]
i.c.

[_separable]

17242

\[ {}y^{\prime } = \frac {x \left (x^{2}+1\right ) y^{5}}{6} \]
i.c.

[_separable]

17246

\[ {}2 y y^{\prime } = \frac {x}{\sqrt {x^{2}-4}} \]
i.c.

[_separable]

17248

\[ {}y^{2} \sqrt {-x^{2}+1}\, y^{\prime } = \arcsin \left (x \right ) \]
i.c.

[_separable]

17251

\[ {}y^{\prime } = 2 y^{2}+x y^{2} \]
i.c.

[_separable]

17255

\[ {}y^{\prime } = \frac {t y \left (4-y\right )}{3} \]
i.c.

[_separable]

17256

\[ {}y^{\prime } = \frac {t y \left (4-y\right )}{t +1} \]
i.c.

[_separable]

17305

\[ {}y^{\prime } = y^{{1}/{3}} \]
i.c.

[_quadrature]

17307

\[ {}y^{\prime } = -\frac {4 t}{y} \]
i.c.

[_separable]

17308

\[ {}y^{\prime } = 2 t y^{2} \]
i.c.

[_separable]

17309

\[ {}y^{\prime }+y^{3} = 0 \]
i.c.

[_quadrature]

17310

\[ {}y^{\prime } = \frac {t^{2}}{y \left (t^{3}+1\right )} \]
i.c.

[_separable]

17311

\[ {}y^{\prime } = t \left (3-y\right ) y \]

[_separable]

17312

\[ {}y^{\prime } = y \left (3-t y\right ) \]

[_Bernoulli]

17313

\[ {}y^{\prime } = -y \left (3-t y\right ) \]

[_Bernoulli]

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]

17342

\[ {}y y^{\prime } = x +1 \]

[_separable]

17345

\[ {}x \left (-1+x \right ) y^{\prime } = y \left (y+1\right ) \]

[_separable]

17352

\[ {}x y y^{\prime } = x^{2}+y^{2} \]
i.c.

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

17354

\[ {}t y^{\prime }+y = t^{2} y^{2} \]

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

17355

\[ {}y^{\prime } = y \left (t y^{3}-1\right ) \]

[_Bernoulli]

17356

\[ {}y^{\prime }+\frac {3 y}{t} = t^{2} y^{2} \]

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

17357

\[ {}t^{2} y^{\prime }+2 t y-y^{3} = 0 \]

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

17358

\[ {}5 \left (t^{2}+1\right ) y^{\prime } = 4 t y \left (y^{3}-1\right ) \]

[_separable]

17359

\[ {}3 t y^{\prime }+9 y = 2 t y^{{5}/{3}} \]

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

17360

\[ {}y^{\prime } = y+\sqrt {y} \]

[_quadrature]

17361

\[ {}y^{\prime } = r y-k^{2} y^{2} \]

[_quadrature]

17362

\[ {}y^{\prime } = a y+b y^{3} \]

[_quadrature]

17366

\[ {}y^{\prime }-4 \,{\mathrm e}^{x} y^{2} = y \]

[[_1st_order, _with_linear_symmetries], _Bernoulli]

17368

\[ {}y^{\prime } = \frac {x y^{2}-\frac {\sin \left (2 x \right )}{2}}{\left (-x^{2}+1\right ) y} \]

[_Bernoulli]

17371

\[ {}2 x y y^{\prime }+\ln \left (x \right ) = -y^{2}-1 \]

[_exact, _Bernoulli]

17375

\[ {}4 x y y^{\prime } = 8 x^{2}+5 y^{2} \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

17376

\[ {}y^{\prime }+y-y^{{1}/{4}} = 0 \]

[_quadrature]

17827

\[ {}x y^{\prime }-4 y = x^{2} \sqrt {y} \]

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

17832

\[ {}x y^{\prime }+y = x y^{2} \ln \left (x \right ) \]

[_Bernoulli]

17833

\[ {}y^{\prime }-\frac {x y}{2 x^{2}-2}-\frac {x}{2 y} = 0 \]

[_rational, _Bernoulli]

17835

\[ {}x -y^{2}+2 x y y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

17855

\[ {}y-x y^{2} \ln \left (x \right )+x y^{\prime } = 0 \]

[_Bernoulli]

17878

\[ {}y^{\prime } = \sqrt {y} \]

[_quadrature]

17979

\[ {}y y^{\prime } = {\mathrm e}^{2 x} \]

