2.3.18 first order ode lie symmetry

Table 2.429: first order ode lie symmetry

#

ODE

CAS classification

Solved?

20

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

[[_linear, ‘class A‘]]

22

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

[[_linear, ‘class A‘]]

23

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

[[_linear, ‘class A‘]]

24

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

[[_linear, ‘class A‘]]

25

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

[[_linear, ‘class A‘]]

26

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

[[_linear, ‘class A‘]]

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]

31

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

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

35

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

[_quadrature]

37

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

[[_linear, ‘class A‘]]

38

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

[[_linear, ‘class A‘]]

41

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

[_separable]

42

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

[_separable]

43

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

[_separable]

44

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

[_separable]

46

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

[[_homogeneous, ‘class G‘]]

47

\[ {}y^{\prime } = 64^{{1}/{3}} \left (x y\right )^{{1}/{3}} \]

[[_homogeneous, ‘class G‘]]

49

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

[_separable]

50

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

[_separable]

51

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

[_separable]

57

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

[_separable]

58

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

[_separable]

59

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

[_separable]

60

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

[_separable]

62

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

[_separable]

63

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

[_quadrature]

64

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

[_separable]

65

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

[_separable]

66

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

[_separable]

67

\[ {}y^{\prime } = 6 \,{\mathrm e}^{2 x -y} \]
i.c.

[_separable]

69

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

[_quadrature]

72

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

[_quadrature]

73

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

[_quadrature]

74

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

[[_linear, ‘class A‘]]

75

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

[[_linear, ‘class A‘]]

76

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

[_linear]

77

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

[_linear]

78

\[ {}x y^{\prime }+5 y = 7 x^{2} \]
i.c.

[_linear]

79

\[ {}2 x y^{\prime }+y = 10 \sqrt {x} \]

[_linear]

80

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

[_linear]

81

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

[_linear]

82

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

[_linear]

84

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

[_linear]

85

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

[[_linear, ‘class A‘]]

86

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

[_linear]

87

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

[_separable]

88

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

[_separable]

90

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

[_linear]

92

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

[_separable]

93

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

[_linear]

94

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

[_linear]

95

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

[_linear]

96

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

[_separable]

98

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

[_linear]

99

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

[[_linear, ‘class A‘]]

100

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

[_linear]

103

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

[_separable]

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

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

[[_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

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

[[_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‘]]

120

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

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

121

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

[[_homogeneous, ‘class C‘], _Riccati]

122

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

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

123

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

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

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]

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]

134

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

[[_1st_order, _with_linear_symmetries]]

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]

159

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

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

162

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

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

163

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

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

164

\[ {}y^{\prime } = \frac {2 y-x +7}{4 x -3 y-18} \]

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

165

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

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

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]

168

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

[[_homogeneous, ‘class C‘], _Riccati]

171

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

[_quadrature]

172

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

[_quadrature]

173

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

[_quadrature]

174

\[ {}x^{\prime } = 9-4 x^{2} \]
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]

178

\[ {}x^{\prime } = 7 x \left (x-13\right ) \]
i.c.

[_quadrature]

179

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

[_linear]

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]

183

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

[_separable]

184

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

[_separable]

185

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

[_linear]

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]

188

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

[_separable]

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‘]]

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]

193

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

[[_linear, ‘class A‘]]

194

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

[[_homogeneous, ‘class C‘], _Riccati]

196

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

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

197

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

[_separable]

198

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

[_linear]

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]

203

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

[_linear]

204

\[ {}9 \sqrt {x}\, y^{{4}/{3}}-12 x^{{1}/{5}} y^{{3}/{2}}+\left (8 x^{{3}/{2}} y^{{1}/{3}}-15 x^{{6}/{5}} \sqrt {y}\right ) y^{\prime } = 0 \]

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

205

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

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

207

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

[_linear]

208

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

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

209

\[ {}y^{\prime } = 3 \left (y+7\right ) x^{2} \]

[_separable]

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]

212

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

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

213

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

[_separable]

231

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

[_quadrature]

662

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

[[_linear, ‘class A‘]]

664

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

[[_linear, ‘class A‘]]

665

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

[[_linear, ‘class A‘]]

666

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

[[_linear, ‘class A‘]]

667

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

[[_linear, ‘class A‘]]

668

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

[[_linear, ‘class A‘]]

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]

675

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

[_quadrature]

677

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

[_separable]

678

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

[_separable]

679

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

[_separable]

680

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

[_separable]

682

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

[[_homogeneous, ‘class G‘]]

683

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

[[_homogeneous, ‘class G‘]]

685

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

[_separable]

686

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

[_separable]

687

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

[_separable]

692

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

[_separable]

693

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

[_separable]

694

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

[_separable]

695

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

[_separable]

697

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

[_separable]

698

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

[_quadrature]

699

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

[_separable]

700

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

[_separable]

701

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

[_separable]

702

\[ {}y^{\prime } = 6 \,{\mathrm e}^{2 x -y} \]
i.c.

[_separable]

704

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

[_quadrature]

705

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

[[_linear, ‘class A‘]]

706

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

[[_linear, ‘class A‘]]

707

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

[_linear]

708

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

[_linear]

709

\[ {}2 x y^{\prime }+y = 10 \sqrt {x} \]
i.c.

[_linear]

710

\[ {}2 x y^{\prime }+y = 10 \sqrt {x} \]

[_linear]

711

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

[_linear]

712

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

[_linear]

713

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

[_linear]

715

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

[_linear]

716

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

[[_linear, ‘class A‘]]

717

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

[_linear]

718

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

[_separable]

719

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

[_separable]

721

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

[_linear]

723

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

[_separable]

724

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

[_linear]

725

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

[_linear]

726

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

[_linear]

727

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

[_separable]

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

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

[[_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

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

[[_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‘]]

744

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

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

745

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

[[_homogeneous, ‘class C‘], _Riccati]

747

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

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

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]

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]

758

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

[[_1st_order, _with_linear_symmetries]]

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]

771

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

[_linear]

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]

775

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

[_separable]

776

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

[_separable]

777

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

[_linear]

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]

780

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

[_separable]

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]

785

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

[[_linear, ‘class A‘]]

786

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

[[_homogeneous, ‘class C‘], _Riccati]

788

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

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

789

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

[_separable]

790

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

[_linear]

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]

795

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

[_linear]

797

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

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

799

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

[_linear]

800

\[ {}y^{\prime } = 3 \left (y+7\right ) x^{2} \]

[_separable]

801

\[ {}y^{\prime } = 3 \left (y+7\right ) x^{2} \]

[_separable]

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]

804

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

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

805

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

[_separable]

1065

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

[_quadrature]

1098

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

[[_linear, ‘class A‘]]

1099

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

[[_linear, ‘class A‘]]

1100

\[ {}y^{\prime }+y = 1+t \,{\mathrm e}^{-t} \]

[[_linear, ‘class A‘]]

1102

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

[[_linear, ‘class A‘]]

1104

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

[_linear]

1105

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

[_linear]

1106

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

[[_linear, ‘class A‘]]

1107

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

[_linear]

1109

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

[[_linear, ‘class A‘]]

1111

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

[[_linear, ‘class A‘]]

1112

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

[_linear]

1114

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

[[_linear, ‘class A‘]]

1119

\[ {}-y+2 y^{\prime } = {\mathrm e}^{\frac {t}{3}} \]
i.c.

[[_linear, ‘class A‘]]

1120

\[ {}-2 y+3 y^{\prime } = {\mathrm e}^{-\frac {\pi t}{2}} \]
i.c.

[[_linear, ‘class A‘]]

1121

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

[_linear]

1125

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

[[_linear, ‘class A‘]]

1128

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

[[_linear, ‘class A‘]]

1129

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

[_separable]

1131

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

[_separable]

1134

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

[_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]

1140

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

[_separable]

1142

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

[_separable]

1143

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

[_separable]

1151

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

[_separable]

1154

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

1157

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

[_quadrature]

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]

1167

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

[_separable]

1169

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

[_linear]

1170

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

[_linear]

1174

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

[_separable]

1175

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

[_separable]

1176

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

[_quadrature]

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]

1183

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

[_quadrature]

1184

\[ {}y^{\prime } = -1+{\mathrm e}^{y} \]

[_quadrature]

1185

\[ {}y^{\prime } = -1+{\mathrm e}^{-y} \]

[_quadrature]

1186

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

[_quadrature]

1187

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

[_quadrature]

1188

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

[_quadrature]

1189

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

[_quadrature]

1190

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

[_quadrature]

1191

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

[_quadrature]

1192

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

[_quadrature]

1193

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

[_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

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

[_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‘]]

1211

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

[[_linear, ‘class A‘]]

1213

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

[[_1st_order, _with_exponential_symmetries]]

1217

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

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

1218

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

[_linear]

1221

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

[_separable]

1230

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

[_separable]

1231

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

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

1232

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

[_separable]

1234

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

[[_linear, ‘class A‘]]

1237

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

[_separable]

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‘]]

1248

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

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

1519

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

[_quadrature]

1520

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

[_linear]

1521

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

[_separable]

1522

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

[_separable]

1523

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

[_separable]

1531

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

[_linear]

1532

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

[_separable]

1533

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

[_separable]

1534

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

[_quadrature]

1536

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

[[_1st_order, _with_linear_symmetries], _Clairaut]

1537

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

[_quadrature]

1538

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

[_separable]

1539

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

[_separable]

1540

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

[_separable]

1541

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

[_separable]

1542

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

[_separable]

1543

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

[_separable]

1544

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

[_separable]

1545

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

[_separable]

1546

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

[_separable]

1547

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

[_separable]

1548

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

[_quadrature]

1550

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

[_linear]

1552

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

[_linear]

1554

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

[_linear]

1555

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

[_linear]

1558

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

[_linear]

1561

\[ {}y^{\prime }+7 y = {\mathrm e}^{3 x} \]
i.c.

[[_linear, ‘class A‘]]

1562

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

[_linear]

1565

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

[_linear]

1567

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

[_linear]

1568

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

[_linear]

1569

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

[_separable]

1572

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

[_linear]

1573

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

[_separable]

1574

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

[_quadrature]

1576

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

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

1577

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

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

1580

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

[_separable]

1582

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

[_separable]

1583

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

[_separable]

1584

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

[_separable]

1585

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

[_separable]

1586

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

[_separable]

1588

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

[_separable]

1590

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

[_separable]

1591

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

[_separable]

1592

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

[_separable]

1593

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

[_separable]

1594

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

[_separable]

1595

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

[_separable]

1596

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

[_quadrature]

1597

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

[_separable]

1598

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

[_separable]

1599

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

[_separable]

1600

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

[_separable]

1601

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

[_separable]

1603

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

[_quadrature]

1605

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

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

1613

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

[_separable]

1615

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

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

1619

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

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

1620

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

[_separable]

1621

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

[_quadrature]

1624

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

[_separable]

1625

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

[_Bernoulli]

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]

1638

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

[_quadrature]

1642

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

[_linear]

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‘]]

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‘]]

1666

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

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

1667

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

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

1668

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

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

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]

1671

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

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

1672

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

[[_1st_order, _with_linear_symmetries], _Riccati]

1675

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

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

1677

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

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

1678

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

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

1679

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

[_Riccati]

1680

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

[_separable]

1682

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

[_quadrature]

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]

1695

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

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

1701

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

[_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]

1710

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

[[_Abel, ‘2nd type‘, ‘class B‘]]

1711

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

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

1712

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

[_separable]

1713

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

[_separable]

1714

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

[_separable]

1715

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

[_quadrature]

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‘]]

1722

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

[_separable]

1723

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

[_separable]

1726

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

[_separable]

1729

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

[_separable]

1731

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

[_separable]

1733

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

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

1735

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

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

1736

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

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

1792

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

[_quadrature]

1793

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

[_quadrature]

1794

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

[_quadrature]

1795

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

[_quadrature]

1796

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

[_quadrature]

1797

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

[_quadrature]

1798

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

[_quadrature]

1800

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

[[_homogeneous, ‘class C‘], _Riccati]

1801

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

[_rational, _Riccati]

1802

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

[_rational, _Riccati]

1804

\[ {}x^{2} \left (y^{\prime }+y^{2}\right )-7 x y+7 = 0 \]

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

2299

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

[_separable]

2300

\[ {}\sqrt {t}\, \sin \left (t \right ) y+y^{\prime } = 0 \]

[_separable]

2304

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

[_separable]

2306

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

[_separable]

2307

\[ {}\sqrt {t^{2}+1}\, y \,{\mathrm e}^{-t}+y^{\prime } = 0 \]

[_separable]

2308

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

[_separable]

2313

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

[_separable]

2318

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

[_separable]

2319

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

[_separable]

2320

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

[_separable]

2321

\[ {}y^{\prime } = {\mathrm e}^{3+t +y} \]

[_separable]

2325

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

[_separable]

2328

\[ {}y^{\prime } = k \left (a -y\right ) \left (b -y\right ) \]
i.c.

[_quadrature]

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]

2335

\[ {}y^{\prime } = \frac {t +y+1}{t -y+3} \]

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

2336

\[ {}1+t -2 y+\left (4 t -3 y-6\right ) y^{\prime } = 0 \]

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

2337

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

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

2341

\[ {}\frac {y^{2}}{2}-2 \,{\mathrm e}^{t} y+\left (-{\mathrm e}^{t}+y\right ) y^{\prime } = 0 \]

[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class A‘]]

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‘]]

2355

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

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

2472

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

[_separable]

2473

\[ {}\sqrt {t}\, \sin \left (t \right ) y+y^{\prime } = 0 \]

[_separable]

2477

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

[_separable]

2479

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

[_separable]

2480

\[ {}\sqrt {t^{2}+1}\, y \,{\mathrm e}^{-t}+y^{\prime } = 0 \]
i.c.

[_separable]

2481

\[ {}\sqrt {t^{2}+1}\, y \,{\mathrm e}^{-t}+y^{\prime } = 0 \]
i.c.

[_separable]

2482

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

[_separable]

2489

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

[_separable]

2490

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

[_separable]

2491

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

[_separable]

2492

\[ {}y^{\prime } = {\mathrm e}^{3+t +y} \]

[_separable]

2499

\[ {}y^{\prime } = k \left (a -y\right ) \left (b -y\right ) \]
i.c.

[_quadrature]

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]

2507

\[ {}y^{\prime } = \frac {t +y+1}{t -y+3} \]

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

2508

\[ {}1+t -2 y+\left (4 t -3 y-6\right ) y^{\prime } = 0 \]

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

2509

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

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

2513

\[ {}\frac {y^{2}}{2}-2 \,{\mathrm e}^{t} y+\left (-{\mathrm e}^{t}+y\right ) y^{\prime } = 0 \]

[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class A‘]]

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‘]]

2519

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

[_separable]

2530

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

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

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]

2841

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

[_separable]

2842

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

[_separable]

2843

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

[_separable]

2844

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

[_separable]

2845

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

[_separable]

2848

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

[_separable]

2849

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

[_separable]

2850

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

[_separable]

2851

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

[_separable]

2853

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

[_separable]

2857

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

[_separable]

2858

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

[_separable]

2860

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

[_separable]

2861

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

[_separable]

2862

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

[_separable]

2864

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

[_separable]

2865

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

[_quadrature]

2866

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

[_quadrature]

2867

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

[_separable]

2869

\[ {}\left (x^{2}+x +1\right ) y^{\prime } = y^{2}+2 y+5 \]
i.c.

[_separable]

2870

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

[_separable]

2871

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

[_linear]

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

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

[[_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‘]]

2880

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

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

2881

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

[[_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‘]]

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]

2894

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

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

2895

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

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

2896

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

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

2897

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

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

2898

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

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

2899

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

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

2900

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

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

2901

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

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

2902

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

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

2903

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

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

2904

\[ {}3 x -y+1+\left (x -3 y-5\right ) y^{\prime } = 0 \]
i.c.

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

2905

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

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

2907

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

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

2908

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

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

2909

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

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

2910

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

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

2911

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

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

2913

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

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

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‘]]

2916

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

[[_homogeneous, ‘class C‘], _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]

2922

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

[[_linear, ‘class A‘]]

2925

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

[_separable]

2927

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

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

2929

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

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

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]

2937

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

[_linear]

2938

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

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

2939

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

[_separable]

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]

2942

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

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

2943

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

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

2944

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

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

2946

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

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

2947

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

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

2948

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

[_Bernoulli]

2950

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

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

2952

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

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

2953

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

[_separable]

2954

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

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

2957

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

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

2958

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

[_linear]

2960

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

[_linear]

2961

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

[[_linear, ‘class A‘]]

2962

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

[[_linear, ‘class A‘]]

2964

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

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

2965

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

[_linear]

2966

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

[[_1st_order, _with_exponential_symmetries]]

2967

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

[_linear]

2968

\[ {}x y^{\prime } = 5 y+x +1 \]

[_linear]

2969

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

[_linear]

2972

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

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

2975

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

[_linear]

2980

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

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

2986

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

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

2988

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

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

2989

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

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

2992

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

[_Bernoulli]

2994

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

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

3000

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

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

3001

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

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

3004

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

[_separable]

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‘]]

3008

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

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

3010

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

[[_1st_order, _with_linear_symmetries]]

3011

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

[_separable]

3012

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

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

3014

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

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

3015

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

[_separable]

3016

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

[_separable]

3018

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

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

3019

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

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

3020

\[ {}r^{\prime } = r \cot \left (\theta \right ) \]

[_separable]

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]

3025

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

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

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]

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]

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]

3037

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

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

3038

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

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

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]

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‘]]

3046

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

[_linear]

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]

3050

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

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

3051

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

[[_linear, ‘class A‘]]

3052

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

[_separable]

3053

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

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

3054

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

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

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]

3057

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

[_separable]

3058

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

[_quadrature]

3296

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

[_separable]

3320

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

[[_1st_order, _with_linear_symmetries]]

3328

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

[[_1st_order, _with_linear_symmetries], _Clairaut]

3331

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

[[_1st_order, _with_linear_symmetries], _Clairaut]

3409

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

[_separable]

3410

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

[_separable]

3411

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

[_separable]

3413

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

[_separable]

3425

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

[_quadrature]

3426

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

[_quadrature]

3427

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

[_separable]

3431

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

[_separable]

3432

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

[_separable]

3433

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

[_quadrature]

3434

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

[_quadrature]

3435

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

[_quadrature]

3436

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

[_quadrature]

3437

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

[_quadrature]

3438

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

[_separable]

3439

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

[_quadrature]

3440

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

[[_linear, ‘class A‘]]

3441

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

[[_linear, ‘class A‘]]

3442

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

[[_linear, ‘class A‘]]

3445

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

[_linear]

3447

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

[_quadrature]

3448

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

[_quadrature]

3449

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

[_linear]

3451

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

[_separable]

3452

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

[_linear]

3453

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

[_separable]

3457

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

[_separable]

3458

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

[_separable]

3459

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

[_separable]

3461

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

[_linear]

3463

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

[_linear]

3465

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

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

3467

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

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

3468

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

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

3469

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

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

3471

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

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

3472

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

[_linear]

3473

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

[_separable]

3474

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

[_linear]

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]

3479

\[ {}\left (5 x +y-7\right ) y^{\prime } = 3 x +3 y+3 \]

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

3480

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

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

3515

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

[_separable]

3516

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

[_separable]

3517

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

[_separable]

3518

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

[_separable]

3519

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

[_separable]

3520

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

[_separable]

3521

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

[_separable]

3523

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

[_separable]

3525

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

[_separable]

3526

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

[_separable]

3527

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

[_separable]

3529

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

[_separable]

3530

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

[[_linear, ‘class A‘]]

3532

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

[_linear]

3533

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

[_linear]

3534

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

[_linear]

3541

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

[_linear]

3542

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

[[_linear, ‘class A‘]]

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]

3561

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

[_quadrature]

3562

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

[_separable]

3593

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

[_separable]

3594

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

[_separable]

3595

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

[_separable]

3596

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

[_separable]

3597

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

[_separable]

3598

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

[_separable]

3599

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

[_separable]

3601

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

[_separable]

3602

\[ {}y^{\prime } = \frac {x^{2} y-32}{-x^{2}+16}+2 \]

[_separable]

3603

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

[_separable]

3604

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

[_separable]

3605

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

[_separable]

3607

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

[_separable]

3608

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

[_quadrature]

3609

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

[_quadrature]

3627

\[ {}x^{\prime }+\frac {2 x}{4-t} = 5 \]
i.c.

[_linear]

3628

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

[[_linear, ‘class A‘]]

3633

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

[[_linear, ‘class A‘]]

3635

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

[_linear]

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]

3642

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

[_separable]

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‘]]

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]

3667

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

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

3672

\[ {}y^{\prime } = \left (9 x -y\right )^{2} \]
i.c.

[[_homogeneous, ‘class C‘], _Riccati]

3673

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

[[_homogeneous, ‘class C‘], _Riccati]

3674

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

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

3675

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

[[_homogeneous, ‘class G‘]]

3676

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

[[_1st_order, _with_linear_symmetries], _Riccati]

3677

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

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

3679

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

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

3680

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

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

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]

4080

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

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

4081

\[ {}5 x +2 y+1+\left (2 x +y+1\right ) y^{\prime } = 0 \]

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

4082

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

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

4083

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

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

4084

\[ {}6 x +4 y+1+\left (4 x +2 y+2\right ) y^{\prime } = 0 \]
i.c.

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

4085

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

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

4086

\[ {}2 x +3 y+1+\left (4 x +6 y+1\right ) y^{\prime } = 0 \]
i.c.

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

4090

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

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

4093

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

[_linear]

4095

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

[_separable]

4096

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

[_separable]

4097

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

[_linear]

4098

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

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

4099

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

[_quadrature]

4100

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

[[_linear, ‘class A‘]]

4102

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

[_separable]

4103

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

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

4104

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

[_linear]

4105

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

[_separable]

4112

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

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

4113

\[ {}y^{\prime } = \frac {3 x -y+1}{3 y-x +5} \]
i.c.

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

4114

\[ {}3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime } = 0 \]
i.c.

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

4190

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

[_separable]

4191

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

[[_linear, ‘class A‘]]

4196

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

[_linear]

4197

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

[_linear]

4198

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

[_linear]

4199

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

[_linear]

4200

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

[_linear]

4213

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

[_separable]

4214

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

[_separable]

4216

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

[_separable]

4218

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

[_quadrature]

4219

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

[_separable]

4220

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

[_separable]

4221

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

[_separable]

4222

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

[_separable]

4223

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

[_separable]

4224

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

[_separable]

4225

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

[_separable]

4226

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

[_separable]

4227

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

[_separable]

4228

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

[_separable]

4230

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

[_separable]

4231

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

[_separable]

4232

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

[_separable]

4233

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

[_separable]

4234

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

[_separable]

4235

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

[_separable]

4238

\[ {}x y y^{\prime } = \sqrt {y^{2}-9} \]
i.c.

[_separable]

4239

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

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

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]

4244

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

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

4245

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

[[_homogeneous, ‘class D‘]]

4246

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

[[_homogeneous, ‘class C‘], _Riccati]

4247

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

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

4248

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

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

4249

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

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

4250

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

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

4254

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

[_separable]

4257

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

[_separable]

4258

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

[_separable]

4261

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

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

4263

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

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

4264

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

[[_1st_order, _with_linear_symmetries], _rational]

4265

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

[_separable]

4267

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

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

4269

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

[_linear]

4272

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

[[_linear, ‘class A‘]]

4274

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

[_linear]

4275

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

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

4276

\[ {}2 x +3 y+1+\left (2 y-3 x +5\right ) y^{\prime } = 0 \]

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

4277

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

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

4278

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

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

4279

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

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

4281

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

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

4283

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

[_linear]

4285

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

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

4286

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

[[_1st_order, _with_linear_symmetries], _exact]

4288

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

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

4289

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

[_linear]

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‘]]

4291

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

[_linear]

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]

4302

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

[_separable]

4304

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

[_separable]

4305

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

[_separable]

4306

\[ {}y^{2} y^{\prime } = 2+3 y^{6} \]
i.c.

[_quadrature]

4311

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

[_separable]

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‘]]

4321

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

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

4322

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

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

4323

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

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

4324

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

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

4325

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

[[_homogeneous, ‘class C‘], _Riccati]

4330

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

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

4333

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

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

4337

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

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

4339

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

[[_1st_order, _with_linear_symmetries], _rational]

4341

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

[[_1st_order, _with_linear_symmetries], _rational]

4347

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

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

4349

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

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

4351

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

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

4352

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

[[_homogeneous, ‘class G‘]]

4353

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

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

4355

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

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

4356

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

[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class A‘]]

4357

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

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

4358

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

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

4361

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

[_separable]

4363

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

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

4364

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

[[_1st_order, _with_exponential_symmetries]]

4365

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

[[_1st_order, _with_linear_symmetries], _rational]

4368

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

[[_1st_order, _with_linear_symmetries]]

4373

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

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

4376

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

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

4382

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

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

4389

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

[[_1st_order, _with_linear_symmetries]]

4390

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

[[_1st_order, _with_linear_symmetries]]

4391

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

[[_1st_order, _with_linear_symmetries]]

4392

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

[[_1st_order, _with_linear_symmetries]]

4393

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

[[_homogeneous, ‘class G‘]]

4395

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

[[_1st_order, _with_linear_symmetries], _dAlembert]

4396

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

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

4398

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

[_separable]

4399

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

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

4401

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

[[_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]

4408

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

[[_homogeneous, ‘class G‘]]

4410

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

[[_homogeneous, ‘class C‘], _rational]

4412

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

[_separable]

4416

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

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

4419

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

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

4420

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

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

4421

\[ {}2 x^{3} y y^{\prime }+3 y^{2} x^{2}+7 = 0 \]

[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli]

4422

\[ {}x -y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _dAlembert]

4423

\[ {}x^{2} \left (-y+x y^{\prime }\right ) = \left (x +y\right ) y \]

[[_homogeneous, ‘class D‘], _rational, _Bernoulli]

4424

\[ {}y^{4}+x y+\left (x y^{3}-x^{2}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _rational]

4425

\[ {}x^{2}+3 \ln \left (y\right )-\frac {x y^{\prime }}{y} = 0 \]

[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]

4427

\[ {}y+\left (x y-x -y^{3}\right ) y^{\prime } = 0 \]

[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]

4428

\[ {}y+2 y^{3} y^{\prime } = \left (x +4 y \ln \left (y\right )\right ) y^{\prime } \]

[[_1st_order, _with_linear_symmetries]]

4433

\[ {}2 y^{\prime }+x = 4 \sqrt {y} \]

[[_1st_order, _with_linear_symmetries], _Chini]

4435

\[ {}y^{\prime }-6 x \,{\mathrm e}^{x -y}-1 = 0 \]

[[_1st_order, _with_linear_symmetries]]

4441

\[ {}x +\sin \left (\frac {y}{x}\right )^{2} \left (y-x y^{\prime }\right ) = 0 \]

[[_homogeneous, ‘class A‘], _dAlembert]

4443

\[ {}x y^{3}-1+x^{2} y^{2} y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

4611

\[ {}y^{\prime } = a +b x +c y \]

[[_linear, ‘class A‘]]

4614

\[ {}y^{\prime } = a +b \,{\mathrm e}^{k x}+c y \]

[[_linear, ‘class A‘]]

4615

\[ {}y^{\prime } = x \left (x^{2}-y\right ) \]

[_linear]

4617

\[ {}y^{\prime } = x^{2} \left (a \,x^{3}+b y\right ) \]

[_linear]

4618

\[ {}y^{\prime } = a \,x^{n} y \]

[_separable]

4621

\[ {}y^{\prime } = y \cot \left (x \right ) \]

[_separable]

4624

\[ {}y^{\prime } = \left (2 \csc \left (2 x \right )+\cot \left (x \right )\right ) y \]

[_separable]

4632

\[ {}y^{\prime } = y \sec \left (x \right ) \]

[_separable]

4634

\[ {}y^{\prime } = y \tan \left (x \right ) \]

[_separable]

4643

\[ {}y^{\prime } = \left (a +\cos \left (\ln \left (x \right )\right )+\sin \left (\ln \left (x \right )\right )\right ) y \]

[_separable]

4650

\[ {}y^{\prime } = \left (x +y\right )^{2} \]

[[_homogeneous, ‘class C‘], _Riccati]

4651

\[ {}y^{\prime } = \left (x -y\right )^{2} \]

[[_homogeneous, ‘class C‘], _Riccati]

4652

\[ {}y^{\prime } = 3-3 x +3 y+\left (x -y\right )^{2} \]

[[_homogeneous, ‘class C‘], _Riccati]

4654

\[ {}y^{\prime } = x \left (x^{3}+2\right )-\left (2 x^{2}-y\right ) y \]

[[_1st_order, _with_linear_symmetries], _Riccati]

4655

\[ {}y^{\prime } = 1+x \left (-x^{3}+2\right )+\left (2 x^{2}-y\right ) y \]

[[_1st_order, _with_linear_symmetries], _Riccati]

4659

\[ {}y^{\prime } = \left (3+x -4 y\right )^{2} \]

[[_homogeneous, ‘class C‘], _Riccati]

4660

\[ {}y^{\prime } = \left (1+4 x +9 y\right )^{2} \]

[[_homogeneous, ‘class C‘], _Riccati]

4662

\[ {}y^{\prime } = a +b y^{2} \]

[_quadrature]

4667

\[ {}y^{\prime } = \operatorname {a0} +\operatorname {a1} y+\operatorname {a2} y^{2} \]

[_quadrature]

4671

\[ {}y^{\prime } = x y \left (3+y\right ) \]

[_separable]

4672

\[ {}y^{\prime } = 1-x -x^{3}+\left (2 x^{2}+1\right ) y-x y^{2} \]

[_Riccati]

4674

\[ {}y^{\prime } = x +\left (1-2 x \right ) y-\left (1-x \right ) y^{2} \]

[_Riccati]

4675

\[ {}y^{\prime } = a x y^{2} \]

[_separable]

4676

\[ {}y^{\prime } = x^{n} \left (a +b y^{2}\right ) \]

[_separable]

4682

\[ {}y^{\prime }+\tan \left (x \right ) \left (1-y^{2}\right ) = 0 \]

[_separable]

4684

\[ {}y^{\prime } = \left (a +b y+c y^{2}\right ) f \left (x \right ) \]

[_separable]

4688

\[ {}y^{\prime } = y \left (a +b y^{2}\right ) \]

[_quadrature]

4689

\[ {}y^{\prime } = \operatorname {a0} +\operatorname {a1} y+\operatorname {a2} y^{2}+\operatorname {a3} y^{3} \]

[_quadrature]

4690

\[ {}y^{\prime } = x y^{3} \]

[_separable]

4691

\[ {}y^{\prime }+y \left (1-x y^{2}\right ) = 0 \]

[_Bernoulli]

4692

\[ {}y^{\prime } = \left (a +b x y\right ) y^{2} \]

[[_homogeneous, ‘class G‘], _Abel]

4695

\[ {}y^{\prime }+y^{3} \sec \left (x \right ) \tan \left (x \right ) = 0 \]

[_separable]

4697

\[ {}y^{\prime } = a \,x^{\frac {n}{1-n}}+b y^{n} \]

[[_homogeneous, ‘class G‘], _Chini]

4701

\[ {}y^{\prime } = a +b y+\sqrt {\operatorname {A0} +\operatorname {B0} y} \]

[_quadrature]

4702

\[ {}y^{\prime } = a x +b \sqrt {y} \]

[[_homogeneous, ‘class G‘], _Chini]

4703

\[ {}y^{\prime }+x^{3} = x \sqrt {x^{4}+4 y} \]

[[_1st_order, _with_linear_symmetries]]

4705

\[ {}y^{\prime } = \sqrt {a +b y^{2}} \]

[_quadrature]

4713

\[ {}y^{\prime } = a +b \cos \left (y\right ) \]

[_quadrature]

4725

\[ {}y^{\prime } = a +b \sin \left (y\right ) \]

[_quadrature]

4729

\[ {}y^{\prime } = \sqrt {a +b \cos \left (y\right )} \]

[_quadrature]

4731

\[ {}y^{\prime } = {\mathrm e}^{x +y} \]

[_separable]

4735

\[ {}y^{\prime } = a f \left (y\right ) \]

[_quadrature]

4736

\[ {}y^{\prime } = f \left (a +b x +c y\right ) \]

[[_homogeneous, ‘class C‘], _dAlembert]

4740

\[ {}2 y^{\prime }+a x = \sqrt {a^{2} x^{2}-4 b \,x^{2}-4 c y} \]

[[_homogeneous, ‘class G‘]]

4741

\[ {}3 y^{\prime } = x +\sqrt {x^{2}-3 y} \]

[[_1st_order, _with_linear_symmetries], _dAlembert]

4743

\[ {}x y^{\prime }+x +y = 0 \]

[_linear]

4744

\[ {}x y^{\prime }+x^{2}-y = 0 \]

[_linear]

4745

\[ {}x y^{\prime } = x^{3}-y \]

[_linear]

4746

\[ {}x y^{\prime } = 1+x^{3}+y \]

[_linear]

4747

\[ {}x y^{\prime } = x^{m}+y \]

[_linear]

4749

\[ {}x y^{\prime } = x^{2} \sin \left (x \right )+y \]

[_linear]

4752

\[ {}x y^{\prime } = a y \]

[_separable]

4753

\[ {}x y^{\prime } = 1+x +a y \]

[_linear]

4754

\[ {}x y^{\prime } = a x +b y \]

[_linear]

4755

\[ {}x y^{\prime } = a \,x^{2}+b y \]

[_linear]

4756

\[ {}x y^{\prime } = a +b \,x^{n}+c y \]

[_linear]

4759

\[ {}x y^{\prime }+\left (b x +a \right ) y = 0 \]

[_separable]

4760

\[ {}x y^{\prime } = x^{3}+\left (-2 x^{2}+1\right ) y \]

[_linear]

4766

\[ {}x y^{\prime } = a +b y^{2} \]

[_separable]

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

\[ {}x y^{\prime } = \left (1+x y\right ) y \]

[[_homogeneous, ‘class D‘], _rational, _Bernoulli]

4776

\[ {}x y^{\prime } = x^{3}+\left (2 x^{2}+1\right ) y+x y^{2} \]

[[_homogeneous, ‘class D‘], _rational, _Riccati]

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]

4784

\[ {}x y^{\prime } = 2 x -y+a \,x^{n} \left (x -y\right )^{2} \]

[[_1st_order, _with_linear_symmetries], _rational, _Riccati]

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]

4792

\[ {}x y^{\prime } = 4 y-4 \sqrt {y} \]

[_separable]

4793

\[ {}x y^{\prime }+2 y = \sqrt {1+y^{2}} \]

[_separable]

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]

4798

\[ {}x y^{\prime } = y+a \sqrt {y^{2}+b^{2} x^{2}} \]

[[_homogeneous, ‘class A‘], _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]

4803

\[ {}x y^{\prime } = y-\cot \left (y\right )^{2} \]

[_separable]

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]

4809

\[ {}x y^{\prime }+\tan \left (y\right ) = 0 \]

[_separable]

4810

\[ {}x y^{\prime }+x +\tan \left (x +y\right ) = 0 \]

[[_1st_order, _with_linear_symmetries]]

4811

\[ {}x y^{\prime } = y-x \tan \left (\frac {y}{x}\right ) \]

[[_homogeneous, ‘class A‘], _dAlembert]

4812

\[ {}x y^{\prime } = \left (1+y^{2}\right ) \left (x^{2}+\arctan \left (y\right )\right ) \]

[‘y=_G(x,y’)‘]

4813

\[ {}x y^{\prime } = y+{\mathrm e}^{\frac {y}{x}} x \]

[[_homogeneous, ‘class A‘], _dAlembert]

4814

\[ {}x y^{\prime } = x +y+{\mathrm e}^{\frac {y}{x}} x \]

[[_homogeneous, ‘class A‘], _dAlembert]

4815

\[ {}x y^{\prime } = y \ln \left (y\right ) \]

[_separable]

4816

\[ {}x y^{\prime } = \left (1+\ln \left (x \right )-\ln \left (y\right )\right ) y \]

[[_homogeneous, ‘class A‘], _dAlembert]

4817

\[ {}x y^{\prime }+\left (1-\ln \left (x \right )-\ln \left (y\right )\right ) y = 0 \]

[[_homogeneous, ‘class G‘]]

4818

\[ {}x y^{\prime } = y-2 x \tanh \left (\frac {y}{x}\right ) \]

[[_homogeneous, ‘class A‘], _dAlembert]

4820

\[ {}x y^{\prime } = y f \left (x^{m} y^{n}\right ) \]

[[_homogeneous, ‘class G‘]]

4821

\[ {}\left (x +1\right ) y^{\prime } = x^{3} \left (4+3 x \right )+y \]

[_linear]

4822

\[ {}\left (x +1\right ) y^{\prime } = \left (x +1\right )^{4}+2 y \]

[_linear]

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]

4827

\[ {}\left (x +1\right ) y^{\prime } = 1+y+\left (x +1\right ) \sqrt {y+1} \]

[[_1st_order, _with_linear_symmetries]]

4829

\[ {}\left (x +a \right ) y^{\prime } = b x +y \]

[_linear]

4830

\[ {}\left (x +a \right ) y^{\prime }+b \,x^{2}+y = 0 \]

[_linear]

4831

\[ {}\left (x +a \right ) y^{\prime } = 2 \left (x +a \right )^{5}+3 y \]

[_linear]

4832

\[ {}\left (x +a \right ) y^{\prime } = b +c y \]

[_separable]

4833

\[ {}\left (x +a \right ) y^{\prime } = b x +c y \]

[_linear]

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]

4836

\[ {}2 x y^{\prime } = 2 x^{3}-y \]

[_linear]

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]

4841

\[ {}2 x y^{\prime }+4 y+a +\sqrt {a^{2}-4 b -4 c y} = 0 \]

[_separable]

4842

\[ {}\left (1-2 x \right ) y^{\prime } = 16+32 x -6 y \]

[_linear]

4843

\[ {}\left (2 x +1\right ) y^{\prime } = 4 \,{\mathrm e}^{-y}-2 \]

[_separable]

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]

4849

\[ {}x^{2} y^{\prime } = -y+a \]

[_separable]

4850

\[ {}x^{2} y^{\prime } = a +b x +c \,x^{2}+x y \]

[_linear]

4851

\[ {}x^{2} y^{\prime } = a +b x +c \,x^{2}-x y \]

[_linear]

4852

\[ {}x^{2} y^{\prime }+\left (1-2 x \right ) y = x^{2} \]

[_linear]

4853

\[ {}x^{2} y^{\prime } = a +b x y \]

[_linear]

4854

\[ {}x^{2} y^{\prime } = \left (b x +a \right ) y \]

[_separable]

4857

\[ {}x^{2} y^{\prime }+x^{2}+x y+y^{2} = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Riccati]

4858

\[ {}x^{2} y^{\prime } = \left (1+2 x -y\right )^{2} \]

[[_homogeneous, ‘class C‘], _rational, _Riccati]

4859

\[ {}x^{2} y^{\prime } = a +b y^{2} \]

[_separable]

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]

4864

\[ {}x^{2} y^{\prime }+2+x y \left (4+x y\right ) = 0 \]

[[_homogeneous, ‘class G‘], _rational, _Riccati]

4866

\[ {}x^{2} y^{\prime } = a +b \,x^{2} y^{2} \]

[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]]

4868

\[ {}x^{2} y^{\prime } = a +b x y+c \,x^{2} y^{2} \]

[[_homogeneous, ‘class G‘], _rational, _Riccati]

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]

4879

\[ {}\left (-x^{2}+1\right ) y^{\prime } = 5-x y \]

[_linear]

4881

\[ {}\left (x^{2}+1\right ) y^{\prime }+a -x y = 0 \]

[_linear]

4883

\[ {}\left (-x^{2}+1\right ) y^{\prime }-x +x y = 0 \]

[_separable]

4886

\[ {}\left (x^{2}+1\right ) y^{\prime } = x \left (x^{2}+1\right )-x y \]

[_linear]

4887

\[ {}\left (x^{2}+1\right ) y^{\prime } = x \left (3 x^{2}-y\right ) \]

[_linear]

4888

\[ {}\left (-x^{2}+1\right ) y^{\prime }+2 x y = 0 \]

[_separable]

4890

\[ {}\left (x^{2}+1\right ) y^{\prime } = 2 x \left (x^{2}+1\right )^{2}+2 x y \]

[_linear]

4894

\[ {}\left (x^{2}+1\right ) y^{\prime } = \left (2 b x +a \right ) y \]

[_separable]

4895

\[ {}\left (x^{2}+1\right ) y^{\prime } = 1+y^{2} \]

[_separable]

4896

\[ {}\left (-x^{2}+1\right ) y^{\prime } = 1-y^{2} \]

[_separable]

4897

\[ {}\left (-x^{2}+1\right ) y^{\prime } = 1-\left (2 x -y\right ) y \]

[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]

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]

4905

\[ {}\left (a^{2}+x^{2}\right ) y^{\prime } = b +x y \]

[_linear]

4906

\[ {}\left (a^{2}+x^{2}\right ) y^{\prime } = \left (b +y\right ) \left (x +\sqrt {a^{2}+x^{2}}\right ) \]

[_separable]

4907

\[ {}\left (a^{2}+x^{2}\right ) y^{\prime }+\left (x -y\right ) y = 0 \]

[_rational, _Bernoulli]

4908

\[ {}\left (a^{2}+x^{2}\right ) y^{\prime } = a^{2}+3 x y-2 y^{2} \]

[_rational, _Riccati]

4909

\[ {}\left (a^{2}+x^{2}\right ) y^{\prime }+x y+b x y^{2} = 0 \]

[_separable]

4913

\[ {}x \left (x +1\right ) y^{\prime } = \left (1-2 x \right ) y \]

[_separable]

4914

\[ {}x \left (1-x \right ) y^{\prime }+\left (2 x +1\right ) y = a \]

[_linear]

4915

\[ {}x \left (1-x \right ) y^{\prime } = a +2 \left (2-x \right ) y \]

[_linear]

4917

\[ {}x \left (x +1\right ) y^{\prime } = \left (x +1\right ) \left (x^{2}-1\right )+\left (x^{2}+x -1\right ) y \]

[_linear]

4919

\[ {}x \left (x +a \right ) y^{\prime } = \left (b +c y\right ) y \]

[_separable]

4920

\[ {}\left (x +a \right )^{2} y^{\prime } = 2 \left (x +a \right ) \left (b +y\right ) \]

[_separable]

4921

\[ {}\left (x -a \right )^{2} y^{\prime }+k \left (x +y-a \right )^{2}+y^{2} = 0 \]

[[_homogeneous, ‘class C‘], _rational, _Riccati]

4922

\[ {}\left (x -a \right ) \left (x -b \right ) y^{\prime }+k y = 0 \]

[_separable]

4923

\[ {}\left (x -a \right ) \left (x -b \right ) y^{\prime } = \left (x -a \right ) \left (x -b \right )+\left (2 x -a -b \right ) y \]

[_linear]

4924

\[ {}\left (x -a \right ) \left (x -b \right ) y^{\prime } = c y^{2} \]

[_separable]

4925

\[ {}\left (x -a \right ) \left (x -b \right ) y^{\prime }+k \left (y-a \right ) \left (y-b \right ) = 0 \]

[_separable]

4926

\[ {}\left (x -a \right ) \left (x -b \right ) y^{\prime }+k \left (x +y-a \right ) \left (x +y-b \right )+y^{2} = 0 \]

[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]

4927

\[ {}2 x^{2} y^{\prime } = y \]

[_separable]

4929

\[ {}2 x^{2} y^{\prime }+1+2 x y-y^{2} x^{2} = 0 \]

[[_homogeneous, ‘class G‘], _rational, _Riccati]

4933

\[ {}x \left (1-2 x \right ) y^{\prime } = 4 x -\left (1+4 x \right ) y+y^{2} \]

[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]

4936

\[ {}2 \left (x^{2}+x +1\right ) y^{\prime } = 1+8 x^{2}-\left (2 x +1\right ) y \]

[_linear]

4938

\[ {}a \,x^{2} y^{\prime } = x^{2}+y a x +b^{2} y^{2} \]

[[_homogeneous, ‘class A‘], _rational, _Riccati]

4939

\[ {}\left (b \,x^{2}+a \right ) y^{\prime } = A +B y^{2} \]

[_separable]

4941

\[ {}x \left (a x +1\right ) y^{\prime }+a -y = 0 \]

[_separable]

4943

\[ {}x^{3} y^{\prime } = a +b \,x^{2} y \]

[_linear]

4944

\[ {}x^{3} y^{\prime } = 3-x^{2}+x^{2} y \]

[_linear]

4945

\[ {}x^{3} y^{\prime } = x^{4}+y^{2} \]

[[_homogeneous, ‘class G‘], _rational, _Riccati]

4946

\[ {}x^{3} y^{\prime } = y \left (y+x^{2}\right ) \]

[[_homogeneous, ‘class D‘], _rational, _Bernoulli]

4947

\[ {}x^{3} y^{\prime } = x^{2} \left (y-1\right )+y^{2} \]

[[_homogeneous, ‘class D‘], _rational, _Riccati]

4948

\[ {}x^{3} y^{\prime } = \left (x +1\right ) y^{2} \]

[_separable]

4949

\[ {}x^{3} y^{\prime }+20+x^{2} y \left (1-x^{2} y\right ) = 0 \]

[[_homogeneous, ‘class G‘], _rational, _Riccati]

4951

\[ {}x^{3} y^{\prime } = \left (2 x^{2}+y^{2}\right ) y \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

4955

\[ {}x \left (x^{2}+1\right ) y^{\prime } = a \,x^{3}+y \]

[_linear]

4957

\[ {}x \left (x^{2}+1\right ) y^{\prime } = \left (-x^{2}+1\right ) y \]

[_separable]

4958

\[ {}x \left (-x^{2}+1\right ) y^{\prime } = \left (x^{2}-x +1\right ) y \]

[_separable]

4959

\[ {}x \left (-x^{2}+1\right ) y^{\prime } = a \,x^{3}+\left (-2 x^{2}+1\right ) y \]

[_linear]

4960

\[ {}x \left (-x^{2}+1\right ) y^{\prime } = x^{3} \left (-x^{2}+1\right )+\left (-2 x^{2}+1\right ) y \]

[_linear]

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]

4969

\[ {}x^{4} y^{\prime } = \left (x^{3}+y\right ) y \]

[[_homogeneous, ‘class D‘], _rational, _Bernoulli]

4970

\[ {}x^{4} y^{\prime }+a^{2}+x^{4} y^{2} = 0 \]

[_rational, [_Riccati, _special]]

4971

\[ {}x^{4} y^{\prime }+x^{3} y+\csc \left (x y\right ) = 0 \]

[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]

4972

\[ {}\left (-x^{4}+1\right ) y^{\prime } = 2 x \left (1-y^{2}\right ) \]

[_separable]

4976

\[ {}x \left (-2 x^{3}+1\right ) y^{\prime } = 2 \left (-x^{3}+1\right ) y \]

[_separable]

4977

\[ {}\left (c \,x^{2}+b x +a \right )^{2} \left (y^{\prime }+y^{2}\right )+A = 0 \]

[_rational, _Riccati]

4978

\[ {}x^{5} y^{\prime } = 1-3 x^{4} y \]

[_linear]

4981

\[ {}x^{n} y^{\prime } = a +b \,x^{n -1} y \]

[_linear]

4984

\[ {}x^{n} y^{\prime } = a^{2} x^{-2+2 n}+b^{2} y^{2} \]

[[_homogeneous, ‘class G‘], _Riccati]

4988

\[ {}y^{\prime } \sqrt {-x^{2}+1} = 1+y^{2} \]

[_separable]

4991

\[ {}y^{\prime } \sqrt {b^{2}+x^{2}} = \sqrt {y^{2}+a^{2}} \]

[_separable]

5009

\[ {}\left (1-4 \cos \left (x \right )^{2}\right ) y^{\prime } = \tan \left (x \right ) \left (1+4 \cos \left (x \right )^{2}\right ) y \]

[_separable]

5010

\[ {}\left (1-\sin \left (x \right )\right ) y^{\prime }+y \cos \left (x \right ) = 0 \]

[_separable]

5011

\[ {}\left (\cos \left (x \right )-\sin \left (x \right )\right ) y^{\prime }+y \left (\cos \left (x \right )+\sin \left (x \right )\right ) = 0 \]

[_separable]

5014

\[ {}y^{\prime } x \ln \left (x \right ) = a x \left (1+\ln \left (x \right )\right )-y \]

[_linear]

5015

\[ {}y y^{\prime }+x = 0 \]

[_separable]

5018

\[ {}y y^{\prime }+a x +b y = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5024

\[ {}y y^{\prime } = \operatorname {a0} +\operatorname {a1} y+\operatorname {a2} y^{2} \]

[_quadrature]

5027

\[ {}y y^{\prime } = \sqrt {y^{2}+a^{2}} \]

[_quadrature]

5028

\[ {}y y^{\prime } = \sqrt {y^{2}-a^{2}} \]

[_quadrature]

5030

\[ {}\left (y+1\right ) y^{\prime } = x +y \]

[[_homogeneous, ‘class C‘], _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

\[ {}\left (x -y\right ) y^{\prime } = y \]

[[_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‘]]

5036

\[ {}1-y^{\prime } = x +y \]

[[_linear, ‘class A‘]]

5039

\[ {}\left (x -y\right ) y^{\prime } = \left ({\mathrm e}^{-\frac {x}{y}}+1\right ) y \]

[[_homogeneous, ‘class A‘], _dAlembert]

5040

\[ {}\left (1+x +y\right ) y^{\prime }+1+4 x +3 y = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5041

\[ {}\left (x +y+2\right ) y^{\prime } = 1-x -y \]

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5042

\[ {}\left (3-x -y\right ) y^{\prime } = 1+x -3 y \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5043

\[ {}\left (3-x +y\right ) y^{\prime } = 11-4 x +3 y \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5044

\[ {}\left (2 x +y\right ) y^{\prime }+x -2 y = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5045

\[ {}\left (2+2 x -y\right ) y^{\prime }+3+6 x -3 y = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5046

\[ {}\left (2 x -y+3\right ) y^{\prime }+2 = 0 \]

[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]

5047

\[ {}\left (4+2 x -y\right ) y^{\prime }+5+x -2 y = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5048

\[ {}\left (5-2 x -y\right ) y^{\prime }+4-x -2 y = 0 \]