[_separable]

17986

\[ {}2 x y y^{\prime } = x^{2}+y^{2} \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

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]

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]

18042

\[ {}y^{\prime } = \frac {1-x y^{2}}{2 x^{2} y} \]

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

18043

\[ {}y^{\prime } = \frac {2+3 x y^{2}}{4 x^{2} y} \]

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

18060

\[ {}1+y^{2} \sin \left (2 x \right )-2 y \cos \left (x \right )^{2} y^{\prime } = 0 \]

[_exact, _Bernoulli]

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]

18071

\[ {}x +3 y^{2}+2 x y y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

18075

\[ {}x^{3}+x y^{3}+3 y^{2} y^{\prime } = 0 \]

[_rational, _Bernoulli]

18081

\[ {}y^{2}-y+x y^{\prime } = 0 \]

[_separable]

18087

\[ {}2 x y^{2}-y+x y^{\prime } = 0 \]

[[_homogeneous, ‘class D‘], _rational, _Bernoulli]

18100

\[ {}x y^{\prime }+y = x^{4} y^{3} \]

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

18101

\[ {}x y^{2} y^{\prime }+y^{3} = x \cos \left (x \right ) \]

[_Bernoulli]

18102

\[ {}x y^{\prime }+y = x y^{2} \]

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

18127

\[ {}x y^{\prime }+y = y^{2}+x^{2} y^{\prime } \]

[_separable]

18145

\[ {}x^{2} y^{4}+x^{6}-x^{3} y^{3} y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

18153

\[ {}x y^{2}+y+x y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

18163

\[ {}x y^{\prime }+y = y^{2} \ln \left (x \right ) \]

[_Bernoulli]

18167

\[ {}x^{2} y^{\prime }-y^{2} = 2 x y \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

18419

\[ {}x^{\prime } = 2 \sqrt {x} \]
i.c.

[_quadrature]

18431

\[ {}x^{\prime }+2 t x+t x^{4} = 0 \]

[_separable]

18467

\[ {}2 x^{2} y+y^{3}-x^{3} y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

18475

\[ {}y^{\prime }+\frac {y}{x} = \frac {\sin \left (x \right )}{y^{3}} \]

[_Bernoulli]

18477

\[ {}\left (T \ln \left (t \right )-1\right ) T = t T^{\prime } \]

[_Bernoulli]

18479

\[ {}y-\cos \left (x \right ) y^{\prime } = y^{2} \cos \left (x \right ) \left (1-\sin \left (x \right )\right ) \]

[_Bernoulli]

18498

\[ {}1+v^{2}+\left (u^{2}+1\right ) v v^{\prime } = 0 \]

[_separable]

18548

\[ {}y^{\prime }+y \sin \left (x \right ) = y^{2} \sin \left (x \right ) \]

[_separable]

18549

\[ {}\left (-x^{2}+1\right ) y^{\prime }-x y = a x y^{2} \]

[_separable]

18550

\[ {}y^{\prime }+y \cos \left (x \right ) = y^{n} \sin \left (2 x \right ) \]

[_Bernoulli]

18551

\[ {}3 y^{2} y^{\prime }+y^{3} = -1+x \]

[_rational, _Bernoulli]

18552

\[ {}y^{\prime }-y \tan \left (x \right ) = y^{4} \sec \left (x \right ) \]

[_Bernoulli]

18562

\[ {}5 x y y^{\prime }-x^{2}-y^{2} = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

18565

\[ {}5 x y y^{\prime }-4 x^{2}-y^{2} = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

18650

\[ {}y-x y^{\prime } = a \left (y^{\prime }+y^{2}\right ) \]

[_separable]

18652

\[ {}x^{2}+y^{2}-2 x y y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

18666

\[ {}x^{4} {\mathrm e}^{x}-2 m x y^{2}+2 m \,x^{2} y y^{\prime } = 0 \]

[[_homogeneous, ‘class D‘], _Bernoulli]

18667

\[ {}y \left (2 x y+{\mathrm e}^{x}\right )-{\mathrm e}^{x} y^{\prime } = 0 \]

[_Bernoulli]

18670

\[ {}2 y y^{\prime }+2 x +x^{2}+y^{2} = 0 \]

[[_homogeneous, ‘class D‘], _rational, _Bernoulli]

18671

\[ {}x^{2}+y^{2}-x^{2} y y^{\prime } = 0 \]

[_rational, _Bernoulli]