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5049

\[ {}\left (1-3 x +y\right ) y^{\prime } = 2 x -2 y \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5050

\[ {}\left (2-3 x +y\right ) y^{\prime }+5-2 x -3 y = 0 \]

[[_homogeneous, ‘class C‘], _exact, _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‘]]

5052

\[ {}\left (6-4 x -y\right ) y^{\prime } = 2 x -y \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5053

\[ {}\left (1+5 x -y\right ) y^{\prime }+5+x -5 y = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5054

\[ {}\left (a +b x +y\right ) y^{\prime }+a -b x -y = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5056

\[ {}\left (x^{2}-y\right ) y^{\prime } = 4 x y \]

[[_homogeneous, ‘class G‘], _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‘]]

5063

\[ {}\left (x -2 y+1\right ) y^{\prime } = 1+2 x -y \]

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5064

\[ {}\left (x +2 y+1\right ) y^{\prime }+1-x -2 y = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5065

\[ {}\left (x +2 y+1\right ) y^{\prime }+7+x -4 y = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5067

\[ {}\left (3+2 x -2 y\right ) y^{\prime } = 1+6 x -2 y \]

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5068

\[ {}\left (1-4 x -2 y\right ) y^{\prime }+2 x +y = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5069

\[ {}\left (6 x -2 y\right ) y^{\prime } = 2+3 x -y \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5070

\[ {}\left (19+9 x +2 y\right ) y^{\prime }+18-2 x -6 y = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5073

\[ {}\left (x \,{\mathrm e}^{-x}-2 y\right ) y^{\prime } = 2 x \,{\mathrm e}^{-2 x}-\left ({\mathrm e}^{-x}+x \,{\mathrm e}^{-x}-2 y\right ) y \]

[[_Abel, ‘2nd type‘, ‘class B‘]]

5076

\[ {}\left (x -3 y\right ) y^{\prime }+4+3 x -y = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5077

\[ {}\left (4-x -3 y\right ) y^{\prime }+3-x -3 y = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5078

\[ {}\left (2 x +3 y+2\right ) y^{\prime } = 1-2 x -3 y \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5079

\[ {}\left (5-2 x -3 y\right ) y^{\prime }+1-2 x -3 y = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5080

\[ {}\left (1+9 x -3 y\right ) y^{\prime }+2+3 x -y = 0 \]

[[_homogeneous, ‘class C‘], _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‘]]

5082

\[ {}\left (3+2 x +4 y\right ) y^{\prime } = x +2 y+1 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5083

\[ {}\left (5+2 x -4 y\right ) y^{\prime } = x -2 y+3 \]

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5084

\[ {}\left (5+3 x -4 y\right ) y^{\prime } = 2+7 x -3 y \]

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5085

\[ {}4 \left (1-x -y\right ) y^{\prime }+2-x = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]

5086

\[ {}\left (11-11 x -4 y\right ) y^{\prime } = 62-8 x -25 y \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5087

\[ {}\left (6+3 x +5 y\right ) y^{\prime } = 2+x +7 y \]

[[_homogeneous, ‘class C‘], _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‘]]

5090

\[ {}\left (5-x +6 y\right ) y^{\prime } = 3-x +4 y \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5091

\[ {}3 \left (x +2 y\right ) y^{\prime } = 1-x -2 y \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5092

\[ {}\left (3-3 x +7 y\right ) y^{\prime }+7-7 x +3 y = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5093

\[ {}\left (1+x +9 y\right ) y^{\prime }+1+x +5 y = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5094

\[ {}\left (8+5 x -12 y\right ) y^{\prime } = 3+2 x -5 y \]

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5095

\[ {}\left (140+7 x -16 y\right ) y^{\prime }+25+8 x +y = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5096

\[ {}\left (3+9 x +21 y\right ) y^{\prime } = 45+7 x -5 y \]

[[_homogeneous, ‘class C‘], _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‘]]

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]

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‘]]

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]

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]

5113

\[ {}\left (1+x y\right ) y^{\prime }+y^{2} = 0 \]

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

5117

\[ {}x \left (y+2\right ) y^{\prime }+a x = 0 \]

[_quadrature]

5119

\[ {}x \left (4+y\right ) y^{\prime } = 2 x +2 y+y^{2} \]

[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]

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

\[ {}x \left (x +y\right ) y^{\prime }-\left (x +y\right ) y+x \sqrt {x^{2}-y^{2}} = 0 \]

[[_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‘]]

5130

\[ {}x \left (x^{3}+y\right ) y^{\prime } = \left (x^{3}-y\right ) y \]

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

5131

\[ {}x \left (2 x^{3}+y\right ) y^{\prime } = \left (2 x^{3}-y\right ) y \]

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

5132

\[ {}x \left (2 x^{3}+y\right ) y^{\prime } = 6 y^{2} \]

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

5134

\[ {}\left (x +a \right ) \left (x +b \right ) y^{\prime } = x y \]

[_separable]

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

\[ {}2 x y y^{\prime }+x^{2}+y^{2} = 0 \]

[[_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]

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‘]]

5148

\[ {}2 x \left (2 x^{2}+y\right ) y^{\prime }+\left (12 x^{2}+y\right ) y = 0 \]

[[_homogeneous, ‘class G‘], _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]

5156

\[ {}x \left (a +b y\right ) y^{\prime } = c y \]

[_separable]

5157

\[ {}x \left (x -a y\right ) y^{\prime } = y \left (y-a x \right ) \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

5158

\[ {}x \left (x^{n}+a y\right ) y^{\prime }+\left (b +c y\right ) y^{2} = 0 \]

[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]]

5161

\[ {}x \left (1-x y\right ) y^{\prime }+\left (1+x y\right ) y = 0 \]

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

5163

\[ {}x \left (2-x y\right ) y^{\prime }+2 y-x y^{2} \left (1+x y\right ) = 0 \]

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘]]

5164

\[ {}x \left (3-x y\right ) y^{\prime } = y \left (x y-1\right ) \]

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

5167

\[ {}\left (x^{2}+1\right ) y y^{\prime }+x \left (1-y^{2}\right ) = 0 \]

[_separable]

5170

\[ {}x \left (1-2 x y\right ) y^{\prime }+\left (2 x y+1\right ) y = 0 \]

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

5171

\[ {}x \left (2 x y+1\right ) y^{\prime }+\left (2+3 x y\right ) y = 0 \]

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

5172

\[ {}x \left (2 x y+1\right ) y^{\prime }+\left (1+2 x y-y^{2} x^{2}\right ) y = 0 \]

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘]]

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]

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]

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]

5177

\[ {}\left (1-x^{3} y\right ) y^{\prime } = y^{2} x^{2} \]

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

5178

\[ {}2 x^{3} y y^{\prime }+a +3 y^{2} x^{2} = 0 \]

[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli]

5180

\[ {}x \left (3+2 x^{2} y\right ) y^{\prime }+\left (4+3 x^{2} y\right ) y = 0 \]

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

5181

\[ {}8 x^{3} y y^{\prime }+3 x^{4}-6 y^{2} x^{2}-y^{4} = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

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]

5192

\[ {}\left (x^{2}+y^{2}\right ) y^{\prime }+x y = 0 \]

[[_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]

5197

\[ {}\left (1-x^{2}+y^{2}\right ) y^{\prime } = 1+x^{2}-y^{2} \]

[[_1st_order, _with_linear_symmetries], _rational]

5201

\[ {}\left (3 x^{2}-y^{2}\right ) y^{\prime } = 2 x y \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

5202

\[ {}\left (x^{4}+y^{2}\right ) y^{\prime } = 4 x^{3} y \]

[[_homogeneous, ‘class G‘], _rational]

5207

\[ {}\left (1+y+x y+y^{2}\right ) y^{\prime }+1+y = 0 \]

[[_1st_order, _with_linear_symmetries], _rational]

5208

\[ {}\left (x +y\right )^{2} y^{\prime } = a^{2} \]

[[_homogeneous, ‘class C‘], _dAlembert]

5209

\[ {}\left (x -y\right )^{2} y^{\prime } = a^{2} \]

[[_homogeneous, ‘class C‘], _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]

5212

\[ {}\left (a +b +x +y\right )^{2} y^{\prime } = 2 \left (a +y\right )^{2} \]

[[_homogeneous, ‘class C‘], _rational]

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]

5215

\[ {}\left (1-3 x -y\right )^{2} y^{\prime } = \left (1-2 y\right ) \left (3-6 x -4 y\right ) \]

[[_homogeneous, ‘class C‘], _rational]

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]

5222

\[ {}\left (1-3 x +2 y\right )^{2} y^{\prime } = \left (4+2 x -3 y\right )^{2} \]

[[_homogeneous, ‘class C‘], _rational]

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]

5230

\[ {}x \left (3 x -y^{2}\right ) y^{\prime }+\left (5 x -2 y^{2}\right ) y = 0 \]

[[_homogeneous, ‘class G‘], _rational]

5232

\[ {}x \left (1-x^{2}+y^{2}\right ) y^{\prime }+\left (1+x^{2}-y^{2}\right ) y = 0 \]

[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]

5233

\[ {}x \left (a -x^{2}-y^{2}\right ) y^{\prime }+\left (a +x^{2}+y^{2}\right ) y = 0 \]

[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]

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]

5235

\[ {}\left (x \left (a -x^{2}-y^{2}\right )+y\right ) y^{\prime }+x -\left (a -x^{2}-y^{2}\right ) y = 0 \]

[[_1st_order, _with_linear_symmetries], _rational]

5236

\[ {}x \left (a +y\right )^{2} y^{\prime } = b y^{2} \]

[_separable]

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]

5244

\[ {}3 x y^{2} y^{\prime } = 2 x -y^{3} \]

[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli]

5246

\[ {}x \left (x -3 y^{2}\right ) y^{\prime }+\left (2 x -y^{2}\right ) y = 0 \]

[[_homogeneous, ‘class G‘], _exact, _rational]

5249

\[ {}6 x y^{2} y^{\prime }+x +2 y^{3} = 0 \]

[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli]

5250

\[ {}x \left (x +6 y^{2}\right ) y^{\prime }+x y-3 y^{3} = 0 \]

[[_homogeneous, ‘class G‘], _rational]

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]

5252

\[ {}x \left (3 x -7 y^{2}\right ) y^{\prime }+\left (5 x -3 y^{2}\right ) y = 0 \]

[[_homogeneous, ‘class G‘], _rational]

5254

\[ {}\left (1-y^{2} x^{2}\right ) y^{\prime } = x y^{3} \]

[[_homogeneous, ‘class G‘], _rational]

5255

\[ {}\left (1-y^{2} x^{2}\right ) y^{\prime } = \left (1+x y\right ) y^{2} \]

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

5256

\[ {}x \left (1+x y^{2}\right ) y^{\prime }+y = 0 \]

[[_homogeneous, ‘class G‘], _rational]

5257

\[ {}x \left (1+x y^{2}\right ) y^{\prime } = \left (2-3 x y^{2}\right ) y \]

[[_homogeneous, ‘class G‘], _rational]

5263

\[ {}x^{3} \left (1+y^{2}\right ) y^{\prime }+3 x^{2} y = 0 \]

[_separable]

5264

\[ {}x \left (1-x y\right )^{2} y^{\prime }+\left (1+y^{2} x^{2}\right ) y = 0 \]

[[_homogeneous, ‘class G‘], _rational]

5265

\[ {}\left (1-x^{4} y^{2}\right ) y^{\prime } = x^{3} y^{3} \]

[[_homogeneous, ‘class G‘], _rational]

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]

5282

\[ {}x \left (x -y^{3}\right ) y^{\prime } = \left (3 x +y^{3}\right ) y \]

[[_homogeneous, ‘class G‘], _rational]

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]

5287

\[ {}x \left (x^{4}-2 y^{3}\right ) y^{\prime }+\left (2 x^{4}+y^{3}\right ) y = 0 \]

[[_homogeneous, ‘class G‘], _rational]

5291

\[ {}x \left (2-x y^{2}-2 x y^{3}\right ) y^{\prime }+1+2 y = 0 \]

[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]

5295

\[ {}x \left (1-x y\right ) \left (1-y^{2} x^{2}\right ) y^{\prime }+\left (1+x y\right ) \left (1+y^{2} x^{2}\right ) y = 0 \]

[[_homogeneous, ‘class G‘], _rational]

5296

\[ {}\left (x^{2}-y^{4}\right ) y^{\prime } = x y \]

[[_homogeneous, ‘class G‘], _rational]

5297

\[ {}\left (x^{3}-y^{4}\right ) y^{\prime } = 3 x^{2} y \]

[[_homogeneous, ‘class G‘], _rational]

5298

\[ {}\left (a^{2} x^{2}+\left (x^{2}+y^{2}\right )^{2}\right ) y^{\prime } = a^{2} x y \]

[_rational]

5299

\[ {}2 \left (x -y^{4}\right ) y^{\prime } = y \]

[[_homogeneous, ‘class G‘], _rational]

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]

5303

\[ {}2 x \left (x^{3}+y^{4}\right ) y^{\prime } = \left (x^{3}+2 y^{4}\right ) y \]

[[_homogeneous, ‘class G‘], _rational]

5304

\[ {}x \left (1-x^{2} y^{4}\right ) y^{\prime }+y = 0 \]

[[_homogeneous, ‘class G‘], _rational]

5305

\[ {}\left (x^{2}-y^{5}\right ) y^{\prime } = 2 x y \]

[[_homogeneous, ‘class G‘], _rational]

5306

\[ {}x \left (x^{3}+y^{5}\right ) y^{\prime } = \left (x^{3}-y^{5}\right ) y \]

[[_homogeneous, ‘class G‘], _rational]

5308

\[ {}\left (1+a \left (x +y\right )\right )^{n} y^{\prime }+a \left (x +y\right )^{n} = 0 \]

[[_homogeneous, ‘class C‘], _dAlembert]

5309

\[ {}x \left (a +x y^{n}\right ) y^{\prime }+b y = 0 \]

[[_homogeneous, ‘class G‘], _rational]

5314

\[ {}\left (1+\sqrt {x +y}\right ) y^{\prime }+1 = 0 \]

[[_homogeneous, ‘class C‘], _dAlembert]

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]

5323

\[ {}\left (x \sqrt {1+x^{2}+y^{2}}-y \left (x^{2}+y^{2}\right )\right ) y^{\prime } = x \left (x^{2}+y^{2}\right )+y \sqrt {1+x^{2}+y^{2}} \]

[[_1st_order, _with_linear_symmetries]]

5327

\[ {}\left (1+\left (x +y\right ) \tan \left (y\right )\right ) y^{\prime }+1 = 0 \]

[[_1st_order, _with_linear_symmetries]]

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]

5330

\[ {}\left (1-2 x -\ln \left (y\right )\right ) y^{\prime }+2 y = 0 \]

[[_1st_order, _with_linear_symmetries]]

5392

\[ {}{y^{\prime }}^{2}-y y^{\prime }+{\mathrm e}^{x} = 0 \]

[[_1st_order, _with_linear_symmetries]]

5403

\[ {}{y^{\prime }}^{2}-x y y^{\prime }+y^{2} \ln \left (a y\right ) = 0 \]

[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]

5421

\[ {}4 {y^{\prime }}^{2}+2 x \,{\mathrm e}^{-2 y} y^{\prime }-{\mathrm e}^{-2 y} = 0 \]

[[_1st_order, _with_linear_symmetries]]

5478

\[ {}x^{2} {y^{\prime }}^{2}-2 x y y^{\prime }-x +y \left (y+1\right ) = 0 \]

[[_1st_order, _with_linear_symmetries], _rational]

5483

\[ {}x^{2} {y^{\prime }}^{2}+2 x \left (2 x +y\right ) y^{\prime }-4 a +y^{2} = 0 \]

[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]

5543

\[ {}x y {y^{\prime }}^{2}-\left (a -b \,x^{2}+y^{2}\right ) y^{\prime }-b x y = 0 \]

[_rational]

5602

\[ {}{y^{\prime }}^{3}-a x y y^{\prime }+2 a y^{2} = 0 \]

[[_1st_order, _with_linear_symmetries]]

5603

\[ {}{y^{\prime }}^{3}-x y^{4} y^{\prime }-y^{5} = 0 \]

[[_1st_order, _with_linear_symmetries]]

5620

\[ {}3 {y^{\prime }}^{3}-x^{4} y^{\prime }+2 x^{3} y = 0 \]

[[_1st_order, _with_linear_symmetries]]

5625

\[ {}x {y^{\prime }}^{3}-2 y {y^{\prime }}^{2}+4 x^{2} = 0 \]

[[_1st_order, _with_linear_symmetries]]

5632

\[ {}2 x^{3} {y^{\prime }}^{3}+6 x^{2} y {y^{\prime }}^{2}-\left (1-6 x y\right ) y y^{\prime }+2 y^{3} = 0 \]

[[_homogeneous, ‘class G‘]]

5633

\[ {}x^{4} {y^{\prime }}^{3}-x^{3} y {y^{\prime }}^{2}-x^{2} y^{2} y^{\prime }+x y^{3} = 1 \]

[[_1st_order, _with_linear_symmetries]]

5634

\[ {}x^{6} {y^{\prime }}^{3}-x y^{\prime }-y = 0 \]

[[_1st_order, _with_linear_symmetries]]

5638

\[ {}y^{2} {y^{\prime }}^{3}-x y^{\prime }+y = 0 \]

[[_1st_order, _with_linear_symmetries]]

5639

\[ {}y^{2} {y^{\prime }}^{3}+2 x y^{\prime }-y = 0 \]

[[_1st_order, _with_linear_symmetries]]

5640

\[ {}4 y^{2} {y^{\prime }}^{3}-2 x y^{\prime }+y = 0 \]

[[_1st_order, _with_linear_symmetries]]

5641

\[ {}16 y^{2} {y^{\prime }}^{3}+2 x y^{\prime }-y = 0 \]

[[_1st_order, _with_linear_symmetries]]

5644

\[ {}y^{4} {y^{\prime }}^{3}-6 x y^{\prime }+2 y = 0 \]

[[_1st_order, _with_linear_symmetries]]

5662

\[ {}2 \left (y+1\right )^{{3}/{2}}+3 x y^{\prime }-3 y = 0 \]

[_separable]

5674

\[ {}y^{\prime } \sin \left (y^{\prime }\right )+\cos \left (y^{\prime }\right ) = y \]

[_quadrature]

5678

\[ {}{\mathrm e}^{y^{\prime }-y}-{y^{\prime }}^{2}+1 = 0 \]

[_quadrature]

5680

\[ {}\ln \left (y^{\prime }\right )+x y^{\prime }+a = y \]

[[_1st_order, _with_linear_symmetries], _Clairaut]

5681

\[ {}\ln \left (y^{\prime }\right )+x y^{\prime }+a +b y = 0 \]

[[_1st_order, _with_linear_symmetries], _dAlembert]

5682

\[ {}\ln \left (y^{\prime }\right )+4 x y^{\prime }-2 y = 0 \]

[[_1st_order, _with_linear_symmetries], _dAlembert]

5683

\[ {}\ln \left (y^{\prime }\right )+a \left (-y+x y^{\prime }\right ) = 0 \]

[[_1st_order, _with_linear_symmetries], _Clairaut]

5684

\[ {}a \left (\ln \left (y^{\prime }\right )-y^{\prime }\right )-x +y = 0 \]

[[_homogeneous, ‘class C‘], _dAlembert]

5685

\[ {}y \ln \left (y^{\prime }\right )+y^{\prime }-y \ln \left (y\right )-x y = 0 \]

[_separable]

5686

\[ {}y^{\prime } \ln \left (y^{\prime }\right )-\left (x +1\right ) y^{\prime }+y = 0 \]

[[_1st_order, _with_linear_symmetries], _Clairaut]

5689

\[ {}y^{\prime } = \frac {x y}{x^{2}-y^{2}} \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

5690

\[ {}y^{\prime } = \frac {x +y-3}{x -y-1} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5691

\[ {}y^{\prime } = \frac {2 x +y-1}{4 x +2 y+5} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5692

\[ {}y^{\prime }-\frac {2 y}{x +1} = \left (x +1\right )^{2} \]

[_linear]

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]

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]

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

\[ {}8 y+10 x +\left (5 y+7 x \right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5710

\[ {}2 x -y+1+\left (2 y-1\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5711

\[ {}3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5713

\[ {}x \left (-x^{2}+1\right ) y^{\prime }+\left (2 x^{2}-1\right ) y = a \,x^{3} \]

[_linear]

5716

\[ {}\left (x^{2}+1\right ) y^{\prime }+y = \arctan \left (x \right ) \]

[_linear]

5717

\[ {}\left (-x^{2}+1\right ) z^{\prime }-x z = a x z^{2} \]

[_separable]

5721

\[ {}x y^{\prime }+y = y^{2} \ln \left (x \right ) \]

[_Bernoulli]

5733

\[ {}-y+x y^{\prime } = \sqrt {x^{2}+y^{2}} \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

5734

\[ {}8 y+10 x +\left (5 y+7 x \right ) y^{\prime } = 0 \]

[[_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

\[ {}y^{2}+\left (x y+x^{2}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

5738

\[ {}\left (y^{2} x^{2}+x y\right ) y+\left (y^{2} x^{2}-1\right ) x y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

5739

\[ {}\left (x^{3} y^{3}+y^{2} x^{2}+x y+1\right ) y+\left (x^{3} y^{3}-y^{2} x^{2}-x y+1\right ) x y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _rational]

5763

\[ {}y = x y^{\prime }+x \sqrt {1+{y^{\prime }}^{2}} \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

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

\[ {}x +y-\left (x -y\right ) y^{\prime } = 0 \]

[[_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]

5785

\[ {}x +2 y-4-\left (2 x -4 y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5786

\[ {}3 x +2 y+1-\left (3 x +2 y-1\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5788

\[ {}x +y-1+\left (2 x +2 y-3\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5789

\[ {}x +y-1-\left (x -y-1\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5790

\[ {}x +y+\left (2 x +2 y-1\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5791

\[ {}7 y-3+\left (2 x +1\right ) y^{\prime } = 0 \]

[_separable]

5792

\[ {}x +2 y+\left (3 x +6 y+3\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5793

\[ {}x +2 y+\left (y-1\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5794

\[ {}3 x -2 y+4-\left (2 x +7 y-1\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5796

\[ {}3 x +2 y+3-\left (x +2 y-1\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5797

\[ {}y+7+\left (2 x +y+3\right ) y^{\prime } = 0 \]
i.c.

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5798

\[ {}x +y+2-\left (x -y-4\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5819

\[ {}y \left (2 y^{3} x^{2}+3\right )+x \left (y^{3} x^{2}-1\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _rational]

5825

\[ {}x^{2}-y^{2}-y-\left (x^{2}-y^{2}-x \right ) y^{\prime } = 0 \]

[[_1st_order, _with_linear_symmetries], _rational]

5839

\[ {}x y^{\prime }+y = x^{3} \]

[_linear]

5840

\[ {}y^{\prime }+a y = b \]

[_quadrature]

5841

\[ {}x y^{\prime }+y = y^{2} \ln \left (x \right ) \]

[_Bernoulli]

5842

\[ {}x^{\prime }+2 x y = {\mathrm e}^{-y^{2}} \]

[_linear]

5844

\[ {}y^{\prime }-\frac {2 x y}{x^{2}+1} = 1 \]

[_linear]

5848

\[ {}y^{\prime }+2 y = 3 \,{\mathrm e}^{-2 x} \]

[[_linear, ‘class A‘]]

5849

\[ {}y^{\prime }+2 y = \frac {3 \,{\mathrm e}^{-2 x}}{4} \]

[[_linear, ‘class A‘]]

5854

\[ {}-y+x y^{\prime } = x^{2} \sin \left (x \right ) \]

[_linear]

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]

5858

\[ {}y^{\prime }-y = {\mathrm e}^{x} \]
i.c.

[[_linear, ‘class A‘]]

5864

\[ {}y^{\prime } = \frac {1}{x^{2}}-\frac {y}{x}-y^{2} \]

[[_homogeneous, ‘class G‘], _rational, _Riccati]

5865

\[ {}y^{\prime } = 1+\frac {y}{x}-\frac {y^{2}}{x^{2}} \]

[[_homogeneous, ‘class A‘], _rational, _Riccati]

5868

\[ {}\left (x +1\right ) y^{\prime }-y-1 = \left (x +1\right ) \sqrt {y+1} \]

[[_1st_order, _with_linear_symmetries]]

5869

\[ {}{\mathrm e}^{y} \left (1+y^{\prime }\right ) = {\mathrm e}^{x} \]

[[_homogeneous, ‘class C‘], _dAlembert]

5871

\[ {}\left (x -y\right )^{2} y^{\prime } = 4 \]

[[_homogeneous, ‘class C‘], _dAlembert]

5872

\[ {}-y+x y^{\prime } = \sqrt {x^{2}+y^{2}} \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

5873

\[ {}\left (3 x +2 y+1\right ) y^{\prime }+4 x +3 y+2 = 0 \]

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5874

\[ {}\left (x^{2}-y^{2}\right ) y^{\prime } = 2 x y \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

5875

\[ {}y+\left (1+y^{2} {\mathrm e}^{2 x}\right ) y^{\prime } = 0 \]

[[_1st_order, _with_linear_symmetries]]

5876

\[ {}x^{2} y+y^{2}+x^{3} y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

5878

\[ {}y^{\prime } = \left (x^{2}+2 y-1\right )^{{2}/{3}}-x \]

[[_1st_order, _with_linear_symmetries]]

5879

\[ {}x y^{\prime }+y = x^{2} \left ({\mathrm e}^{x}+1\right ) y^{2} \]

[_Bernoulli]

5880

\[ {}2 y-x y \ln \left (x \right )-2 y^{\prime } x \ln \left (x \right ) = 0 \]

[_separable]

5881

\[ {}y^{\prime }+a y = k \,{\mathrm e}^{b x} \]

[[_linear, ‘class A‘]]

5882

\[ {}y^{\prime } = \left (x +y\right )^{2} \]

[[_homogeneous, ‘class C‘], _Riccati]

5886

\[ {}x y^{\prime }-y^{2}+1 = 0 \]

[_separable]

5888

\[ {}x y^{\prime } = {\mathrm e}^{\frac {y}{x}} x +x +y \]

[[_homogeneous, ‘class A‘], _dAlembert]

5890

\[ {}x y^{\prime }-y \left (\ln \left (x y\right )-1\right ) = 0 \]

[[_homogeneous, ‘class G‘]]

5891

\[ {}x^{3} y^{\prime }-y^{2}-x^{2} y = 0 \]

[[_homogeneous, ‘class D‘], _rational, _Bernoulli]

5892

\[ {}x y^{\prime }+a y+b \,x^{n} = 0 \]

[_linear]

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

\[ {}x^{2} y^{\prime }+y^{2}+x y+x^{2} = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Riccati]

5899

\[ {}\left (x^{2}-1\right ) y^{\prime }+x y-3 x y^{2} = 0 \]

[_separable]

5900

\[ {}\left (x^{2}-1\right ) y^{\prime }-2 x y \ln \left (y\right ) = 0 \]

[_separable]

5903

\[ {}\left (2 x y+4 x^{3}\right ) y^{\prime }+y^{2}+12 x^{2} y = 0 \]

[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

5905

\[ {}\left (x^{2}-y\right ) y^{\prime }-4 x y = 0 \]

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

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]

5909

\[ {}\left (x y-1\right )^{2} x y^{\prime }+\left (1+y^{2} x^{2}\right ) y = 0 \]

[[_homogeneous, ‘class G‘], _rational]

5910

\[ {}\left (x^{2}+y^{2}\right ) y^{\prime }+2 x \left (2 x +y\right ) = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]

5911

\[ {}3 x y^{2} y^{\prime }+y^{3}-2 x = 0 \]

[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli]

5912

\[ {}2 y^{3} y^{\prime }+x y^{2}-x^{3} = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

6019

\[ {}-a y^{3}-\frac {b}{x^{{3}/{2}}}+y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _rational, _Abel]

6020

\[ {}a x y^{3}+b y^{2}+y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _Abel]

6025

\[ {}y^{\prime }+y \tan \left (x \right ) = 0 \]

[_separable]

6029

\[ {}y^{\prime } = {\mathrm e}^{a x}+a y \]

[[_linear, ‘class A‘]]

6032

\[ {}y^{\prime } = a x y^{2} \]

[_separable]

6034

\[ {}x y \left (x^{2}+1\right ) y^{\prime } = 1+y^{2} \]

[_separable]

6036

\[ {}y^{\prime }+b^{2} y^{2} = a^{2} \]

[_quadrature]

6037

\[ {}y^{\prime } = \frac {1+y^{2}}{x^{2}+1} \]

[_separable]

6039

\[ {}a x y^{\prime }+2 y = x y y^{\prime } \]

[_separable]

6075

\[ {}y^{\prime }+y^{2} = \frac {a^{2}}{x^{4}} \]

[_rational, _Riccati]

6092

\[ {}y^{\prime } = y \]

[_quadrature]

6093

\[ {}x y^{\prime } = y \]
i.c.

[_separable]

6096

\[ {}x y y^{\prime }+1+y^{2} = 0 \]
i.c.

[_separable]

6100

\[ {}y^{\prime }+2 x y^{2} = 0 \]
i.c.

[_separable]

6101

\[ {}\left (y+1\right ) y^{\prime } = y \]
i.c.

[_quadrature]

6102

\[ {}y^{\prime }-x y = x \]
i.c.

[_separable]

6103

\[ {}2 y^{\prime } = 3 \left (y-2\right )^{{1}/{3}} \]
i.c.

[_quadrature]

6104

\[ {}\left (x +x y\right ) y^{\prime }+y = 0 \]
i.c.

[_separable]

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]

6123

\[ {}\left (x -y\right ) y^{\prime }+y+x +1 = 0 \]

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

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

\[ {}y^{2}-x y+\left (x y+x^{2}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

6129

\[ {}y^{\prime } = \cos \left (x +y\right ) \]

[[_homogeneous, ‘class C‘], _dAlembert]

6130

\[ {}y^{\prime } = \frac {y}{x}-\tan \left (\frac {y}{x}\right ) \]

[[_homogeneous, ‘class A‘], _dAlembert]

6131

\[ {}\left (-1+x \right ) y^{\prime }+y-\frac {1}{x^{2}}+\frac {2}{x^{3}} = 0 \]

[_linear]

6132

\[ {}y^{\prime } = x y^{2}-\frac {2 y}{x}-\frac {1}{x^{3}} \]

[[_homogeneous, ‘class G‘], _rational, _Riccati]

6134

\[ {}y^{\prime } = {\mathrm e}^{-x} y^{2}+y-{\mathrm e}^{x} \]

[[_1st_order, _with_linear_symmetries], _Riccati]

6208

\[ {}x^{2} y^{\prime }-x y = \frac {1}{x} \]

[_linear]

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]

6218

\[ {}y+2 x -x y^{\prime } = 0 \]

[_linear]

6224

\[ {}\left (2 x +y\right ) y^{\prime }-x +2 y = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

6226

\[ {}\sin \left (x \right )^{2} y^{\prime }+\sin \left (x \right )^{2}+\left (x +y\right ) \sin \left (2 x \right ) = 0 \]

[_linear]

6232

\[ {}3 x^{2} y+x^{3} y^{\prime } = 0 \]
i.c.

[_separable]

6233

\[ {}-y+x y^{\prime } = x^{2} \]
i.c.

[_linear]

6237

\[ {}x y^{\prime } = x y+y \]

[_separable]

6239

\[ {}y^{\prime } = 3 x^{2} y \]

[_separable]

6241

\[ {}x y^{\prime } = y \]

[_separable]

6256

\[ {}y^{\prime }-\sin \left (x +y\right ) = 0 \]

[[_homogeneous, ‘class C‘], _dAlembert]

6257

\[ {}y^{\prime } = 4 y^{2}-3 y+1 \]

[_quadrature]

6262

\[ {}x y^{\prime } = \frac {1}{y^{3}} \]

[_separable]

6263

\[ {}x^{\prime } = 3 x t^{2} \]

[_separable]

6266

\[ {}v^{\prime } x = \frac {1-4 v^{2}}{3 v} \]

[_separable]

6267

\[ {}y^{\prime } = \frac {\sec \left (y\right )^{2}}{x^{2}+1} \]

[_separable]

6268

\[ {}y^{\prime } = 3 x^{2} \left (1+y^{2}\right )^{{3}/{2}} \]

[_separable]

6269

\[ {}x^{\prime }-x^{3} = x \]

[_quadrature]

6271

\[ {}\frac {y^{\prime }}{y}+y \,{\mathrm e}^{\cos \left (x \right )} \sin \left (x \right ) = 0 \]

[_separable]

6272

\[ {}y^{\prime } = \left (1+y^{2}\right ) \tan \left (x \right ) \]
i.c.

[_separable]

6273

\[ {}y^{\prime } = x^{3} \left (1-y\right ) \]
i.c.

[_separable]

6277

\[ {}x^{2}+2 y y^{\prime } = 0 \]
i.c.

[_separable]

6279

\[ {}y^{\prime } = 8 x^{3} {\mathrm e}^{-2 y} \]
i.c.

[_separable]

6280

\[ {}y^{\prime } = x^{2} \left (y+1\right ) \]
i.c.

[_separable]

6284

\[ {}y^{\prime } = \sqrt {\sin \left (x \right )+1}\, \left (1+y^{2}\right ) \]
i.c.

[_separable]

6285

\[ {}y^{\prime } = 2 y-2 t y \]
i.c.

[_separable]

6286

\[ {}y^{\prime } = y^{{1}/{3}} \]

[_quadrature]

6287

\[ {}y^{\prime } = y^{{1}/{3}} \]
i.c.

[_quadrature]

6288

\[ {}y^{\prime } = \left (x -3\right ) \left (y+1\right )^{{2}/{3}} \]

[_separable]

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]

6293

\[ {}y^{\prime } = y^{2}-3 y+2 \]
i.c.

[_quadrature]

6296

\[ {}\left (t^{2}+1\right ) y^{\prime } = t y-y \]

[_separable]

6299

\[ {}3 r = r^{\prime }-\theta ^{3} \]

[[_linear, ‘class A‘]]

6300

\[ {}y^{\prime }-y-{\mathrm e}^{3 x} = 0 \]

[[_linear, ‘class A‘]]

6301

\[ {}y^{\prime } = \frac {y}{x}+2 x +1 \]

[_linear]

6303

\[ {}x y^{\prime }+2 y = \frac {1}{x^{3}} \]

[_linear]

6304

\[ {}t +y+1-y^{\prime } = 0 \]

[[_linear, ‘class A‘]]

6305

\[ {}y^{\prime } = x^{2} {\mathrm e}^{-4 x}-4 y \]

[[_linear, ‘class A‘]]

6306

\[ {}x^{\prime } y +2 x = 5 y^{3} \]

[_linear]

6308

\[ {}\left (x^{2}+1\right ) y^{\prime }+x y-x = 0 \]

[_separable]

6310

\[ {}y^{\prime }-\frac {y}{x} = x \,{\mathrm e}^{x} \]
i.c.

[_linear]

6311

\[ {}y^{\prime }+4 y-{\mathrm e}^{-x} = 0 \]
i.c.

[[_linear, ‘class A‘]]

6313

\[ {}y^{\prime }+\frac {3 y}{x}+2 = 3 x \]
i.c.

[_linear]

6317

\[ {}\left ({\mathrm e}^{4 y}+2 x \right ) y^{\prime }-1 = 0 \]

[[_1st_order, _with_exponential_symmetries]]

6319

\[ {}y^{\prime }+\frac {3 y}{x} = x^{2} \]

[_linear]

6321

\[ {}u^{\prime } = \alpha \left (1-u\right )-\beta u \]

[_quadrature]

6322

\[ {}x^{2} y+x^{4} \cos \left (x \right )-x^{3} y^{\prime } = 0 \]

[_linear]

6323

\[ {}x^{{10}/{3}}-2 y+x y^{\prime } = 0 \]

[_linear]

6324

\[ {}\sqrt {-2 y-y^{2}}+\left (-x^{2}+2 x +3\right ) y^{\prime } = 0 \]

[_separable]

6340

\[ {}y^{\prime }-4 y = 32 x^{2} \]

[[_linear, ‘class A‘]]

6342

\[ {}y^{\prime }+\frac {3 y}{x} = x^{2}-4 x +3 \]

[_linear]

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]

6398

\[ {}y^{\prime }-y = {\mathrm e}^{2 x} \]

[[_linear, ‘class A‘]]

6399

\[ {}x^{2} y^{\prime }+2 x y-x +1 = 0 \]
i.c.

[_linear]

6400

\[ {}y^{\prime }+y = \left (x +1\right )^{2} \]
i.c.

[[_linear, ‘class A‘]]

6402

\[ {}y^{\prime }+\frac {y}{1-x}+2 x -x^{2} = 0 \]

[_linear]

6403

\[ {}y^{\prime }+\frac {y}{1-x}+x -x^{2} = 0 \]

[_linear]

6404

\[ {}\left (x^{2}+1\right ) y^{\prime } = 1+x y \]

[_linear]

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]

6415

\[ {}y^{\prime }-\frac {2 y}{x}-x^{2} = 0 \]

[_linear]

6416

\[ {}y^{\prime }+\frac {2 y}{x}-x^{3} = 0 \]

[_linear]

6419

\[ {}\left (x +1\right )^{2} y^{\prime } = 1+y^{2} \]

[_separable]

6420

\[ {}y^{\prime }+2 y = {\mathrm e}^{3 x} \]

[[_linear, ‘class A‘]]

6421

\[ {}-y+x y^{\prime } = x^{2} \]

[_linear]

6423

\[ {}x \cos \left (y\right ) y^{\prime }-\sin \left (y\right ) = 0 \]

[_separable]

6424

\[ {}\left (x^{3}+x y^{2}\right ) y^{\prime } = 2 y^{3} \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

6425

\[ {}\left (x^{2}-1\right ) y^{\prime }+2 x y = x \]

[_separable]

6427

\[ {}x y^{\prime }-2 y = x^{3} \cos \left (x \right ) \]

[_linear]

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]

6430

\[ {}x \left (y-3\right ) y^{\prime } = 4 y \]

[_separable]

6431

\[ {}\left (x^{3}+1\right ) y^{\prime } = x^{2} y \]
i.c.

[_separable]

6432

\[ {}x^{3}+\left (y+1\right )^{2} y^{\prime } = 0 \]

[_separable]

6435

\[ {}\left (2 y-x \right ) y^{\prime } = 2 x +y \]

[[_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

\[ {}y-3 x +\left (4 y+3 x \right ) y^{\prime } = 0 \]

[[_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]

6445

\[ {}\left (3 x +3 y-4\right ) y^{\prime } = -x -y \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

6447

\[ {}x -y-1+\left (4 y+x -1\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

6448

\[ {}3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

6449

\[ {}\left (1+x y\right ) y+x \left (1+x y+y^{2} x^{2}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _rational]

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]

6459

\[ {}y+\left (x^{2}-4 x \right ) y^{\prime } = 0 \]

[_separable]

6461

\[ {}y^{\prime } = \frac {2 x y+y^{2}}{x^{2}+2 x y} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

6462

\[ {}\left (x^{2}+1\right ) y^{\prime } = x \left (y+1\right ) \]

[_separable]

6463

\[ {}x y^{\prime }+2 y = 3 x -1 \]
i.c.

[_linear]

6464

\[ {}x^{2} y^{\prime } = y^{2}-x y y^{\prime } \]
i.c.

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

6465

\[ {}y^{\prime } = {\mathrm e}^{-2 y+3 x} \]
i.c.

[_separable]

6467

\[ {}y^{2}+x^{2} y^{\prime } = x y y^{\prime } \]

[[_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]

6469

\[ {}y^{\prime } = \frac {x -2 y+1}{2 x -4 y} \]
i.c.

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

6470

\[ {}\left (-x^{3}+1\right ) y^{\prime }+x^{2} y = x^{2} \left (-x^{3}+1\right ) \]

[_linear]

6472

\[ {}y^{\prime }+x +x y^{2} = 0 \]
i.c.

[_separable]

6475

\[ {}x \left (1+y^{2}\right )-\left (x^{2}+1\right ) y y^{\prime } = 0 \]

[_separable]

6478

\[ {}y^{\prime }+\frac {y}{x} = x y^{2} \]

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

6516

\[ {}y^{\prime }-5 y = 3 \,{\mathrm e}^{x}-2 x +1 \]

[[_linear, ‘class A‘]]

6523

\[ {}y^{\prime }-y = {\mathrm e}^{x} \]

[[_linear, ‘class A‘]]

6533

\[ {}y^{\prime }+\frac {4 y}{x} = x^{4} \]

[_linear]

6542

\[ {}y^{\prime }-\frac {y}{x} = x^{2} \]

[_linear]

6569

\[ {}x y^{\prime } = 2 y \]

[_separable]

6570

\[ {}y y^{\prime }+x = 0 \]

[_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]

6580

\[ {}1+2 y+\left (-x^{2}+4\right ) y^{\prime } = 0 \]

[_separable]

6581

\[ {}y^{2}-x^{2} y^{\prime } = 0 \]

[_separable]

6582

\[ {}1+y-\left (x +1\right ) y^{\prime } = 0 \]

[_separable]

6583

\[ {}x y^{2}+y+\left (x^{2} y-x \right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

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]

6587

\[ {}x +y+1+\left (2 x +2 y+1\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

6588

\[ {}1+2 y-\left (4-x \right ) y^{\prime } = 0 \]

[_separable]

6589

\[ {}x y+\left (x^{2}+1\right ) y^{\prime } = 0 \]

[_separable]

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]

6592

\[ {}3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

6594

\[ {}y^{2}-x^{2}+x y y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

6595

\[ {}y \left (2 x y+1\right )+x \left (1-x y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

6596

\[ {}1+\left (-x^{2}+1\right ) \cot \left (y\right ) y^{\prime } = 0 \]

[_separable]

6597

\[ {}x^{3}+y^{3}+3 x y^{2} y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli]

6598

\[ {}3 x +2 y+1-\left (3 x +2 y-1\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

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]

6603

\[ {}y^{\prime } = -2 \left (2 x +3 y\right )^{2} \]

[[_homogeneous, ‘class C‘], _Riccati]

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

\[ {}2 x y y^{\prime }+x^{2}+y^{2} = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli]

6619

\[ {}x +y+1-\left (x -y-3\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

6632

\[ {}1+y^{2} = \left (x^{2}+x \right ) y^{\prime } \]

[_separable]

6641

\[ {}y^{\prime }+y = 2+2 x \]

[[_linear, ‘class A‘]]

6642

\[ {}y^{\prime }-y = x y \]

[_separable]

6643

\[ {}-3 y-\left (-2+x \right ) {\mathrm e}^{x}+x y^{\prime } = 0 \]

[_linear]

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]

6655

\[ {}2+y^{2}-\left (x y+2 y+y^{3}\right ) y^{\prime } = 0 \]

[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]

6657

\[ {}2 x y^{5}-y+2 x y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

6659

\[ {}x y^{\prime } = 2 y+x^{3} {\mathrm e}^{x} \]
i.c.

[_linear]

6676

\[ {}y = 2 x y^{\prime }+y^{2} {y^{\prime }}^{3} \]

[[_1st_order, _with_linear_symmetries]]

6689

\[ {}{y^{\prime }}^{3}-4 x^{4} y^{\prime }+8 x^{3} y = 0 \]

[[_1st_order, _with_linear_symmetries]]

6794

\[ {}x y^{\prime } = 1-x +2 y \]

[_linear]

6883

\[ {}\sin \left (y^{\prime }\right ) = x +y \]

[[_homogeneous, ‘class C‘], _dAlembert]

6885

\[ {}y^{2}-1+x y^{\prime } = 0 \]

[_separable]

6886

\[ {}2 y^{\prime }+y = 0 \]

[_quadrature]

6887

\[ {}y^{\prime }+20 y = 24 \]

[_quadrature]

6891

\[ {}y^{\prime } = 25+y^{2} \]

[_quadrature]

6892

\[ {}y^{\prime } = 2 x y^{2} \]

[_separable]

6893

\[ {}2 y^{\prime } = y^{3} \cos \left (x \right ) \]

[_separable]

6894

\[ {}x^{\prime } = \left (x-1\right ) \left (1-2 x\right ) \]

[_quadrature]

6895

\[ {}2 x y+\left (x^{2}-y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

6896

\[ {}p^{\prime } = p \left (1-p\right ) \]

[_quadrature]

6897

\[ {}y^{\prime }+4 x y = 8 x^{3} \]

[_linear]

6904

\[ {}x y^{\prime }-2 y = 0 \]

[_separable]

6905

\[ {}y^{\prime } = -\frac {x}{y} \]

[_separable]

6906

\[ {}y^{\prime }+2 y = 0 \]

[_quadrature]

6907

\[ {}5 y^{\prime } = 2 y \]

[_quadrature]

6914

\[ {}3 x y^{\prime }+5 y = 10 \]

[_separable]

6915

\[ {}y^{\prime } = y^{2}+2 y-3 \]

[_quadrature]

6916

\[ {}\left (y-1\right ) y^{\prime } = 1 \]

[_quadrature]

6920

\[ {}y y^{\prime }+\sqrt {16-y^{2}} = 0 \]

[_quadrature]

6924

\[ {}y^{\prime } = \sqrt {1-y^{2}} \]

[_quadrature]

6929

\[ {}y^{\prime } = 5-y \]

[_quadrature]

6930

\[ {}y^{\prime } = y^{2}+4 \]

[_quadrature]

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]

6948

\[ {}x y^{\prime } = 2 y \]
i.c.

[_separable]

6950

\[ {}y^{\prime } = \sqrt {x y} \]

[[_homogeneous, ‘class G‘]]

6951

\[ {}x y^{\prime } = y \]

[_separable]

6952

\[ {}y^{\prime }-y = x \]

[[_linear, ‘class A‘]]

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‘]]

6958

\[ {}y^{\prime } = \sqrt {y^{2}-9} \]
i.c.

[_quadrature]

6959

\[ {}y^{\prime } = \sqrt {y^{2}-9} \]
i.c.

[_quadrature]

6961

\[ {}x y^{\prime } = y \]
i.c.

[_separable]

6962

\[ {}y^{\prime } = 1+y^{2} \]
i.c.

[_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]

6977

\[ {}y^{\prime } = x -2 y \]
i.c.

[[_linear, ‘class A‘]]

6980

\[ {}y^{\prime }+2 y = 3 x -6 \]

[[_linear, ‘class A‘]]

6984

\[ {}y^{\prime } = 2 y-4 \]

[_quadrature]

6985

\[ {}x y^{\prime } = y \]

[_separable]

6989

\[ {}y^{\prime } = y \left (y-3\right ) \]

[_quadrature]

6990

\[ {}3 x y^{\prime }-2 y = 0 \]

[_separable]

6991

\[ {}\left (2 y-2\right ) y^{\prime } = 2 x -1 \]
i.c.

[_separable]

6992

\[ {}x y^{\prime }+y = 2 x \]
i.c.

[_linear]

7004

\[ {}x y^{\prime }+y = \frac {1}{y^{2}} \]

[_separable]

7007

\[ {}\left (1-x y\right ) y^{\prime } = y^{2} \]

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

7009

\[ {}y^{\prime }+2 y = 3 x \]

[[_linear, ‘class A‘]]

7032

\[ {}y^{\prime } = x +y \]
i.c.

[[_linear, ‘class A‘]]

7033

\[ {}y^{\prime } = x +y \]
i.c.

[[_linear, ‘class A‘]]

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]

7038

\[ {}y^{\prime } = \frac {x^{2}}{5}+y \]
i.c.

[[_linear, ‘class A‘]]

7039

\[ {}y^{\prime } = \frac {x^{2}}{5}+y \]
i.c.

[[_linear, ‘class A‘]]

7040

\[ {}y^{\prime } = x \,{\mathrm e}^{y} \]
i.c.

[_separable]

7041

\[ {}y^{\prime } = x \,{\mathrm e}^{y} \]
i.c.

[_separable]

7044

\[ {}y^{\prime } = 1-\frac {y}{x} \]
i.c.

[_linear]

7045

\[ {}y^{\prime } = 1-\frac {y}{x} \]
i.c.

[_linear]

7046

\[ {}y^{\prime } = x +y \]

[[_linear, ‘class A‘]]

7049

\[ {}y^{\prime } = x^{2}-2 y \]

[[_linear, ‘class A‘]]

7050

\[ {}y^{\prime } = y-y^{3} \]

[_quadrature]

7051

\[ {}y^{\prime } = y^{2}-y^{4} \]

[_quadrature]

7052

\[ {}y^{\prime } = y^{2}-3 y \]

[_quadrature]

7053

\[ {}y^{\prime } = y^{2}-y^{3} \]

[_quadrature]

7054

\[ {}y^{\prime } = \left (y-2\right )^{4} \]

[_quadrature]

7055

\[ {}y^{\prime } = 10+3 y-y^{2} \]

[_quadrature]

7056

\[ {}y^{\prime } = y^{2} \left (4-y^{2}\right ) \]

[_quadrature]

7057

\[ {}y^{\prime } = y \left (2-y\right ) \left (4-y\right ) \]

[_quadrature]

7058

\[ {}y^{\prime } = y \ln \left (y+2\right ) \]

[_quadrature]

7059

\[ {}y^{\prime } = \left (y \,{\mathrm e}^{y}-9 y\right ) {\mathrm e}^{-y} \]

[_quadrature]

7060

\[ {}y^{\prime } = \frac {2 y}{\pi }-\sin \left (y\right ) \]

[_quadrature]

7061

\[ {}y^{\prime } = y^{2}-y-6 \]

[_quadrature]

7062

\[ {}m v^{\prime } = m g -k v^{2} \]

[_quadrature]

7066

\[ {}y^{\prime }-\left (y-1\right )^{2} = 0 \]

[_quadrature]

7067

\[ {}x y^{\prime } = 4 y \]

[_separable]

7068

\[ {}y^{\prime }+2 x y^{2} = 0 \]

[_separable]

7069

\[ {}y^{\prime } = {\mathrm e}^{3 x +2 y} \]

[_separable]

7072

\[ {}y^{\prime } = \frac {\left (2 y+3\right )^{2}}{\left (4 x +5\right )^{2}} \]

[_separable]

7077

\[ {}s^{\prime } = k s \]

[_quadrature]

7078

\[ {}q^{\prime } = k \left (q-70\right ) \]

[_quadrature]

7079

\[ {}p^{\prime } = p-p^{2} \]

[_quadrature]

7080

\[ {}n^{\prime }+n = n t \,{\mathrm e}^{t +2} \]

[_separable]

7084

\[ {}\left ({\mathrm e}^{x}+{\mathrm e}^{-x}\right ) y^{\prime } = y^{2} \]

[_separable]

7085

\[ {}x^{\prime } = 4 x^{2}+4 \]
i.c.