18682

\[ {}y^{\prime }+\frac {y}{x} = x^{2} y^{6} \]

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

18684

\[ {}y^{\prime }+\frac {2 y}{x} = 3 x^{2} y^{{1}/{3}} \]

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

18685

\[ {}y^{\prime }+\frac {x y}{-x^{2}+1} = x \sqrt {y} \]

[_rational, _Bernoulli]

18686

\[ {}3 x \left (-x^{2}+1\right ) y^{2} y^{\prime }+\left (2 x^{2}-1\right ) y^{3} = a \,x^{3} \]

[_rational, _Bernoulli]

18693

\[ {}3 y^{\prime }+\frac {2 y}{x +1} = \frac {x^{3}}{y^{2}} \]

[_rational, _Bernoulli]

18696

\[ {}x y^{\prime }+\frac {y^{2}}{x} = y \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

18701

\[ {}x^{2}+y^{2}+1-2 x y y^{\prime } = 0 \]

[_rational, _Bernoulli]

18703

\[ {}y^{\prime }+y \cos \left (x \right ) = y^{n} \sin \left (2 x \right ) \]

[_Bernoulli]

18705

\[ {}y^{\prime } = x^{3} y^{3}-x y \]

[_Bernoulli]

18710

\[ {}y y^{\prime } = a x \]

[_separable]

18713

\[ {}y y^{\prime }+b y^{2} = a \cos \left (x \right ) \]

[_Bernoulli]

18742

\[ {}x y \left (y-x y^{\prime }\right ) = x +y y^{\prime } \]

[_separable]

18771

\[ {}y^{\prime } \sqrt {x} = \sqrt {y} \]

[_separable]

18969

\[ {}y \left (1+x y\right )-x y^{\prime } = 0 \]

[[_homogeneous, ‘class D‘], _rational, _Bernoulli]

18970

\[ {}y^{\prime } \sin \left (x \right )-y \cos \left (x \right )+y^{2} = 0 \]

[_Bernoulli]

18974

\[ {}x y^{\prime }+y = y^{2} \ln \left (x \right ) \]

[_Bernoulli]

18982

\[ {}x y^{2}+x +\left (y+x^{2} y\right ) y^{\prime } = 0 \]

[_separable]

18993

\[ {}y-x y^{\prime } = a \left (y^{\prime }+y^{2}\right ) \]

[_separable]

18999

\[ {}x^{2}-y^{2}+2 x y y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

19006

\[ {}x^{2} y^{\prime }+\left (x +y\right ) y = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

19007

\[ {}2 y^{\prime } = \frac {y}{x}+\frac {y^{2}}{x^{2}} \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

19013

\[ {}x^{2}+3 y^{2}-2 x y y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

19035

\[ {}y \left (2 x y+{\mathrm e}^{x}\right )-{\mathrm e}^{x} y^{\prime } = 0 \]

[_Bernoulli]

19036

\[ {}2 y^{\prime }-y \sec \left (x \right ) = y^{3} \tan \left (x \right ) \]

[_Bernoulli]

19037

\[ {}y^{\prime }+y \cos \left (x \right ) = y^{n} \sin \left (2 x \right ) \]

[_Bernoulli]

19044

\[ {}x^{2}+y^{2}-2 x y y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

19057

\[ {}y^{\prime } = \frac {1+x^{2}+y^{2}}{2 x y} \]

[_rational, _Bernoulli]

19062

\[ {}y y^{\prime }+b y^{2} = a \cos \left (x \right ) \]

[_Bernoulli]

19074

\[ {}y \left (2 x y+{\mathrm e}^{x}\right )-{\mathrm e}^{x} y^{\prime } = 0 \]

[_Bernoulli]

19179

\[ {}y = x y^{\prime }+x \sqrt {1+{y^{\prime }}^{2}} \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

19203

\[ {}y^{2} x^{2}-3 x y y^{\prime } = 2 y^{2}+x^{3} \]

[_rational, _Bernoulli]

19233

\[ {}y-x y^{\prime } = a \left (y^{\prime }+y^{2}\right ) \]

[_separable]

19435

\[ {}1+y^{2}-x y y^{\prime } = 0 \]

[_separable]

19442

\[ {}y^{\prime }+p \left (x \right ) y = q \left (x \right ) y^{n} \]

[_Bernoulli]

19481

\[ {}x y \left (y-x y^{\prime }\right ) = x +y y^{\prime } \]

[_separable]