[_quadrature]

7086

\[ {}y^{\prime } = \frac {y^{2}-1}{x^{2}-1} \]
i.c.

[_separable]

7087

\[ {}x^{2} y^{\prime } = y-x y \]
i.c.

[_separable]

7088

\[ {}y^{\prime }+2 y = 1 \]
i.c.

[_quadrature]

7089

\[ {}\sqrt {1-y^{2}}-\sqrt {-x^{2}+1}\, y^{\prime } = 0 \]
i.c.

[_separable]

7090

\[ {}\left (x^{4}+1\right ) y^{\prime }+x \left (1+4 y^{2}\right ) = 0 \]
i.c.

[_separable]

7091

\[ {}y^{\prime } = -y \ln \left (y\right ) \]
i.c.

[_quadrature]

7092

\[ {}x \sinh \left (y\right ) y^{\prime } = \cosh \left (y\right ) \]
i.c.

[_separable]

7093

\[ {}y^{\prime } = y \,{\mathrm e}^{-x^{2}} \]
i.c.

[_separable]

7094

\[ {}y^{\prime } = y^{2} \sin \left (x^{2}\right ) \]
i.c.

[_separable]

7095

\[ {}y^{\prime } = \left (1+y^{2}\right ) \sqrt {1+\cos \left (x^{3}\right )} \]
i.c.

[_separable]

7097

\[ {}y^{\prime } = \frac {3 x +1}{2 y} \]
i.c.

[_separable]

7099

\[ {}{\mathrm e}^{y}-{\mathrm e}^{-x} y^{\prime } = 0 \]
i.c.

[_separable]

7101

\[ {}y^{\prime } = y^{2}-4 \]
i.c.

[_quadrature]

7102

\[ {}y^{\prime } = y^{2}-4 \]
i.c.

[_quadrature]

7103

\[ {}y^{\prime } = y^{2}-4 \]
i.c.

[_quadrature]

7104

\[ {}x y^{\prime } = y^{2}-y \]
i.c.

[_separable]

7106

\[ {}x y^{\prime } = y^{2}-y \]
i.c.

[_separable]

7107

\[ {}x y^{\prime } = y^{2}-y \]
i.c.

[_separable]

7109

\[ {}y^{\prime } = \left (y-1\right )^{2} \]
i.c.

[_quadrature]

7110

\[ {}y^{\prime } = \left (y-1\right )^{2} \]
i.c.

[_quadrature]

7111

\[ {}y^{\prime } = \left (y-1\right )^{2}+\frac {1}{100} \]
i.c.

[_quadrature]

7112

\[ {}y^{\prime } = \left (y-1\right )^{2}-\frac {1}{100} \]
i.c.

[_quadrature]

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]

7117

\[ {}y^{\prime } = \frac {1}{y-3} \]
i.c.

[_quadrature]

7118

\[ {}y^{\prime } = \frac {1}{y-3} \]
i.c.

[_quadrature]

7119

\[ {}y^{\prime } = \frac {1}{y-3} \]
i.c.

[_quadrature]

7120

\[ {}y^{\prime } = \frac {1}{y-3} \]
i.c.

[_quadrature]

7124

\[ {}y^{\prime } = y^{{2}/{3}}-y \]

[_quadrature]

7127

\[ {}y^{\prime } = -\frac {x}{y} \]
i.c.

[_separable]

7128

\[ {}y^{\prime } = x \sqrt {y} \]

[_separable]

7129

\[ {}y^{\prime } = \sqrt {1+y^{2}}\, \sin \left (y\right )^{2} \]
i.c.

[_quadrature]

7130

\[ {}y^{\prime } = y \]
i.c.

[_quadrature]

7131

\[ {}y^{\prime } = y+\frac {y}{\ln \left (x \right ) x} \]
i.c.

[_separable]

7134

\[ {}m^{\prime } = -\frac {k}{m^{2}} \]
i.c.

[_quadrature]

7135

\[ {}u^{\prime } = a \sqrt {1+u^{2}} \]
i.c.

[_quadrature]

7136

\[ {}x^{\prime } = k \left (A -x\right )^{2} \]
i.c.

[_quadrature]

7145

\[ {}y^{\prime } = 5 y \]

[_quadrature]

7146

\[ {}y^{\prime }+2 y = 0 \]

[_quadrature]

7147

\[ {}y^{\prime }+y = {\mathrm e}^{3 x} \]

[[_linear, ‘class A‘]]

7148

\[ {}3 y^{\prime }+12 y = 4 \]

[_quadrature]

7149

\[ {}y^{\prime }+3 x^{2} y = x^{2} \]

[_separable]

7150

\[ {}y^{\prime }+2 x y = x^{3} \]

[_linear]

7151

\[ {}x^{2} y^{\prime }+x y = 1 \]

[_linear]

7152

\[ {}y^{\prime } = 2 y+x^{2}+5 \]

[[_linear, ‘class A‘]]

7153

\[ {}-y+x y^{\prime } = x^{2} \sin \left (x \right ) \]

[_linear]

7154

\[ {}x y^{\prime }+2 y = 3 \]

[_separable]

7155

\[ {}4 y+x y^{\prime } = x^{3}-x \]

[_linear]

7159

\[ {}y-4 \left (x +y^{6}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _rational]

7164

\[ {}\left (2+x \right )^{2} y^{\prime } = 5-8 y-4 x y \]

[_linear]

7166

\[ {}p^{\prime }+2 t p = p+4 t -2 \]

[_separable]

7167

\[ {}x y^{\prime }+\left (3 x +1\right ) y = {\mathrm e}^{-3 x} \]

[_linear]

7168

\[ {}\left (x^{2}-1\right ) y^{\prime }+2 y = \left (x +1\right )^{2} \]

[_linear]

7169

\[ {}y^{\prime } = x +5 y \]
i.c.

[[_linear, ‘class A‘]]

7170

\[ {}y^{\prime } = 2 x -3 y \]
i.c.

[[_linear, ‘class A‘]]

7173

\[ {}L i^{\prime }+R i = E \]
i.c.

[_quadrature]

7174

\[ {}T^{\prime } = k \left (T-T_{m} \right ) \]
i.c.

[_quadrature]

7175

\[ {}x y^{\prime }+y = 1+4 x \]
i.c.

[_linear]

7179

\[ {}y^{\prime }-y \sin \left (x \right ) = 2 \sin \left (x \right ) \]
i.c.

[_separable]

7192

\[ {}y^{\prime }-\sin \left (x^{2}\right ) y = 0 \]
i.c.

[_separable]

7193

\[ {}1 = \left (x +y^{2}\right ) y^{\prime } \]

[[_1st_order, _with_exponential_symmetries]]

7199

\[ {}e^{\prime } = -\frac {e}{r c} \]
i.c.

[_quadrature]

7200

\[ {}2 x -1+\left (3 y+7\right ) y^{\prime } = 0 \]

[_separable]

7382

\[ {}y^{\prime } = \frac {x^{2}}{y} \]

[_separable]

7384

\[ {}y^{\prime } = y \sin \left (x \right ) \]

[_separable]

7385

\[ {}x y^{\prime } = \sqrt {1-y^{2}} \]

[_separable]

7387

\[ {}x y y^{\prime } = \sqrt {1+y^{2}} \]

[_separable]

7388

\[ {}\left (x^{2}-1\right ) y^{\prime }+2 x y^{2} = 0 \]
i.c.

[_separable]

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]

7393

\[ {}\left (1+z^{\prime }\right ) {\mathrm e}^{-z} = 1 \]

[_quadrature]

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]

7399

\[ {}\frac {1}{\sqrt {-x^{2}+1}}+\frac {y^{\prime }}{\sqrt {1-y^{2}}} = 0 \]

[_separable]

7401

\[ {}y^{\prime } = \left (y-1\right ) \left (x +1\right ) \]

[_separable]

7402

\[ {}y^{\prime } = {\mathrm e}^{x -y} \]

[_separable]

7403

\[ {}y^{\prime } = \frac {\sqrt {y}}{\sqrt {x}} \]

[_separable]

7404

\[ {}y^{\prime } = \frac {\sqrt {y}}{x} \]

[_separable]

7405

\[ {}z^{\prime } = 10^{x +z} \]

[_separable]

7407

\[ {}y^{\prime } = \cos \left (x -y\right ) \]

[[_homogeneous, ‘class C‘], _dAlembert]

7408

\[ {}y^{\prime }-y = 2 x -3 \]

[[_linear, ‘class A‘]]

7410

\[ {}y^{\prime }+y = 2 x +1 \]

[[_linear, ‘class A‘]]

7411

\[ {}y^{\prime } = \cos \left (x -y-1\right ) \]

[[_homogeneous, ‘class C‘], _dAlembert]

7412

\[ {}y^{\prime }+\sin \left (x +y\right )^{2} = 0 \]

[[_homogeneous, ‘class C‘], _dAlembert]

7413

\[ {}y^{\prime } = 2 \sqrt {2 x +y+1} \]

[[_homogeneous, ‘class C‘], _dAlembert]

7414

\[ {}y^{\prime } = \left (x +y+1\right )^{2} \]

[[_homogeneous, ‘class C‘], _Riccati]

7417

\[ {}\left (x +y\right ) y^{\prime }+x -y = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7418

\[ {}y-2 x y+x^{2} y^{\prime } = 0 \]

[_separable]

7420

\[ {}y^{2}+x^{2} y^{\prime } = x y y^{\prime } \]

[[_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

\[ {}x +y-\left (x -y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

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]

7436

\[ {}x y^{\prime } = y+\sqrt {y^{2}-x^{2}} \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

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]

7442

\[ {}-y+x y^{\prime } = \sqrt {x^{2}+y^{2}} \]

[[_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‘]]

7447

\[ {}y^{\prime } = \frac {x +y-2}{y-x -4} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7448

\[ {}2 x -4 y+6+\left (x +y-2\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7449

\[ {}y^{\prime } = \frac {2 y-x +5}{2 x -y-4} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7450

\[ {}y^{\prime } = -\frac {4 x +3 y+15}{2 x +y+7} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7451

\[ {}y^{\prime } = \frac {x +3 y-5}{x -y-1} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7452

\[ {}y^{\prime } = \frac {2 \left (y+2\right )^{2}}{\left (x +y+1\right )^{2}} \]

[[_homogeneous, ‘class C‘], _rational]

7453

\[ {}2 x +y+1-\left (4 x +2 y-3\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7454

\[ {}x -y-1+\left (y-x +2\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7455

\[ {}\left (x +4 y\right ) y^{\prime } = 2 x +3 y-5 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7456

\[ {}y+2 = \left (2 x +y-4\right ) y^{\prime } \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7457

\[ {}\left (1+y^{\prime }\right ) \ln \left (\frac {x +y}{x +3}\right ) = \frac {x +y}{x +3} \]

[[_homogeneous, ‘class C‘], _exact, _dAlembert]

7458

\[ {}y^{\prime } = \frac {x -2 y+5}{y-2 x -4} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7459

\[ {}y^{\prime } = \frac {3 x -y+1}{2 x +y+4} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7460

\[ {}2 x y^{\prime }+\left (x^{2} y^{4}+1\right ) y = 0 \]

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

7476

\[ {}2 x +3+\left (2 y-2\right ) y^{\prime } = 0 \]

[_separable]

7477

\[ {}2 x +4 y+\left (2 x -2 y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7502

\[ {}y^{\prime } = x^{2} \left (1+y^{2}\right ) \]

[_separable]

7505

\[ {}x y^{\prime }-2 \sqrt {x y} = y \]

[[_homogeneous, ‘class A‘], _dAlembert]

7506

\[ {}y^{\prime } = \frac {x +y-1}{x -y+3} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7509

\[ {}y^{2}-x y+x^{2} y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

7510

\[ {}x +y-\left (x -y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7511

\[ {}y^{\prime } = \frac {y}{2 x}+\frac {x^{2}}{2 y} \]

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

7512

\[ {}y^{\prime } = -\frac {2}{t}+\frac {y}{t}+\frac {y^{2}}{t} \]

[_separable]

7543

\[ {}y+\sqrt {x^{2}+y^{2}}-x y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

7547

\[ {}\left (1+y^{2} x^{2}\right ) y+\left (y^{2} x^{2}-1\right ) x y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _rational]

7550

\[ {}\phi ^{\prime }-\frac {\phi ^{2}}{2}-\phi \cot \left (\theta \right ) = 0 \]

[_Bernoulli]

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‘]]

7583

\[ {}y^{\prime }+y \cos \left (x \right ) = 0 \]

[_separable]

7588

\[ {}y^{\prime }+5 y = 2 \]

[_quadrature]

7590

\[ {}y^{\prime } = k y \]

[_quadrature]

7591

\[ {}y^{\prime }-2 y = 1 \]

[_quadrature]

7592

\[ {}y^{\prime }+y = {\mathrm e}^{x} \]

[[_linear, ‘class A‘]]

7593

\[ {}y^{\prime }-2 y = x^{2}+x \]

[[_linear, ‘class A‘]]

7594

\[ {}3 y^{\prime }+y = 2 \,{\mathrm e}^{-x} \]

[[_linear, ‘class A‘]]

7595

\[ {}y^{\prime }+3 y = {\mathrm e}^{i x} \]

[[_linear, ‘class A‘]]

7596

\[ {}y^{\prime }+i y = x \]

[[_linear, ‘class A‘]]

7597

\[ {}L y^{\prime }+R y = E \]

[_quadrature]

7599

\[ {}L y^{\prime }+R y = E \,{\mathrm e}^{i \omega x} \]
i.c.

[[_linear, ‘class A‘]]

7601

\[ {}y^{\prime }+2 x y = x \]

[_separable]

7602

\[ {}x y^{\prime }+y = 3 x^{3}-1 \]

[_linear]

7603

\[ {}y^{\prime }+y \,{\mathrm e}^{x} = 3 \,{\mathrm e}^{x} \]

[_separable]

7605

\[ {}y^{\prime }+2 x y = x \,{\mathrm e}^{-x^{2}} \]

[_linear]

7607

\[ {}x^{2} y^{\prime }+2 x y = 1 \]

[_linear]

7609

\[ {}y^{\prime } = y+1 \]
i.c.

[_quadrature]

7610

\[ {}y^{\prime } = 1+y^{2} \]
i.c.

[_quadrature]

7611

\[ {}y^{\prime } = 1+y^{2} \]
i.c.

[_quadrature]

7731

\[ {}y^{\prime } = x^{2} y \]

[_separable]

7732

\[ {}y y^{\prime } = x \]

[_separable]

7735

\[ {}y^{\prime } = y^{2} x^{2}-4 x^{2} \]

[_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]

7739

\[ {}y^{\prime } = \frac {x +y}{x -y} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7740

\[ {}y^{\prime } = \frac {y^{2}}{x y+x^{2}} \]

[[_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]

7743

\[ {}y^{\prime } = \frac {x -y+2}{x +y-1} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7744

\[ {}y^{\prime } = \frac {2 x +3 y+1}{x -2 y-1} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7745

\[ {}y^{\prime } = \frac {x +y+1}{2 x +2 y-1} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7746

\[ {}y^{\prime } = \frac {\left (x +y-1\right )^{2}}{2 \left (2+x \right )^{2}} \]

[[_homogeneous, ‘class C‘], _rational, _Riccati]

7774

\[ {}x y^{\prime } = 2 y \]

[_separable]

7775

\[ {}y y^{\prime } = {\mathrm e}^{2 x} \]

[_separable]

7776

\[ {}y^{\prime } = k y \]

[_quadrature]

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‘]]

7785

\[ {}\left (y \cos \left (y\right )-\sin \left (y\right )+x \right ) y^{\prime } = y \]

[[_1st_order, _with_linear_symmetries]]

7786

\[ {}1+y^{2}+y^{2} y^{\prime } = 0 \]

[_quadrature]

7805

\[ {}y^{\prime } = \frac {2 x y^{2}}{1-x^{2} y} \]

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

7807

\[ {}x^{5} y^{\prime }+y^{5} = 0 \]

[_separable]

7808

\[ {}y^{\prime } = 4 x y \]

[_separable]

7809

\[ {}y^{\prime }+y \tan \left (x \right ) = 0 \]

[_separable]

7810

\[ {}\left (x^{2}+1\right ) y^{\prime }+1+y^{2} = 0 \]

[_separable]

7811

\[ {}y \ln \left (y\right )-x y^{\prime } = 0 \]

[_separable]

7814

\[ {}y^{\prime }-y \tan \left (x \right ) = 0 \]

[_separable]

7815

\[ {}x y y^{\prime } = y-1 \]

[_separable]

7816

\[ {}x y^{2}-x^{2} y^{\prime } = 0 \]

[_separable]

7817

\[ {}y y^{\prime } = x +1 \]
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]

7843

\[ {}x y^{\prime }+y = x y^{2} \]

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

7846

\[ {}y-x y^{\prime } = y^{\prime } y^{2} {\mathrm e}^{y} \]

[[_1st_order, _with_linear_symmetries]]

7847

\[ {}x y^{\prime }+2 = x^{3} \left (y-1\right ) y^{\prime } \]

[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]]

7848

\[ {}x y^{\prime } = 2 x^{2} y+y \ln \left (x \right ) \]

[_separable]

7850

\[ {}\left (x +\frac {2}{y}\right ) y^{\prime }+y = 0 \]

[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

7854

\[ {}y+y \cos \left (x y\right )+\left (x +x \cos \left (x y\right )\right ) y^{\prime } = 0 \]

[_separable]

7858

\[ {}1+y+\left (1-x \right ) y^{\prime } = 0 \]

[_separable]

7863

\[ {}2 x \left (1+\sqrt {x^{2}-y}\right ) = \sqrt {x^{2}-y}\, y^{\prime } \]

[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]

7869

\[ {}\frac {y-x y^{\prime }}{\left (x +y\right )^{2}}+y^{\prime } = 1 \]

[[_1st_order, _with_linear_symmetries], _exact, _rational]

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]

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]

7881

\[ {}y^{\prime } = \frac {x +y+4}{x -y-6} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7882

\[ {}y^{\prime } = \frac {x +y+4}{x +y-6} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7883

\[ {}2 x -2 y+\left (y-1\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7884

\[ {}y^{\prime } = \frac {x +y-1}{x +4 y+2} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7885

\[ {}2 x +3 y-1-4 \left (x +1\right ) y^{\prime } = 0 \]

[_linear]

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]

7888

\[ {}y^{\prime } = \frac {y-x y^{2}}{x +x^{2} y} \]

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

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]

7904

\[ {}y^{\prime } = \frac {2 y}{x}+\frac {x^{3}}{y}+x \tan \left (\frac {y}{x^{2}}\right ) \]

[[_homogeneous, ‘class G‘]]

7917

\[ {}x y^{\prime }+y = x \]

[_linear]

7919

\[ {}x^{2} y^{\prime } = y \]

[_separable]

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

\[ {}x^{2} y^{\prime }+2 x y = 0 \]

[_separable]

7925

\[ {}-y+x y^{\prime } = 2 x \]
i.c.

[_linear]

7927

\[ {}y^{2} y^{\prime } = x \]
i.c.

[_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]

7931

\[ {}2 x \cos \left (y\right )-x^{2} \sin \left (y\right ) y^{\prime } = 0 \]
i.c.

[_separable]

7932

\[ {}\frac {1}{y}-\frac {x y^{\prime }}{y^{2}} = 0 \]

[_separable]

8073

\[ {}y^{\prime } = 2 x y \]

[_separable]

8075

\[ {}y^{\prime }+y = 1 \]

[_quadrature]

8077

\[ {}y^{\prime }-y = 2 \]

[_quadrature]

8079

\[ {}y^{\prime }+y = 0 \]

[_quadrature]

8081

\[ {}y^{\prime }-y = 0 \]

[_quadrature]

8083

\[ {}y^{\prime }-y = x^{2} \]

[[_linear, ‘class A‘]]

8085

\[ {}x y^{\prime } = y \]

[_separable]

8087

\[ {}x^{2} y^{\prime } = y \]

[_separable]

8089

\[ {}y^{\prime }-\frac {y}{x} = x^{2} \]

[_linear]

8090

\[ {}y^{\prime }+\frac {y}{x} = x \]

[_linear]

8094

\[ {}y^{\prime } = x -y \]
i.c.

[[_linear, ‘class A‘]]

8215

\[ {}y^{\prime }-2 y = x^{2} \]
i.c.

[[_linear, ‘class A‘]]

8462

\[ {}y^{4} {y^{\prime }}^{3}-6 x y^{\prime }+2 y = 0 \]

[[_1st_order, _with_linear_symmetries]]

8465

\[ {}2 x {y^{\prime }}^{3}-6 y {y^{\prime }}^{2}+x^{4} = 0 \]

[[_1st_order, _with_linear_symmetries]]

8474

\[ {}x^{6} {y^{\prime }}^{3}-3 x y^{\prime }-3 y = 0 \]

[[_1st_order, _with_linear_symmetries]]

8475

\[ {}y = x^{6} {y^{\prime }}^{3}-x y^{\prime } \]

[[_1st_order, _with_linear_symmetries]]

8541

\[ {}4 y^{2} {y^{\prime }}^{3}-2 x y^{\prime }+y = 0 \]

[[_1st_order, _with_linear_symmetries]]

8556

\[ {}x {y^{\prime }}^{3}-2 y {y^{\prime }}^{2}+4 x^{2} = 0 \]

[[_1st_order, _with_linear_symmetries]]

8697

\[ {}y^{\prime } = \frac {y}{\ln \left (x \right ) x} \]

[_separable]

8698

\[ {}\left (x^{2}+1\right ) y^{\prime }+y^{2} = -1 \]
i.c.

[_separable]

8699

\[ {}y^{\prime }+\frac {2 y}{x} = 5 x^{2} \]

[_linear]

8701

\[ {}y^{\prime } = \frac {2 x -y}{x +4 y} \]
i.c.

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

8702

\[ {}y^{\prime }+\frac {2 y}{x} = 6 x^{4} y^{2} \]

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

8717

\[ {}y^{\prime } = y+1 \]

[_quadrature]

8720

\[ {}y^{\prime } = y \]

[_quadrature]

8724

\[ {}y^{\prime } = \frac {2 y}{x} \]
i.c.

[_separable]

8725

\[ {}y^{\prime } = \frac {2 y}{x} \]

[_separable]

8728

\[ {}y^{\prime } = \frac {-x y-1}{4 x^{3} y-2 x^{2}} \]

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

8733

\[ {}y^{\prime } = \sqrt {y}+x \]

[[_1st_order, _with_linear_symmetries], _Chini]

8734

\[ {}y^{2}+x^{2} y^{\prime } = x y y^{\prime } \]

[[_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]

8743

\[ {}2 t +3 x+\left (x+2\right ) x^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

8744

\[ {}y^{\prime } = \frac {1}{1-y} \]
i.c.

[_quadrature]

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]

8751

\[ {}y y^{\prime }-y = x \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

8758

\[ {}f^{\prime } = \frac {1}{f} \]

[_quadrature]

8771

\[ {}y^{\prime }+\sin \left (x -y\right ) = 0 \]

[[_homogeneous, ‘class C‘], _dAlembert]

8789

\[ {}x^{\prime } = 4 A k \left (\frac {x}{A}\right )^{{3}/{4}}-3 k x \]

[_quadrature]

8792

\[ {}y^{\prime } = \frac {y \left (1+\frac {a^{2} x}{\sqrt {a^{2} \left (x^{2}+1\right )}}\right )}{\sqrt {a^{2} \left (x^{2}+1\right )}} \]

[_separable]

8794

\[ {}y^{\prime } = 2 \sqrt {y} \]
i.c.

[_quadrature]

8796

\[ {}y^{\prime } = \sqrt {1-y^{2}} \]

[_quadrature]

8860

\[ {}w^{\prime } = -\frac {1}{2}-\frac {\sqrt {1-12 w}}{2} \]
i.c.

[_quadrature]

8886

\[ {}y^{\prime } = {\mathrm e}^{-\frac {y}{x}} \]

[[_homogeneous, ‘class A‘], _dAlembert]

8952

\[ {}y^{\prime } = y \left (1-y^{2}\right ) \]

[_quadrature]

8980

\[ {}y^{\prime } = \frac {y}{2 y \ln \left (y\right )+y-x} \]

[[_1st_order, _with_linear_symmetries]]

8982

\[ {}x^{2} y^{\prime }+{\mathrm e}^{-y} = 0 \]

[_separable]

8990

\[ {}y^{\prime } = y a x \]

[_separable]

8991

\[ {}y^{\prime } = a x +y \]

[[_linear, ‘class A‘]]

8992

\[ {}y^{\prime } = a x +b y \]

[[_linear, ‘class A‘]]

8993

\[ {}y^{\prime } = y \]

[_quadrature]

8994

\[ {}y^{\prime } = b y \]

[_quadrature]

8999

\[ {}c y^{\prime } = a x +y \]

[[_linear, ‘class A‘]]

9000

\[ {}c y^{\prime } = a x +b y \]

[[_linear, ‘class A‘]]

9001

\[ {}c y^{\prime } = y \]

[_quadrature]

9002

\[ {}c y^{\prime } = b y \]

[_quadrature]

9012

\[ {}y^{\prime } = \cos \left (x \right )+\frac {y}{x} \]

[_linear]

9044

\[ {}y^{\prime } = \sqrt {1+6 x +y} \]

[[_homogeneous, ‘class C‘], _dAlembert]

9045

\[ {}y^{\prime } = \left (1+6 x +y\right )^{{1}/{3}} \]

[[_homogeneous, ‘class C‘], _dAlembert]

9046

\[ {}y^{\prime } = \left (1+6 x +y\right )^{{1}/{4}} \]

[[_homogeneous, ‘class C‘], _dAlembert]

9047

\[ {}y^{\prime } = \left (a +b x +y\right )^{4} \]

[[_homogeneous, ‘class C‘], _dAlembert]

9048

\[ {}y^{\prime } = \left (\pi +x +7 y\right )^{{7}/{2}} \]

[[_homogeneous, ‘class C‘], _dAlembert]

9049

\[ {}y^{\prime } = \left (a +b x +c y\right )^{6} \]

[[_homogeneous, ‘class C‘], _dAlembert]

9050

\[ {}y^{\prime } = {\mathrm e}^{x +y} \]

[_separable]

9051

\[ {}y^{\prime } = 10+{\mathrm e}^{x +y} \]

[[_homogeneous, ‘class C‘], _dAlembert]

9130

\[ {}y^{\prime } = \left (x +y\right )^{4} \]

[[_homogeneous, ‘class C‘], _dAlembert]

9171

\[ {}y^{\prime } = y^{{1}/{3}} \]
i.c.

[_quadrature]

10016

\[ {}y^{\prime }+a y-c \,{\mathrm e}^{b x} = 0 \]

[[_linear, ‘class A‘]]

10018

\[ {}y^{\prime }+2 x y-x \,{\mathrm e}^{-x^{2}} = 0 \]

[_linear]

10023

\[ {}y^{\prime }-\left (\sin \left (\ln \left (x \right )\right )+\cos \left (\ln \left (x \right )\right )+a \right ) y = 0 \]

[_separable]

10026

\[ {}y^{\prime }+y^{2}-1 = 0 \]

[_quadrature]

10029

\[ {}y^{\prime }+y^{2}-2 x^{2} y+x^{4}-2 x -1 = 0 \]

[[_1st_order, _with_linear_symmetries], _Riccati]

10031

\[ {}y^{\prime }-y^{2}-3 y+4 = 0 \]

[_quadrature]

10033

\[ {}y^{\prime }-\left (x +y\right )^{2} = 0 \]

[[_homogeneous, ‘class C‘], _Riccati]

10037

\[ {}y^{\prime }+a y^{2}-b = 0 \]

[_quadrature]

10040

\[ {}y^{\prime }-\left (A y-a \right ) \left (B y-b \right ) = 0 \]

[_quadrature]

10043

\[ {}y^{\prime }-x y^{2}-3 x y = 0 \]

[_separable]

10045

\[ {}y^{\prime }-a \,x^{n} \left (1+y^{2}\right ) = 0 \]

[_separable]

10049

\[ {}y^{\prime }+f \left (x \right ) \left (y^{2}+2 a y+b \right ) = 0 \]

[_separable]

10052

\[ {}-a y^{3}-\frac {b}{x^{{3}/{2}}}+y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _rational, _Abel]

10053

\[ {}y^{\prime }-\operatorname {a3} y^{3}-\operatorname {a2} y^{2}-\operatorname {a1} y-\operatorname {a0} = 0 \]

[_quadrature]

10055

\[ {}a x y^{3}+b y^{2}+y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _Abel]

10065

\[ {}y^{\prime }-a y^{n}-b \,x^{\frac {n}{1-n}} = 0 \]

[[_homogeneous, ‘class G‘], _Chini]

10071

\[ {}y^{\prime }-a \sqrt {y}-b x = 0 \]

[[_homogeneous, ‘class G‘], _Chini]

10072

\[ {}y^{\prime }-a \sqrt {1+y^{2}}-b = 0 \]

[_quadrature]

10073

\[ {}y^{\prime }-\frac {\sqrt {y^{2}-1}}{\sqrt {x^{2}-1}} = 0 \]

[_separable]

10089

\[ {}y^{\prime }-a \cos \left (y\right )+b = 0 \]

[_quadrature]

10090

\[ {}y^{\prime }-\cos \left (b x +a y\right ) = 0 \]

[[_homogeneous, ‘class C‘], _dAlembert]

10097

\[ {}y^{\prime }-f \left (a x +b y\right ) = 0 \]

[[_homogeneous, ‘class C‘], _dAlembert]

10099

\[ {}y^{\prime }-\frac {y-x f \left (x^{2}+a y^{2}\right )}{x +a y f \left (x^{2}+a y^{2}\right )} = 0 \]

[[_1st_order, _with_linear_symmetries]]

10103

\[ {}x y^{\prime }-y-\frac {x}{\ln \left (x \right )} = 0 \]

[_linear]

10104

\[ {}x y^{\prime }-y-x^{2} \sin \left (x \right ) = 0 \]

[_linear]

10105

\[ {}x y^{\prime }-y-\frac {x \cos \left (\ln \left (\ln \left (x \right )\right )\right )}{\ln \left (x \right )} = 0 \]

[_linear]

10106

\[ {}x y^{\prime }+a y+b \,x^{n} = 0 \]

[_linear]

10108

\[ {}x y^{\prime }-y^{2}+1 = 0 \]

[_separable]

10113

\[ {}x y^{\prime }+x y^{2}-y = 0 \]

[[_homogeneous, ‘class D‘], _rational, _Bernoulli]

10114

\[ {}x y^{\prime }+x y^{2}-y-a \,x^{3} = 0 \]

[[_homogeneous, ‘class D‘], _rational, _Riccati]

10115

\[ {}x y^{\prime }+x y^{2}-\left (2 x^{2}+1\right ) y-x^{3} = 0 \]

[[_homogeneous, ‘class D‘], _rational, _Riccati]

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]

10124

\[ {}x y^{\prime }-\sqrt {x^{2}+y^{2}}-y = 0 \]

[[_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]

10129

\[ {}x y^{\prime }-y \ln \left (y\right ) = 0 \]

[_separable]

10130

\[ {}x y^{\prime }-y \left (\ln \left (x y\right )-1\right ) = 0 \]

[[_homogeneous, ‘class G‘]]

10134

\[ {}x y^{\prime }-y-x \sin \left (\frac {y}{x}\right ) = 0 \]

[[_homogeneous, ‘class A‘], _dAlembert]

10135

\[ {}x y^{\prime }+x \cos \left (\frac {y}{x}\right )-y+x = 0 \]

[[_homogeneous, ‘class A‘], _dAlembert]

10136

\[ {}x y^{\prime }+x \tan \left (\frac {y}{x}\right )-y = 0 \]

[[_homogeneous, ‘class A‘], _dAlembert]

10137

\[ {}x y^{\prime }-y f \left (x y\right ) = 0 \]

[[_homogeneous, ‘class G‘]]

10138

\[ {}x y^{\prime }-y f \left (x^{a} y^{b}\right ) = 0 \]

[[_homogeneous, ‘class G‘]]

10141

\[ {}2 x y^{\prime }-y-2 x^{3} = 0 \]

[_linear]

10142

\[ {}\left (2 x +1\right ) y^{\prime }-4 \,{\mathrm e}^{-y}+2 = 0 \]

[_separable]

10146

\[ {}x^{2} y^{\prime }-\left (-1+x \right ) y = 0 \]

[_separable]

10147

\[ {}x^{2} y^{\prime }+y^{2}+x y+x^{2} = 0 \]

[[_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]

10151

\[ {}x^{2} \left (y^{\prime }+y^{2}\right )+4 x y+2 = 0 \]

[[_homogeneous, ‘class G‘], _rational, _Riccati]

10152

\[ {}x^{2} \left (y^{\prime }+y^{2}\right )+y a x +b = 0 \]

[[_homogeneous, ‘class G‘], _rational, _Riccati]

10154

\[ {}x^{2} \left (y^{\prime }+a y^{2}\right )-b = 0 \]

[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]]

10160

\[ {}\left (x^{2}+1\right ) y^{\prime }+x y-x \left (x^{2}+1\right ) = 0 \]

[_linear]

10164

\[ {}\left (x^{2}-1\right ) y^{\prime }-x y+a = 0 \]

[_linear]

10166

\[ {}\left (x^{2}-1\right ) y^{\prime }+y^{2}-2 x y+1 = 0 \]

[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]

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]

10170

\[ {}\left (x^{2}-1\right ) y^{\prime }-2 x y \ln \left (y\right ) = 0 \]

[_separable]

10173

\[ {}\left (x -a \right ) \left (x -b \right ) y^{\prime }+y^{2}+k \left (y+x -a \right ) \left (x +y-b \right ) = 0 \]

[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]

10176

\[ {}x \left (2 x -1\right ) y^{\prime }+y^{2}-\left (1+4 x \right ) y+4 x = 0 \]

[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]

10178

\[ {}3 x^{2} y^{\prime }-7 y^{2}-3 x y-x^{2} = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Riccati]

10181

\[ {}x^{3} y^{\prime }-y^{2}-x^{4} = 0 \]

[[_homogeneous, ‘class G‘], _rational, _Riccati]

10182

\[ {}x^{3} y^{\prime }-y^{2}-x^{2} y = 0 \]

[[_homogeneous, ‘class D‘], _rational, _Bernoulli]

10183

\[ {}x^{3} y^{\prime }-x^{4} y^{2}+x^{2} y+20 = 0 \]

[[_homogeneous, ‘class G‘], _rational, _Riccati]

10185

\[ {}x \left (x^{2}+1\right ) y^{\prime }+x^{2} y = 0 \]

[_separable]

10186

\[ {}x \left (x^{2}-1\right ) y^{\prime }-\left (2 x^{2}-1\right ) y+a \,x^{3} = 0 \]

[_linear]

10188

\[ {}x^{2} \left (-1+x \right ) y^{\prime }-y^{2}-x \left (-2+x \right ) y = 0 \]

[[_homogeneous, ‘class D‘], _rational, _Bernoulli]

10192

\[ {}x^{4} \left (y^{\prime }+y^{2}\right )+a = 0 \]

[_rational, [_Riccati, _special]]

10194

\[ {}\left (2 x^{4}-x \right ) y^{\prime }-2 \left (x^{3}-1\right ) y = 0 \]

[_separable]

10195

\[ {}\left (a \,x^{2}+b x +c \right )^{2} \left (y^{\prime }+y^{2}\right )+A = 0 \]

[_rational, _Riccati]

10197

\[ {}x^{n} y^{\prime }+y^{2}-\left (n -1\right ) x^{n -1} y+x^{-2+2 n} = 0 \]

[[_homogeneous, ‘class G‘], _Riccati]

10198

\[ {}x^{n} y^{\prime }-a y^{2}-b \,x^{-2+2 n} = 0 \]

[[_homogeneous, ‘class G‘], _Riccati]

10199

\[ {}x^{2 n +1} y^{\prime }-a y^{3}-b \,x^{3 n} = 0 \]

[[_homogeneous, ‘class G‘], _Abel]

10200

\[ {}x^{m \left (n -1\right )+n} y^{\prime }-a y^{n}-b \,x^{n \left (m +1\right )} = 0 \]

[[_homogeneous, ‘class G‘]]

10201

\[ {}\sqrt {x^{2}-1}\, y^{\prime }-\sqrt {y^{2}-1} = 0 \]

[_separable]

10204

\[ {}y^{\prime } x \ln \left (x \right )+y-a x \left (\ln \left (x \right )+1\right ) = 0 \]

[_linear]

10214

\[ {}y y^{\prime }+a y+x = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

10219

\[ {}y y^{\prime }-\sqrt {a y^{2}+b} = 0 \]

[_quadrature]

10221

\[ {}y y^{\prime }-x \,{\mathrm e}^{\frac {x}{y}} = 0 \]

[[_homogeneous, ‘class A‘], _dAlembert]

10223

\[ {}\left (y+1\right ) y^{\prime }-y-x = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

10224

\[ {}\left (x +y-1\right ) y^{\prime }-y+2 x +3 = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

10225

\[ {}\left (y+2 x -2\right ) y^{\prime }-y+x +1 = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

10226

\[ {}\left (y-2 x +1\right ) y^{\prime }+y+x = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

10228

\[ {}\left (y-x^{2}\right ) y^{\prime }+4 x y = 0 \]

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

10230

\[ {}\left (x +2 y+1\right ) y^{\prime }-x -2 y+1 = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

10231

\[ {}\left (2 y+x +7\right ) y^{\prime }-y+2 x +4 = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

10232

\[ {}\left (2 y-x \right ) y^{\prime }-y-2 x = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

10233

\[ {}\left (2 y-6 x \right ) y^{\prime }-y+3 x +2 = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

10234

\[ {}\left (4 y+2 x +3\right ) y^{\prime }-2 y-x -1 = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

10235

\[ {}\left (4 y-2 x -3\right ) y^{\prime }+2 y-x -1 = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

10236

\[ {}\left (4 y-3 x -5\right ) y^{\prime }-3 y+7 x +2 = 0 \]

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

10237

\[ {}\left (4 y+11 x -11\right ) y^{\prime }-25 y-8 x +62 = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

10238

\[ {}\left (12 y-5 x -8\right ) y^{\prime }-5 y+2 x +3 = 0 \]

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

10240

\[ {}\left (a y+b x +c \right ) y^{\prime }+\alpha y+\beta x +\gamma = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

10241

\[ {}x y y^{\prime }+y^{2}+x^{2} = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

10245

\[ {}x \left (y+4\right ) y^{\prime }-y^{2}-2 y-2 x = 0 \]

[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]

10247

\[ {}\left (\left (x +y\right ) x +a \right ) y^{\prime }-y \left (x +y\right )-b = 0 \]

[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

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‘]]

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]

10254

\[ {}\left (2 x y+4 x^{3}\right ) y^{\prime }+y^{2}+112 x^{2} y = 0 \]

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

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‘]]

10256

\[ {}\left (3 x +2\right ) \left (y-2 x -1\right ) y^{\prime }-y^{2}+x y-7 x^{2}-9 x -3 = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

10258

\[ {}\left (y a x +b \,x^{n}\right ) y^{\prime }+\alpha y^{3}+\beta y^{2} = 0 \]

[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]]

10263

\[ {}x \left (x y-2\right ) y^{\prime }+y^{3} x^{2}+x y^{2}-2 y = 0 \]

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘]]

10264

\[ {}x \left (x y-3\right ) y^{\prime }+x y^{2}-y = 0 \]

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

10269

\[ {}\left (2 x^{2} y+x \right ) y^{\prime }-y^{3} x^{2}+2 x y^{2}+y = 0 \]

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘]]

10270

\[ {}\left (2 x^{2} y-x \right ) y^{\prime }-2 x y^{2}-y = 0 \]

[[_homogeneous, ‘class G‘], _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]

10273

\[ {}2 x \left (x^{3} y+1\right ) y^{\prime }+\left (3 x^{3} y-1\right ) y = 0 \]

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

10275

\[ {}\left (y-x \right ) \sqrt {x^{2}+1}\, y^{\prime }-a \sqrt {\left (1+y^{2}\right )^{3}} = 0 \]

[‘x=_G(y,y’)‘]

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]

10285

\[ {}\left (y^{2}+x^{4}\right ) y^{\prime }-4 x^{3} y = 0 \]

[[_homogeneous, ‘class G‘], _rational]

10288

\[ {}\left (x +y\right )^{2} y^{\prime }-a^{2} = 0 \]

[[_homogeneous, ‘class C‘], _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]

10290

\[ {}\left (y+3 x -1\right )^{2} y^{\prime }-\left (2 y-1\right ) \left (4 y+6 x -3\right ) = 0 \]

[[_homogeneous, ‘class C‘], _rational]

10292

\[ {}\left (4 y^{2}+x^{2}\right ) y^{\prime }-x y = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

10293

\[ {}\left (4 y^{2}+2 x y+3 x^{2}\right ) y^{\prime }+y^{2}+6 x y+2 x^{2} = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]

10294

\[ {}\left (1-3 x +2 y\right )^{2} y^{\prime }-\left (3 y-2 x -4\right )^{2} = 0 \]

[[_homogeneous, ‘class C‘], _rational]

10295

\[ {}\left (2 y-4 x +1\right )^{2} y^{\prime }-\left (-2 x +y\right )^{2} = 0 \]

[[_homogeneous, ‘class C‘], _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]

10299

\[ {}\left (b \left (\beta y+\alpha x \right )^{2}-\beta \left (a x +b y\right )\right ) y^{\prime }+a \left (\beta y+\alpha x \right )^{2}-\alpha \left (a x +b y\right ) = 0 \]

[[_1st_order, _with_linear_symmetries], _rational]

10300

\[ {}\left (a y+b x +c \right )^{2} y^{\prime }+\left (\alpha y+\beta x +\gamma \right )^{2} = 0 \]

[[_homogeneous, ‘class C‘], _rational]

10301

\[ {}x \left (y^{2}-3 x \right ) y^{\prime }+2 y^{3}-5 x y = 0 \]

[[_homogeneous, ‘class G‘], _rational]

10302

\[ {}x \left (y^{2}+x^{2}-a \right ) y^{\prime }-y \left (y^{2}+x^{2}+a \right ) = 0 \]

[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]

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]

10304

\[ {}x \left (y^{2}+x^{2} y+x^{2}\right ) y^{\prime }-2 y^{3}-2 y^{2} x^{2}+x^{4} = 0 \]

[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]

10305

\[ {}2 x \left (5 x^{2}+y^{2}\right ) y^{\prime }+y^{3}-x^{2} y = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

10306

\[ {}3 x y^{2} y^{\prime }+y^{3}-2 x = 0 \]

[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli]

10307

\[ {}\left (3 x y^{2}-x^{2}\right ) y^{\prime }+y^{3}-2 x y = 0 \]

[[_homogeneous, ‘class G‘], _exact, _rational]

10308

\[ {}6 x y^{2} y^{\prime }+2 y^{3}+x = 0 \]

[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli]

10309

\[ {}\left (6 x y^{2}+x^{2}\right ) y^{\prime }-y \left (3 y^{2}-x \right ) = 0 \]

[[_homogeneous, ‘class G‘], _rational]

10310

\[ {}\left (y^{2} x^{2}+x \right ) y^{\prime }+y = 0 \]

[[_homogeneous, ‘class G‘], _rational]

10311

\[ {}\left (x y-1\right )^{2} x y^{\prime }+\left (1+y^{2} x^{2}\right ) y = 0 \]

[[_homogeneous, ‘class G‘], _rational]

10312

\[ {}\left (10 x^{3} y^{2}+x^{2} y+2 x \right ) y^{\prime }+5 y^{3} x^{2}+x y^{2} = 0 \]

[[_homogeneous, ‘class G‘], _rational]

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

\[ {}\left (3 x^{3}+6 x^{2} y-3 x y^{2}+20 y^{3}\right ) y^{\prime }-y^{3}+6 x y^{2}+9 x^{2} y+4 x^{3} = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]

10323

\[ {}\left (2 x y^{3}-x^{4}\right ) y^{\prime }-y^{4}+2 x^{3} y = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

10329

\[ {}\left (2 y^{3} x^{2}+y^{2} x^{2}-2 x \right ) y^{\prime }-2 y-1 = 0 \]

[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]

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]

10336

\[ {}a \,x^{2} y^{n} y^{\prime }-2 x y^{\prime }+y = 0 \]

[[_homogeneous, ‘class G‘], _rational]

10337

\[ {}y^{m} x^{n} \left (a x y^{\prime }+b y\right )+\alpha x y^{\prime }+\beta y = 0 \]

[[_homogeneous, ‘class G‘], _rational]

10338

\[ {}\left (f \left (x +y\right )+1\right ) y^{\prime }+f \left (x +y\right ) = 0 \]

[[_homogeneous, ‘class C‘], _exact, _dAlembert]

10339

\[ {}\left (\sqrt {x y}-1\right ) x y^{\prime }-\left (\sqrt {x y}+1\right ) y = 0 \]

[[_homogeneous, ‘class G‘]]

10340

\[ {}\left (2 x^{{5}/{2}} y^{{3}/{2}}+x^{2} y-x \right ) y^{\prime }-x^{{3}/{2}} y^{{5}/{2}}+x y^{2}-y = 0 \]

[[_homogeneous, ‘class G‘], _rational]

10341

\[ {}\left (1+\sqrt {x +y}\right ) y^{\prime }+1 = 0 \]

[[_homogeneous, ‘class C‘], _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]

10346

\[ {}\left (x \sqrt {1+x^{2}+y^{2}}-y \left (x^{2}+y^{2}\right )\right ) y^{\prime }-y \sqrt {1+x^{2}+y^{2}}-x \left (x^{2}+y^{2}\right ) = 0 \]

[[_1st_order, _with_linear_symmetries]]

10349

\[ {}x \left (3 \,{\mathrm e}^{x y}+2 \,{\mathrm e}^{-x y}\right ) \left (x y^{\prime }+y\right )+1 = 0 \]

[[_homogeneous, ‘class G‘]]

10351

\[ {}\left (\ln \left (y\right )+2 x -1\right ) y^{\prime }-2 y = 0 \]

[[_1st_order, _with_linear_symmetries]]

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‘]]

10360

\[ {}x \cos \left (y\right ) y^{\prime }+\sin \left (y\right ) = 0 \]

[_separable]

10367

\[ {}y^{\prime } \cos \left (a y\right )-b \left (1-c \cos \left (a y\right )\right ) \sqrt {\cos \left (a y\right )^{2}-1+c \cos \left (a y\right )} = 0 \]

[_quadrature]

10369

\[ {}\left (x^{2} y \sin \left (x y\right )-4 x \right ) y^{\prime }+x y^{2} \sin \left (x y\right )-y = 0 \]

[[_homogeneous, ‘class G‘]]

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]

10372

\[ {}\left (y f \left (x^{2}+y^{2}\right )-x \right ) y^{\prime }+y+x f \left (x^{2}+y^{2}\right ) = 0 \]

[[_1st_order, _with_linear_symmetries]]

10392

\[ {}{y^{\prime }}^{2}+\left (y^{\prime }-y\right ) {\mathrm e}^{x} = 0 \]

[[_1st_order, _with_linear_symmetries]]

10397

\[ {}{y^{\prime }}^{2}-x y y^{\prime }+y^{2} \ln \left (a y\right ) = 0 \]

[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]

10436

\[ {}\left (x y^{\prime }+y+2 x \right )^{2}-4 x y-4 x^{2}-4 a = 0 \]

[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]

10438

\[ {}x^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+y \left (y+1\right )-x = 0 \]

[[_1st_order, _with_linear_symmetries], _rational]

10486

\[ {}a x y {y^{\prime }}^{2}-\left (a y^{2}+b \,x^{2}+c \right ) y^{\prime }+b x y = 0 \]

[_rational]

10528

\[ {}{y^{\prime }}^{3}-x y^{4} y^{\prime }-y^{5} = 0 \]

[[_1st_order, _with_linear_symmetries]]

10538

\[ {}x^{3} {y^{\prime }}^{3}-3 x^{2} y {y^{\prime }}^{2}+\left (3 x y^{2}+x^{6}\right ) y^{\prime }-y^{3}-2 x^{5} y = 0 \]

[[_1st_order, _with_linear_symmetries]]

10539

\[ {}2 \left (x y^{\prime }+y\right )^{3}-y y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘]]

10542

\[ {}y^{2} {y^{\prime }}^{3}+2 x y^{\prime }-y = 0 \]

[[_1st_order, _with_linear_symmetries]]

10543

\[ {}16 y^{2} {y^{\prime }}^{3}+2 x y^{\prime }-y = 0 \]

[[_1st_order, _with_linear_symmetries]]

10545

\[ {}x^{7} y^{2} {y^{\prime }}^{3}-\left (3 x^{6} y^{3}-1\right ) {y^{\prime }}^{2}+3 x^{5} y^{4} y^{\prime }-x^{4} y^{5} = 0 \]

[[_homogeneous, ‘class G‘]]

10551

\[ {}{y^{\prime }}^{r}-a y^{s}-b \,x^{\frac {r s}{r -s}} = 0 \]

[[_homogeneous, ‘class G‘]]

10554

\[ {}a {y^{\prime }}^{m}+b {y^{\prime }}^{n}-y = 0 \]

[_quadrature]

10558

\[ {}x \left (\sqrt {1+{y^{\prime }}^{2}}+y^{\prime }\right )-y = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

10561

\[ {}a y \sqrt {1+{y^{\prime }}^{2}}-2 x y y^{\prime }+y^{2}-x^{2} = 0 \]

[‘y=_G(x,y’)‘]

10564

\[ {}\ln \left (y^{\prime }\right )+x y^{\prime }+a y+b = 0 \]

[[_1st_order, _with_linear_symmetries], _dAlembert]

10565

\[ {}\ln \left (y^{\prime }\right )+a \left (-y+x y^{\prime }\right ) = 0 \]

[[_1st_order, _with_linear_symmetries], _Clairaut]

10566

\[ {}y \ln \left (y^{\prime }\right )+y^{\prime }-y \ln \left (y\right )-x y = 0 \]

[_separable]

10569

\[ {}{y^{\prime }}^{2} \sin \left (y^{\prime }\right )-y = 0 \]

[_quadrature]

10575

\[ {}y^{\prime } = F \left (\frac {y}{x +a}\right ) \]

[[_homogeneous, ‘class C‘], _dAlembert]

10576

\[ {}y^{\prime } = 2 x +F \left (y-x^{2}\right ) \]

[[_1st_order, _with_linear_symmetries]]

10577

\[ {}y^{\prime } = -\frac {a x}{2}+F \left (y+\frac {a \,x^{2}}{4}+\frac {b x}{2}\right ) \]

[[_1st_order, _with_linear_symmetries]]

10578

\[ {}y^{\prime } = F \left (y \,{\mathrm e}^{-b x}\right ) {\mathrm e}^{b x} \]

[[_1st_order, _with_linear_symmetries]]

10582

\[ {}y^{\prime } = \frac {2 a}{y+2 F \left (y^{2}-4 a x \right ) a} \]

[[_1st_order, _with_linear_symmetries]]

10587

\[ {}y^{\prime } = \frac {F \left (-\frac {-1+y \ln \left (x \right )}{y}\right ) y^{2}}{x} \]

[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]

10594

\[ {}y^{\prime } = \frac {-2 x^{2}+x +F \left (y+x^{2}-x \right )}{x} \]

[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]

10595

\[ {}y^{\prime } = \frac {2 a}{x^{2} \left (-y+2 F \left (\frac {x y^{2}-4 a}{x}\right ) a \right )} \]

[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]

10596

\[ {}y^{\prime } = \frac {y+F \left (\frac {y}{x}\right )}{-1+x} \]

[[_homogeneous, ‘class D‘]]

10598

\[ {}y^{\prime } = \frac {F \left (-\frac {-1+2 y \ln \left (x \right )}{y}\right ) y^{2}}{x} \]

[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]

10603

\[ {}y^{\prime } = -\frac {y^{2} \left (2 x -F \left (-\frac {x y-2}{2 y}\right )\right )}{4 x} \]

[NONE]

10606

\[ {}y^{\prime } = \frac {\sqrt {y}}{\sqrt {y}+F \left (\frac {x -y}{\sqrt {y}}\right )} \]

[[_1st_order, _with_linear_symmetries]]

10610

\[ {}y^{\prime } = \frac {\left (y \,{\mathrm e}^{-\frac {x^{2}}{4}} x +2 F \left (y \,{\mathrm e}^{-\frac {x^{2}}{4}}\right )\right ) {\mathrm e}^{\frac {x^{2}}{4}}}{2} \]

[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]

10614

\[ {}y^{\prime } = -\frac {-x^{2}+2 x^{3} y-F \left (\left (x y-1\right ) x \right )}{x^{4}} \]

[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]

10618

\[ {}y^{\prime } = \frac {y^{2}+2 x y+x^{2}+{\mathrm e}^{2 F \left (-\left (x -y\right ) \left (x +y\right )\right )}}{y^{2}+2 x y+x^{2}-{\mathrm e}^{2 F \left (-\left (x -y\right ) \left (x +y\right )\right )}} \]

[[_1st_order, _with_linear_symmetries]]

10619

\[ {}y^{\prime } = \frac {1}{y+\sqrt {x}} \]

[[_homogeneous, ‘class G‘], [_Abel, ‘2nd type‘, ‘class C‘]]

10620

\[ {}y^{\prime } = \frac {1}{y+2+\sqrt {3 x +1}} \]

[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class C‘]]

10621

\[ {}y^{\prime } = \frac {x^{2}}{y+x^{{3}/{2}}} \]

[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class C‘]]

10622

\[ {}y^{\prime } = \frac {x^{{5}/{3}}}{y+x^{{4}/{3}}} \]

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘]]

10625

\[ {}y^{\prime } = \frac {\left (-1+y \ln \left (x \right )\right )^{2}}{x} \]

[_Riccati]

10626

\[ {}y^{\prime } = \frac {x \left (-2+3 \sqrt {x^{2}+3 y}\right )}{3} \]

[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]

10627

\[ {}y^{\prime } = \frac {\left (-1+2 y \ln \left (x \right )\right )^{2}}{x} \]

[_Riccati]

10628

\[ {}y^{\prime } = \frac {{\mathrm e}^{b x}}{y \,{\mathrm e}^{-b x}+1} \]

[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class C‘]]

10629

\[ {}y^{\prime } = \frac {x^{2} \left (1+2 \sqrt {x^{3}-6 y}\right )}{2} \]

[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]

10630

\[ {}y^{\prime } = \frac {{\mathrm e}^{x}}{y \,{\mathrm e}^{-x}+1} \]

[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class C‘]]

10631

\[ {}y^{\prime } = \frac {{\mathrm e}^{\frac {2 x}{3}}}{y \,{\mathrm e}^{-\frac {2 x}{3}}+1} \]

[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class C‘]]

10633

\[ {}y^{\prime } = \frac {x \left (x +2 \sqrt {x^{3}-6 y}\right )}{2} \]

[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]

10634

\[ {}y^{\prime } = \left (-\ln \left (y\right )+x^{2}\right ) y \]

[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]

10641

\[ {}y^{\prime } = \frac {x \left (-2+3 x \sqrt {x^{2}+3 y}\right )}{3} \]

[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]

10643

\[ {}y^{\prime } = \left (-\ln \left (y\right )+x \right ) y \]

[[_1st_order, _with_linear_symmetries]]

10644

\[ {}y^{\prime } = \frac {x^{3}+x^{2}+2 \sqrt {x^{3}-6 y}}{2 x +2} \]

[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]

10647

\[ {}y^{\prime } = -\frac {x}{4}+\frac {1}{4}+x \sqrt {x^{2}-2 x +1+8 y} \]

[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]

10648

\[ {}y^{\prime } = -\frac {x}{2}-\frac {a}{2}+x \sqrt {x^{2}+2 a x +a^{2}+4 y} \]

[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]

10649

\[ {}y^{\prime } = \frac {\left (\ln \left (y\right )+x^{2}\right ) y}{x} \]

[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]

10651

\[ {}y^{\prime } = -\frac {x}{2}+1+x \sqrt {x^{2}-4 x +4 y} \]

[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]

10652

\[ {}y^{\prime } = -\frac {2 x^{2}+2 x -3 \sqrt {x^{2}+3 y}}{3 \left (x +1\right )} \]

[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]

10653

\[ {}y^{\prime } = \frac {y^{3} {\mathrm e}^{-\frac {4 x}{3}}}{y \,{\mathrm e}^{-\frac {2 x}{3}}+1} \]

[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class C‘]]

10654

\[ {}y^{\prime } = \frac {\left (\ln \left (y\right )+x^{3}\right ) y}{x} \]

[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]

10655

\[ {}y^{\prime } = -\frac {x}{4}+\frac {1}{4}+x^{2} \sqrt {x^{2}-2 x +1+8 y} \]

[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]

10656

\[ {}y^{\prime } = -\frac {x^{2}-1-4 \sqrt {x^{2}-2 x +1+8 y}}{4 \left (x +1\right )} \]

[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]

10657

\[ {}y^{\prime } = -\frac {a x}{2}-\frac {b}{2}+x \sqrt {a^{2} x^{2}+2 a b x +b^{2}+4 a y-4 c} \]

[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]

10658

\[ {}y^{\prime } = -\frac {x}{2}-\frac {a}{2}+x^{2} \sqrt {x^{2}+2 a x +a^{2}+4 y} \]

[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]

10659

\[ {}y^{\prime } = -\frac {a x}{2}-\frac {b}{2}+x^{2} \sqrt {a^{2} x^{2}+2 a b x +b^{2}+4 a y-4 c} \]

[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]

10660

\[ {}y^{\prime } = \frac {x}{2}+\frac {1}{2}+x^{2} \sqrt {x^{2}+2 x +1-4 y} \]

[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]

10662

\[ {}y^{\prime } = -\frac {x}{2}+1+x^{2} \sqrt {x^{2}-4 x +4 y} \]

[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]

10664

\[ {}y^{\prime } = \left (-\ln \left (y\right )+1+x^{2}+x^{3}\right ) y \]

[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]

10665

\[ {}y^{\prime } = \frac {y^{3} {\mathrm e}^{-2 b x}}{y \,{\mathrm e}^{-b x}+1} \]

[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class C‘]]

10666

\[ {}y^{\prime } = \frac {y^{3} {\mathrm e}^{-2 x}}{y \,{\mathrm e}^{-x}+1} \]

[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class C‘]]

10672

\[ {}y^{\prime } = -\frac {x^{2}-x -2-2 \sqrt {x^{2}-4 x +4 y}}{2 \left (x +1\right )} \]

[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]

10678

\[ {}y^{\prime } = \frac {x^{2}+2 x +1+2 \sqrt {x^{2}+2 x +1-4 y}}{2 x +2} \]

[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]

10680

\[ {}y^{\prime } = \frac {2 a}{x \left (-x y+2 a x y^{2}-8 a^{2}\right )} \]

[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]

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]

10691

\[ {}y^{\prime } = \left (1+y^{2} {\mathrm e}^{-2 b x}+y^{3} {\mathrm e}^{-3 b x}\right ) {\mathrm e}^{b x} \]

[[_1st_order, _with_linear_symmetries], _Abel]

10695

\[ {}y^{\prime } = \left (1+y^{2} {\mathrm e}^{-\frac {4 x}{3}}+y^{3} {\mathrm e}^{-2 x}\right ) {\mathrm e}^{\frac {2 x}{3}} \]

[[_1st_order, _with_linear_symmetries], _Abel]

10696

\[ {}y^{\prime } = \left (1+y^{2} {\mathrm e}^{-2 x}+y^{3} {\mathrm e}^{-3 x}\right ) {\mathrm e}^{x} \]

[[_1st_order, _with_linear_symmetries], _Abel]

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]

10703

\[ {}y^{\prime } = \frac {\left (\ln \left (y\right )+x +x^{3}+x^{4}\right ) y}{x} \]

[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]

10708

\[ {}y^{\prime } = \frac {-\ln \left (x \right )+{\mathrm e}^{\frac {1}{x}}+4 x^{2} y+2 x +2 x y^{2}+2 x^{3}}{\ln \left (x \right )-{\mathrm e}^{\frac {1}{x}}} \]

[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]

10711

\[ {}y^{\prime } = \frac {-b y a +b^{2}+a b +b^{2} x -b a \sqrt {x}-a^{2}}{a \left (-a y+b +a +b x -a \sqrt {x}\right )} \]

[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

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]

10715

\[ {}y^{\prime } = -\frac {x^{2}+x +a x +a -2 \sqrt {x^{2}+2 a x +a^{2}+4 y}}{2 \left (x +1\right )} \]

[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]

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]

10719

\[ {}y^{\prime } = \frac {\left (18 x^{{3}/{2}}+36 y^{2}-12 x^{3} y+x^{6}\right ) \sqrt {x}}{36} \]

[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]

10720

\[ {}y^{\prime } = -\frac {y^{3}}{\left (-1+2 y \ln \left (x \right )-y\right ) x} \]

[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]]

10721

\[ {}y^{\prime } = \frac {2 a}{y+2 a y^{4}-16 a^{2} x y^{2}+32 a^{3} x^{2}} \]

[[_1st_order, _with_linear_symmetries]]

10722

\[ {}y^{\prime } = -\frac {y^{3}}{\left (-1+y \ln \left (x \right )-y\right ) x} \]

[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]]

10723

\[ {}y^{\prime } = \frac {-\ln \left (x \right )+2 \ln \left (2 x \right ) x y+\ln \left (2 x \right )+\ln \left (2 x \right ) y^{2}+\ln \left (2 x \right ) x^{2}}{\ln \left (x \right )} \]

[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]

10724

\[ {}y^{\prime } = -\frac {b y a -c b +b^{2} x +b a \sqrt {x}-a^{2}}{a \left (a y-c +b x +a \sqrt {x}\right )} \]

[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

10729

\[ {}y^{\prime } = \frac {2 y+1}{x \left (-2+x y^{2}+2 x y^{3}\right )} \]

[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]

10733

\[ {}y^{\prime } = \frac {\left (-1+2 y \ln \left (x \right )\right )^{3}}{\left (-1+2 y \ln \left (x \right )-y\right ) x} \]

[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], [_Abel, ‘2nd type‘, ‘class C‘]]

10734

\[ {}y^{\prime } = \frac {2 x^{2}+2 x +x^{4}-2 x^{2} y-1+y^{2}}{x +1} \]

[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]

10736

\[ {}y^{\prime } = \frac {2 a}{-x^{2} y+2 a y^{4} x^{2}-16 a^{2} x y^{2}+32 a^{3}} \]

[‘y=_G(x,y’)‘]

10737

\[ {}y^{\prime } = \frac {2 y+1}{x \left (-2+x y+2 x y^{2}\right )} \]

[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]

10743

\[ {}y^{\prime } = \frac {\left (-1+y \ln \left (x \right )\right )^{3}}{\left (-1+y \ln \left (x \right )-y\right ) x} \]

[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], [_Abel, ‘2nd type‘, ‘class C‘]]

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]

10749

\[ {}y^{\prime } = \frac {\left (\ln \left (y\right ) x +\ln \left (y\right )+x^{4}\right ) y}{x \left (x +1\right )} \]

[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]

10753

\[ {}y^{\prime } = \frac {y^{{3}/{2}}}{y^{{3}/{2}}+x^{2}-2 x y+y^{2}} \]

[[_1st_order, _with_linear_symmetries], _rational]

10755

\[ {}y^{\prime } = \frac {-4 x y+x^{3}+2 x^{2}-4 x -8}{-8 y+2 x^{2}+4 x -8} \]

[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

10759

\[ {}y^{\prime } = \frac {-4 x y-x^{3}+4 x^{2}-4 x +8}{8 y+2 x^{2}-8 x +8} \]

[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

10761

\[ {}y^{\prime } = \frac {\left (\ln \left (y\right ) x +\ln \left (y\right )+x \right ) y}{x \left (x +1\right )} \]

[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]

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]

10765

\[ {}y^{\prime } = \frac {-8 x y-x^{3}+2 x^{2}-8 x +32}{32 y+4 x^{2}-8 x +32} \]

[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

10766

\[ {}y^{\prime } = \frac {y \left (y+1\right )}{x \left (-y-1+x y\right )} \]

[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]]

10769

\[ {}y^{\prime } = \frac {-4 y a x -a^{2} x^{3}-2 a \,x^{2} b -4 a x +8}{8 y+2 a \,x^{2}+4 b x +8} \]

[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

10771

\[ {}y^{\prime } = \frac {x y+x +y^{2}}{\left (-1+x \right ) \left (x +y\right )} \]

[[_homogeneous, ‘class D‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

10772

\[ {}y^{\prime } = \frac {-4 x y-x^{3}-2 a \,x^{2}-4 x +8}{8 y+2 x^{2}+4 a x +8} \]

[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

10773

\[ {}y^{\prime } = \frac {x -y+\sqrt {y}}{x -y+\sqrt {y}+1} \]

[[_1st_order, _with_linear_symmetries], _rational]

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]

10775

\[ {}y^{\prime } = \frac {y \left (y+1\right )}{x \left (-y-1+x y^{4}\right )} \]

[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]

10777

\[ {}y^{\prime } = \frac {x^{3} y+x^{3}+x y^{2}+y^{3}}{\left (-1+x \right ) x^{3}} \]

[[_homogeneous, ‘class D‘], _rational, _Abel]

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]

10782

\[ {}y^{\prime } = \frac {-\sinh \left (x \right )+x^{2} \ln \left (x \right )+2 x y \ln \left (x \right )+\ln \left (x \right )+y^{2} \ln \left (x \right )}{\sinh \left (x \right )} \]

[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]

10783

\[ {}y^{\prime } = -\frac {\ln \left (x \right )-\sinh \left (x \right ) x^{2}-2 \sinh \left (x \right ) x y-\sinh \left (x \right )-\sinh \left (x \right ) y^{2}}{\ln \left (x \right )} \]

[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]

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]

10787

\[ {}y^{\prime } = -\frac {\ln \left (-1+x \right )-\coth \left (x +1\right ) x^{2}-2 \coth \left (x +1\right ) x y-\coth \left (x +1\right )-\coth \left (x +1\right ) y^{2}}{\ln \left (-1+x \right )} \]

[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]

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]

10791

\[ {}y^{\prime } = -\frac {y \left (1+x y\right )}{x \left (x y+1-y\right )} \]

[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]

10793

\[ {}y^{\prime } = \frac {x^{3}+3 a \,x^{2}+3 a^{2} x +a^{3}+x y^{2}+a y^{2}+y^{3}}{\left (x +a \right )^{3}} \]

[[_homogeneous, ‘class C‘], _rational, _Abel]

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]

10798

\[ {}y^{\prime } = \frac {-b^{3}+6 b^{2} x -12 b \,x^{2}+8 x^{3}-4 b y^{2}+8 x y^{2}+8 y^{3}}{\left (2 x -b \right )^{3}} \]

[[_homogeneous, ‘class C‘], _rational, _Abel]

10799

\[ {}y^{\prime } = \frac {\left (y \,{\mathrm e}^{-\frac {x^{2}}{4}} x +2+2 y^{2} {\mathrm e}^{-\frac {x^{2}}{2}}+2 y^{3} {\mathrm e}^{-\frac {3 x^{2}}{4}}\right ) {\mathrm e}^{\frac {x^{2}}{4}}}{2} \]

[_Abel]

10806

\[ {}y^{\prime } = \frac {\left (2 y+1\right ) \left (y+1\right )}{x \left (-2 y-2+x +2 x y\right )} \]

[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]]

10807

\[ {}y^{\prime } = \frac {-125+300 x -240 x^{2}+64 x^{3}-80 y^{2}+64 x y^{2}+64 y^{3}}{\left (4 x -5\right )^{3}} \]

[[_homogeneous, ‘class C‘], _rational, _Abel]

10816

\[ {}y^{\prime } = \frac {y}{x \left (-1+x y+x y^{3}+x y^{4}\right )} \]

[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]

10822

\[ {}y^{\prime } = \frac {y \left (x^{3}+x^{2} y+y^{2}\right )}{x^{2} \left (-1+x \right ) \left (x +y\right )} \]

[[_homogeneous, ‘class D‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘]]

10826

\[ {}y^{\prime } = \frac {\left (2 y+1\right ) \left (y+1\right )}{x \left (-2 y-2+x y^{3}+2 x y^{4}\right )} \]

[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]

10836

\[ {}y^{\prime } = \frac {\left ({\mathrm e}^{-\frac {y}{x}} y+{\mathrm e}^{-\frac {y}{x}} x +x^{2}\right ) {\mathrm e}^{\frac {y}{x}}}{x} \]

[[_1st_order, _with_linear_symmetries]]

10837

\[ {}y^{\prime } = \frac {\left ({\mathrm e}^{-\frac {y}{x}} y+{\mathrm e}^{-\frac {y}{x}} x +x^{3}\right ) {\mathrm e}^{\frac {y}{x}}}{x} \]

[[_1st_order, _with_linear_symmetries]]

10848

\[ {}y^{\prime } = \frac {b^{3}+y^{2} b^{3}+2 y b^{2} a x +x^{2} b \,a^{2}+y^{3} b^{3}+3 y^{2} b^{2} a x +3 y b \,a^{2} x^{2}+a^{3} x^{3}}{b^{3}} \]

[[_homogeneous, ‘class C‘], _Abel]

10849

\[ {}y^{\prime } = \frac {\alpha ^{3}+y^{2} \alpha ^{3}+2 y \alpha ^{2} \beta x +\alpha \,\beta ^{2} x^{2}+y^{3} \alpha ^{3}+3 y^{2} \alpha ^{2} \beta x +3 y \alpha \,\beta ^{2} x^{2}+\beta ^{3} x^{3}}{\alpha ^{3}} \]

[[_homogeneous, ‘class C‘], _Abel]

10855

\[ {}y^{\prime } = \frac {a^{3}+y^{2} a^{3}+2 y a^{2} b x +a \,b^{2} x^{2}+y^{3} a^{3}+3 y^{2} a^{2} b x +3 y a \,b^{2} x^{2}+b^{3} x^{3}}{a^{3}} \]

[[_homogeneous, ‘class C‘], _Abel]

10860

\[ {}y^{\prime } = \frac {y \left ({\mathrm e}^{-\frac {x^{2}}{2}} x y+{\mathrm e}^{-\frac {x^{2}}{4}} x +2 y^{2} {\mathrm e}^{-\frac {3 x^{2}}{4}}\right ) {\mathrm e}^{\frac {x^{2}}{4}}}{2 y \,{\mathrm e}^{-\frac {x^{2}}{4}}+2} \]

[[_Abel, ‘2nd type‘, ‘class C‘], [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]

10863

\[ {}y^{\prime } = -\frac {2 x}{3}+1+y^{2}+\frac {2 x^{2} y}{3}+\frac {x^{4}}{9}+y^{3}+y^{2} x^{2}+\frac {y x^{4}}{3}+\frac {x^{6}}{27} \]

[[_1st_order, _with_linear_symmetries], _Abel]

10864

\[ {}y^{\prime } = 2 x +1+y^{2}-2 x^{2} y+x^{4}+y^{3}-3 y^{2} x^{2}+3 y x^{4}-x^{6} \]

[[_1st_order, _with_linear_symmetries], _Abel]

10869

\[ {}y^{\prime } = \frac {2 y+1}{x \left (-2+x +x y^{2}+3 x y^{3}+2 x y+2 x y^{4}\right )} \]

[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]

10872

\[ {}y^{\prime } = -\frac {y^{2} \left (x^{2} y-2 x -2 x y+y\right )}{2 \left (-2+x y-2 y\right ) x} \]

[_rational, [_Abel, ‘2nd type‘, ‘class C‘]]

10873

\[ {}y^{\prime } = \frac {-2 x y+2 x^{3}-2 x -y^{3}+3 y^{2} x^{2}-3 y x^{4}+x^{6}}{-y+x^{2}-1} \]

[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class C‘]]

10876

\[ {}y^{\prime } = -\frac {2 a}{-y-2 a -2 a y^{4}+16 a^{2} x y^{2}-32 a^{3} x^{2}-2 a y^{6}+24 y^{4} a^{2} x -96 y^{2} a^{3} x^{2}+128 a^{4} x^{3}} \]

[[_1st_order, _with_linear_symmetries]]

10877

\[ {}y^{\prime } = \frac {-18 x y-6 x^{3}-18 x +27 y^{3}+27 y^{2} x^{2}+9 y x^{4}+x^{6}}{27 y+9 x^{2}+27} \]

[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class C‘]]

10882

\[ {}y^{\prime } = \frac {2 x^{2}-4 x^{3} y+1+x^{4} y^{2}+x^{6} y^{3}-3 y^{2} x^{5}+3 y x^{4}-x^{3}}{x^{4}} \]

[_rational, _Abel]

10884

\[ {}y^{\prime } = \frac {6 x^{2} y-2 x +1-5 x^{3} y^{2}-2 x y+y^{3} x^{4}}{x^{2} \left (x^{2} y-x +1\right )} \]

[_rational, [_Abel, ‘2nd type‘, ‘class C‘], [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]

10888

\[ {}y^{\prime } = \frac {y^{2}+2 x y+x^{2}+{\mathrm e}^{-\frac {2}{-y^{2}+x^{2}-1}}}{y^{2}+2 x y+x^{2}-{\mathrm e}^{-\frac {2}{-y^{2}+x^{2}-1}}} \]

[[_1st_order, _with_linear_symmetries]]

10896

\[ {}y^{\prime } = \frac {2 a \left (-y^{2}+4 a x -1\right )}{-y^{3}+4 y a x -y-2 a y^{6}+24 y^{4} a^{2} x -96 y^{2} a^{3} x^{2}+128 a^{4} x^{3}} \]

[[_1st_order, _with_linear_symmetries], _rational]

10908

\[ {}y^{\prime } = \frac {2 a x}{-x^{3} y+2 a \,x^{3}+2 a y^{4} x^{3}-16 y^{2} a^{2} x^{2}+32 a^{3} x +2 a y^{6} x^{3}-24 y^{4} a^{2} x^{2}+96 y^{2} x \,a^{3}-128 a^{4}} \]

[_rational]

10909

\[ {}y^{\prime } = -\frac {-y^{3}-y+2 y^{2} \ln \left (x \right )-\ln \left (x \right )^{2} y^{3}-1+3 y \ln \left (x \right )-3 \ln \left (x \right )^{2} y^{2}+\ln \left (x \right )^{3} y^{3}}{y x} \]

[[_Abel, ‘2nd type‘, ‘class C‘]]

10910

\[ {}y^{\prime } = \frac {2 a \left (x y^{2}-4 a +x \right )}{-x^{3} y^{3}+4 a \,x^{2} y-x^{3} y+2 a y^{6} x^{3}-24 y^{4} a^{2} x^{2}+96 y^{2} x \,a^{3}-128 a^{4}} \]

[_rational]

10911

\[ {}y^{\prime } = -\frac {-y^{3}-y+4 y^{2} \ln \left (x \right )-4 \ln \left (x \right )^{2} y^{3}-1+6 y \ln \left (x \right )-12 \ln \left (x \right )^{2} y^{2}+8 \ln \left (x \right )^{3} y^{3}}{y x} \]

[[_Abel, ‘2nd type‘, ‘class C‘]]

10915

\[ {}y^{\prime } = \frac {y^{{3}/{2}} \left (x -y+\sqrt {y}\right )}{y^{{3}/{2}} x -y^{{5}/{2}}+y^{2}+x^{3}-3 x^{2} y+3 x y^{2}-y^{3}} \]

[[_1st_order, _with_linear_symmetries], _rational]

10918

\[ {}y^{\prime } = \frac {y^{2}}{y^{2}+y^{{3}/{2}}+\sqrt {y}\, x^{2}-2 y^{{3}/{2}} x +y^{{5}/{2}}+x^{3}-3 x^{2} y+3 x y^{2}-y^{3}} \]

[[_1st_order, _with_linear_symmetries], _rational]

10919

\[ {}y^{\prime } = \frac {y^{2}+2 x y+x^{2}+{\mathrm e}^{-2 \left (x -y\right ) \left (x +y\right )}}{y^{2}+2 x y+x^{2}-{\mathrm e}^{-2 \left (x -y\right ) \left (x +y\right )}} \]

[[_1st_order, _with_linear_symmetries]]

10921

\[ {}y^{\prime } = \frac {y^{2}+2 x y+x^{2}+{\mathrm e}^{2 \left (x -y\right )^{2} \left (x +y\right )^{2}}}{y^{2}+2 x y+x^{2}-{\mathrm e}^{2 \left (x -y\right )^{2} \left (x +y\right )^{2}}} \]

[[_1st_order, _with_linear_symmetries]]

10922

\[ {}y^{\prime } = \frac {-8 y^{3} x^{2}+16 x y^{2}+16 x y^{3}-8+12 x y-6 y^{2} x^{2}+x^{3} y^{3}}{16 \left (-2+x y-2 y\right ) x} \]

[_rational, [_Abel, ‘2nd type‘, ‘class C‘]]

10925

\[ {}y^{\prime } = -\frac {16 x y^{3}-8 y^{3}-8 y+8 x y^{2}-2 y^{3} x^{2}-8+12 x y-6 y^{2} x^{2}+x^{3} y^{3}}{32 y x} \]

[_rational, [_Abel, ‘2nd type‘, ‘class C‘]]

10927

\[ {}y^{\prime } = \frac {-3 x^{2} y-2 x^{3}-2 x -x y^{2}-y+x^{3} y^{3}+3 x^{4} y^{2}+3 x^{5} y+x^{6}}{x \left (x y+x^{2}+1\right )} \]

[_rational, [_Abel, ‘2nd type‘, ‘class C‘], [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]

10930

\[ {}y^{\prime } = \frac {x}{2}+1+y^{2}+\frac {x^{2} y}{4}-x y-\frac {x^{4}}{8}+\frac {x^{3}}{8}+\frac {x^{2}}{4}+y^{3}-\frac {3 y^{2} x^{2}}{4}-\frac {3 x y^{2}}{2}+\frac {3 y x^{4}}{16}+\frac {3 x^{3} y}{4}-\frac {x^{6}}{64}-\frac {3 x^{5}}{32} \]

[[_1st_order, _with_linear_symmetries], _Abel]

10931

\[ {}y^{\prime } = -\frac {x}{2}+1+y^{2}+\frac {7 x^{2} y}{2}-2 x y+\frac {13 x^{4}}{16}-\frac {3 x^{3}}{2}+x^{2}+y^{3}+\frac {3 y^{2} x^{2}}{4}-3 x y^{2}+\frac {3 y x^{4}}{16}-\frac {3 x^{3} y}{2}+\frac {x^{6}}{64}-\frac {3 x^{5}}{16} \]

[[_1st_order, _with_linear_symmetries], _Abel]

10932

\[ {}y^{\prime } = -\frac {x}{4}+1+y^{2}+\frac {7 x^{2} y}{16}-\frac {x y}{2}+\frac {5 x^{4}}{128}-\frac {5 x^{3}}{64}+\frac {x^{2}}{16}+y^{3}+\frac {3 y^{2} x^{2}}{8}-\frac {3 x y^{2}}{4}+\frac {3 y x^{4}}{64}-\frac {3 x^{3} y}{16}+\frac {x^{6}}{512}-\frac {3 x^{5}}{256} \]

[[_1st_order, _with_linear_symmetries], _Abel]

10934

\[ {}y^{\prime } = \frac {-x^{2}+x +1+y^{2}+5 x^{2} y-2 x y+4 x^{4}-3 x^{3}+y^{3}+3 y^{2} x^{2}-3 x y^{2}+3 y x^{4}-6 x^{3} y+x^{6}-3 x^{5}}{x} \]

[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel]

10935

\[ {}y^{\prime } = \frac {-32 x y+16 x^{3}+16 x^{2}-32 x -64 y^{3}+48 y^{2} x^{2}+96 x y^{2}-12 y x^{4}-48 x^{3} y-48 x^{2} y+x^{6}+6 x^{5}+12 x^{4}}{-64 y+16 x^{2}+32 x -64} \]

[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class C‘]]

10937

\[ {}y^{\prime } = \frac {-32 x y-72 x^{3}+32 x^{2}-32 x +64 y^{3}+48 y^{2} x^{2}-192 x y^{2}+12 y x^{4}-96 x^{3} y+192 x^{2} y+x^{6}-12 x^{5}+48 x^{4}}{64 y+16 x^{2}-64 x +64} \]

[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class C‘]]

10938

\[ {}y^{\prime } = -\frac {y^{2}+2 x y+x^{2}+{\mathrm e}^{\frac {2 \left (x -y\right )^{3} \left (x +y\right )^{3}}{-y^{2}+x^{2}-1}}}{-y^{2}-2 x y-x^{2}+{\mathrm e}^{\frac {2 \left (x -y\right )^{3} \left (x +y\right )^{3}}{-y^{2}+x^{2}-1}}} \]

[[_1st_order, _with_linear_symmetries]]

10939

\[ {}y^{\prime } = \frac {-128 x y-24 x^{3}+32 x^{2}-128 x +512 y^{3}+192 y^{2} x^{2}-384 x y^{2}+24 y x^{4}-96 x^{3} y+96 x^{2} y+x^{6}-6 x^{5}+12 x^{4}}{512 y+64 x^{2}-128 x +512} \]

[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class C‘]]

10940

\[ {}y^{\prime } = \frac {-32 y a x -8 a^{2} x^{3}-16 a \,x^{2} b -32 a x +64 y^{3}+48 a \,x^{2} y^{2}+96 y^{2} b x +12 y a^{2} x^{4}+48 y a \,x^{3} b +48 y b^{2} x^{2}+a^{3} x^{6}+6 a^{2} x^{5} b +12 a \,x^{4} b^{2}+8 b^{3} x^{3}}{64 y+16 a \,x^{2}+32 b x +64} \]

[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class C‘]]

10941

\[ {}y^{\prime } = \frac {-32 x y-8 x^{3}-16 a \,x^{2}-32 x +64 y^{3}+48 y^{2} x^{2}+96 a x y^{2}+12 y x^{4}+48 y a \,x^{3}+48 a^{2} x^{2} y+x^{6}+6 x^{5} a +12 a^{2} x^{4}+8 a^{3} x^{3}}{64 y+16 x^{2}+32 a x +64} \]

[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class C‘]]

10945

\[ {}y^{\prime } = \frac {x^{2} y+x^{4}+2 x^{3}-3 x^{2}+x y+x +y^{3}+3 y^{2} x^{2}-3 x y^{2}+3 y x^{4}-6 x^{3} y+x^{6}-3 x^{5}}{x \left (y+x^{2}-x +1\right )} \]

[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class C‘]]

10946

\[ {}y^{\prime } = -\frac {a x}{2}+1+y^{2}+\frac {a \,x^{2} y}{2}+b x y+\frac {a^{2} x^{4}}{16}+\frac {a \,x^{3} b}{4}+\frac {b^{2} x^{2}}{4}+y^{3}+\frac {3 a \,x^{2} y^{2}}{4}+\frac {3 y^{2} b x}{2}+\frac {3 y a^{2} x^{4}}{16}+\frac {3 y a \,x^{3} b}{4}+\frac {3 y b^{2} x^{2}}{4}+\frac {a^{3} x^{6}}{64}+\frac {3 a^{2} x^{5} b}{32}+\frac {3 a \,x^{4} b^{2}}{16}+\frac {b^{3} x^{3}}{8} \]

[[_1st_order, _with_linear_symmetries], _Abel]

10947

\[ {}y^{\prime } = -\frac {x}{2}+1+y^{2}+\frac {x^{2} y}{2}+y a x +\frac {x^{4}}{16}+\frac {a \,x^{3}}{4}+\frac {a^{2} x^{2}}{4}+y^{3}+\frac {3 y^{2} x^{2}}{4}+\frac {3 a x y^{2}}{2}+\frac {3 y x^{4}}{16}+\frac {3 y a \,x^{3}}{4}+\frac {3 a^{2} x^{2} y}{4}+\frac {x^{6}}{64}+\frac {3 x^{5} a}{32}+\frac {3 a^{2} x^{4}}{16}+\frac {a^{3} x^{3}}{8} \]

[[_1st_order, _with_linear_symmetries], _Abel]

10957

\[ {}y^{\prime } = \frac {y^{2}+2 x y+x^{2}+{\mathrm e}^{2+2 y^{4}-4 y^{2} x^{2}+2 x^{4}+2 y^{6}-6 x^{2} y^{4}+6 x^{4} y^{2}-2 x^{6}}}{y^{2}+2 x y+x^{2}-{\mathrm e}^{2+2 y^{4}-4 y^{2} x^{2}+2 x^{4}+2 y^{6}-6 x^{2} y^{4}+6 x^{4} y^{2}-2 x^{6}}} \]

[[_1st_order, _with_linear_symmetries]]

10965

\[ {}y^{\prime } = \frac {y \sin \left (\frac {3 y}{2 x}\right ) \cos \left (\frac {y}{2 x}\right ) x +y \sin \left (\frac {3 y}{2 x}\right ) \cos \left (\frac {y}{2 x}\right )+y \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right ) x +y \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right )-\sin \left (\frac {y}{x}\right ) y x -y \sin \left (\frac {y}{x}\right )+2 \sin \left (\frac {y}{x}\right ) \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right ) x}{2 \cos \left (\frac {y}{x}\right ) \sin \left (\frac {y}{2 x}\right ) x \cos \left (\frac {y}{2 x}\right ) \left (x +1\right )} \]

[[_homogeneous, ‘class D‘]]

10967

\[ {}y^{\prime } = \frac {\left (1+x y\right )^{3}}{x^{5}} \]

[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel]

10969

\[ {}y^{\prime } = y \left (y^{2}+y \,{\mathrm e}^{b x}+{\mathrm e}^{2 b x}\right ) {\mathrm e}^{-2 b x} \]

[[_1st_order, _with_linear_symmetries], _Abel]

10970

\[ {}y^{\prime } = y^{3}-3 y^{2} x^{2}+3 y x^{4}-x^{6}+2 x \]

[[_1st_order, _with_linear_symmetries], _Abel]

10971

\[ {}y^{\prime } = y^{3}+y^{2} x^{2}+\frac {y x^{4}}{3}+\frac {x^{6}}{27}-\frac {2 x}{3} \]

[[_1st_order, _with_linear_symmetries], _Abel]

10975

\[ {}y^{\prime } = \frac {y^{3}-3 x y^{2}+3 x^{2} y-x^{3}+x}{x} \]

[[_1st_order, _with_linear_symmetries], _rational, _Abel]

10978

\[ {}y^{\prime } = \frac {y \,{\mathrm e}^{-\frac {x^{2}}{2}} \left (2 y^{2}+2 y \,{\mathrm e}^{\frac {x^{2}}{4}}+2 \,{\mathrm e}^{\frac {x^{2}}{2}}+x \,{\mathrm e}^{\frac {x^{2}}{2}}\right )}{2} \]

[_Abel]

10979

\[ {}y^{\prime } = \frac {y^{3}-3 x y^{2}+3 x^{2} y-x^{3}+x^{2}}{\left (-1+x \right ) \left (x +1\right )} \]

[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel]

10981

\[ {}y^{\prime } = \frac {\left (1+x y\right ) \left (y^{2} x^{2}+x^{2} y+2 x y+1+x +x^{2}\right )}{x^{5}} \]

[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel]

10995

\[ {}y^{\prime } = \frac {\left (y-x +\ln \left (x +1\right )\right )^{2}+x}{x +1} \]

[[_1st_order, _with_linear_symmetries], _Riccati]

11923

\[ {}y^{\prime } = f \left (y\right ) \]

[_quadrature]

11927

\[ {}y^{\prime } = f \left (\frac {y}{x}\right ) \]

[[_homogeneous, ‘class A‘], _dAlembert]

11934

\[ {}y^{\prime } = a \,x^{n} y^{2}+b \,x^{-n -2} \]

[[_homogeneous, ‘class G‘], _Riccati]

11940

\[ {}x^{2} y^{\prime } = a \,x^{2} y^{2}+b \]

[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]]

11945

\[ {}x^{4} y^{\prime } = -x^{4} y^{2}-a^{2} \]

[_rational, [_Riccati, _special]]

11947

\[ {}\left (a \,x^{2}+b x +c \right )^{2} \left (y^{\prime }+y^{2}\right )+A = 0 \]

[_rational, _Riccati]

11966

\[ {}x y^{\prime } = a \,x^{n} y^{2}+b y+c \,x^{-n} \]

[[_homogeneous, ‘class G‘], _rational, _Riccati]

11973

\[ {}\left (a x +c \right ) y^{\prime } = \alpha \left (b x +a y\right )^{2}+\beta \left (b x +a y\right )-b x +\gamma \]

[[_1st_order, _with_linear_symmetries], _rational, _Riccati]

11976

\[ {}x^{2} y^{\prime } = a \,x^{2} y^{2}+b x y+c \]

[[_homogeneous, ‘class G‘], _rational, _Riccati]

11985

\[ {}\left (a \,x^{2}+b \right ) y^{\prime }+y^{2}-2 x y+\left (1-a \right ) x^{2}-b = 0 \]

[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]

11986

\[ {}\left (a \,x^{2}+b x +c \right ) y^{\prime } = y^{2}+\left (2 \lambda x +b \right ) y+\lambda \left (\lambda -a \right ) x^{2}+\mu \]

[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]

11990

\[ {}\left (x -a \right ) \left (x -b \right ) y^{\prime }+y^{2}+k \left (y+x -a \right ) \left (y+x -b \right ) = 0 \]

[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]

12016

\[ {}y^{\prime } = a \,{\mathrm e}^{\lambda x} y^{2}+b y+c \,{\mathrm e}^{-\lambda x} \]

[[_1st_order, _with_linear_symmetries], _Riccati]

12028

\[ {}y^{\prime } = a \,{\mathrm e}^{\lambda x} y^{2}+b \,{\mathrm e}^{-\lambda x} \]

[[_1st_order, _with_linear_symmetries], _Riccati]

12089

\[ {}x y^{\prime } = \left (a y+b \ln \left (x \right )\right )^{2} \]

[[_1st_order, _with_linear_symmetries], _Riccati]

12247

\[ {}y y^{\prime }-y = A \]

[_quadrature]

12248

\[ {}y y^{\prime }-y = A x +B \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

12326

\[ {}y y^{\prime } = \frac {y}{\sqrt {a x +b}}+1 \]

[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class B‘]]

12336

\[ {}y y^{\prime } = \left (3 a x +b \right ) y-a^{2} x^{3}-a \,x^{2} b +c x \]

[_rational, [_Abel, ‘2nd type‘, ‘class A‘]]

12415

\[ {}\left (A y+B x +a \right ) y^{\prime }+B y+k x +b = 0 \]

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

12416

\[ {}\left (y+a x +b \right ) y^{\prime } = \alpha y+\beta x +\gamma \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

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]

12723

\[ {}6 x -2 y+1+\left (2 y-2 x -3\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

12725

\[ {}\left (x +1\right ) y^{2}-x^{3} y^{\prime } = 0 \]

[_separable]

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

\[ {}y^{2}-x y+x^{2} y^{\prime } = 0 \]

[[_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]

12734

\[ {}4 x +3 y+1+\left (x +y+1\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

12735

\[ {}4 x -y+2+\left (x +y+3\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

12736

\[ {}2 x +y-\left (4 x +2 y-1\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

12737

\[ {}y+2 x y^{2}-y^{3} x^{2}+2 x^{2} y y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _rational, _Riccati]

12738

\[ {}2 y+3 x y^{2}+\left (2 x^{2} y+x \right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

12739

\[ {}y+x y^{2}+\left (x -x^{2} y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

12742

\[ {}y^{\prime }-\frac {2 y}{x +1} = \left (x +1\right )^{3} \]

[_linear]

12744

\[ {}x^{2} y^{\prime }+\left (1-2 x \right ) y = x^{2} \]

[_linear]

12749

\[ {}y^{\prime }-\frac {y+1}{x +1} = \sqrt {y+1} \]

[[_1st_order, _with_linear_symmetries]]

12750

\[ {}x^{4} y \left (3 y+2 x y^{\prime }\right )+x^{2} \left (4 y+3 x y^{\prime }\right ) = 0 \]

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

12751

\[ {}y^{2} \left (3 y-6 x y^{\prime }\right )-x \left (y-2 x y^{\prime }\right ) = 0 \]

[_separable]

12752

\[ {}2 x^{3} y-y^{2}-\left (2 x^{4}+x y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

12753

\[ {}y^{2}-x y+x^{2} y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

12755

\[ {}x +y-\left (x -y\right ) y^{\prime } = 0 \]

[[_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]

12757

\[ {}x -y^{2}+2 x y y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _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‘]]

12762

\[ {}x^{3} y-y^{4}+\left (x y^{3}-x^{4}\right ) y^{\prime } = 0 \]

[_separable]

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]

12764

\[ {}x y^{\prime }-y+2 x^{2} y-x^{3} = 0 \]

[_linear]

12765

\[ {}\left (x +y\right ) y^{\prime }-1 = 0 \]

[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]

12766

\[ {}x +y y^{\prime }+y-x y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

12769

\[ {}\sqrt {1-y^{2}}+\sqrt {-x^{2}+1}\, y^{\prime } = 0 \]

[_separable]

12770

\[ {}y^{\prime }-x^{2} y = x^{5} \]

[_linear]

12771

\[ {}\left (y-x \right )^{2} y^{\prime } = 1 \]

[[_homogeneous, ‘class C‘], _dAlembert]

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]

12778

\[ {}x -2 y+5+\left (2 x -y+4\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

12780

\[ {}\left (-x^{2}+1\right ) y^{\prime }-x y = a x y^{2} \]

[_separable]

12781

\[ {}x y^{2} \left (3 y+x y^{\prime }\right )-2 y+x y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _rational]

12782

\[ {}\left (x^{2}+1\right ) y^{\prime }+y = \arctan \left (x \right ) \]

[_linear]

12783

\[ {}5 x y-3 y^{3}+\left (3 x^{2}-7 x y^{2}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _rational]

12785

\[ {}x y^{2}+y-x y^{\prime } = 0 \]

[[_homogeneous, ‘class D‘], _rational, _Bernoulli]

12787

\[ {}3 x^{2} y+\left (x^{3}+x^{3} y^{2}\right ) y^{\prime } = 0 \]

[_separable]

12789

\[ {}2 x +3 y-1+\left (2 x +3 y-5\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

12790

\[ {}y^{3}-2 x^{2} y+\left (2 x y^{2}-x^{3}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

12792

\[ {}\left (x^{2}+y^{2}\right ) \left (y y^{\prime }+x \right )+\sqrt {1+x^{2}+y^{2}}\, \left (y-x y^{\prime }\right ) = 0 \]

[[_1st_order, _with_linear_symmetries]]

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]

12794

\[ {}x y^{\prime }+y-y^{2} \ln \left (x \right ) = 0 \]

[_Bernoulli]

12796

\[ {}\left (2 \sqrt {x y}-x \right ) y^{\prime }+y = 0 \]

[[_homogeneous, ‘class A‘], _dAlembert]

12803

\[ {}2 x y^{\prime }-y+\ln \left (y^{\prime }\right ) = 0 \]

[[_1st_order, _with_linear_symmetries], _dAlembert]

12806

\[ {}y^{\prime }+2 x y = x^{2}+y^{2} \]

[[_homogeneous, ‘class C‘], _Riccati]

12809

\[ {}x +y^{\prime } y \left (2 {y^{\prime }}^{2}+3\right ) = 0 \]

[[_homogeneous, ‘class A‘], _dAlembert]

12812

\[ {}{y^{\prime }}^{3}-4 x y y^{\prime }+8 y^{2} = 0 \]

[[_1st_order, _with_linear_symmetries]]

12819

\[ {}y = 2 x y^{\prime }+y^{2} {y^{\prime }}^{3} \]

[[_1st_order, _with_linear_symmetries]]

12827

\[ {}\left (-y+x y^{\prime }\right ) \left (y y^{\prime }+x \right ) = a^{2} y^{\prime } \]

[_rational]

12946

\[ {}x^{\prime } = \frac {2 x}{t} \]

[_separable]

12947

\[ {}x^{\prime } = -\frac {t}{x} \]

[_separable]

12948

\[ {}x^{\prime } = -x^{2} \]

[_quadrature]

12950

\[ {}x^{\prime } = {\mathrm e}^{-x} \]

[_quadrature]

12951

\[ {}x^{\prime }+2 x = t^{2}+4 t +7 \]

[[_linear, ‘class A‘]]

12952

\[ {}2 t x^{\prime } = x \]

[_separable]

12955

\[ {}x^{\prime } = x \left (1-\frac {x}{4}\right ) \]

[_quadrature]

12965

\[ {}x^{\prime } = \sqrt {x} \]
i.c.

[_quadrature]

12966

\[ {}x^{\prime } = {\mathrm e}^{-2 x} \]
i.c.

[_quadrature]

12967

\[ {}y^{\prime } = 1+y^{2} \]

[_quadrature]

12968

\[ {}u^{\prime } = \frac {1}{5-2 u} \]

[_quadrature]

12969

\[ {}x^{\prime } = a x+b \]

[_quadrature]

12970

\[ {}Q^{\prime } = \frac {Q}{4+Q^{2}} \]

[_quadrature]

12971

\[ {}x^{\prime } = {\mathrm e}^{x^{2}} \]

[_quadrature]

12972

\[ {}y^{\prime } = r \left (a -y\right ) \]

[_quadrature]

12973

\[ {}x^{\prime } = \frac {2 x}{t +1} \]

[_separable]

12975

\[ {}\left (2 u+1\right ) u^{\prime }-t -1 = 0 \]

[_separable]

12976

\[ {}R^{\prime } = \left (t +1\right ) \left (1+R^{2}\right ) \]

[_separable]

12977

\[ {}y^{\prime }+y+\frac {1}{y} = 0 \]

[_quadrature]

12978

\[ {}\left (t +1\right ) x^{\prime }+x^{2} = 0 \]

[_separable]

12979

\[ {}y^{\prime } = \frac {1}{2 y+1} \]
i.c.

[_quadrature]

12980

\[ {}x^{\prime } = \left (4 t -x\right )^{2} \]
i.c.

[[_homogeneous, ‘class C‘], _Riccati]

12981

\[ {}x^{\prime } = 2 t x^{2} \]
i.c.

[_separable]

12982

\[ {}x^{\prime } = t^{2} {\mathrm e}^{-x} \]
i.c.

[_separable]

12983

\[ {}x^{\prime } = x \left (x+4\right ) \]
i.c.

[_quadrature]

12984

\[ {}x^{\prime } = {\mathrm e}^{t +x} \]
i.c.

[_separable]

12985

\[ {}T^{\prime } = 2 a t \left (T^{2}-a^{2}\right ) \]
i.c.

[_separable]

12988

\[ {}y^{\prime } = \frac {2 t y^{2}}{t^{2}+1} \]
i.c.

[_separable]

12990

\[ {}x^{\prime } = 6 t \left (x-1\right )^{{2}/{3}} \]

[_separable]

12991

\[ {}x^{\prime } = \frac {4 t^{2}+3 x^{2}}{2 t x} \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

12992

\[ {}x^{\prime } {\mathrm e}^{2 t}+2 x \,{\mathrm e}^{2 t} = {\mathrm e}^{-t} \]
i.c.

[[_linear, ‘class A‘]]

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]

13002

\[ {}x^{\prime } = -\frac {2 x}{t}+t \]

[_linear]

13003

\[ {}y^{\prime }+y = {\mathrm e}^{t} \]

[[_linear, ‘class A‘]]

13004

\[ {}x^{\prime }+2 t x = {\mathrm e}^{-t^{2}} \]

[_linear]

13005

\[ {}t x^{\prime } = -x+t^{2} \]

[_linear]

13006

\[ {}\theta ^{\prime } = -a \theta +{\mathrm e}^{t b} \]

[[_linear, ‘class A‘]]

13007

\[ {}\left (t^{2}+1\right ) x^{\prime } = -3 t x+6 t \]

[_separable]

13008

\[ {}x^{\prime }+\frac {5 x}{t} = t +1 \]
i.c.

[_linear]

13009

\[ {}x^{\prime } = \left (a +\frac {b}{t}\right ) x \]
i.c.

[_separable]

13011

\[ {}N^{\prime } = N-9 \,{\mathrm e}^{-t} \]

[[_linear, ‘class A‘]]

13012

\[ {}\cos \left (\theta \right ) v^{\prime }+v = 3 \]

[_separable]

13013

\[ {}R^{\prime } = \frac {R}{t}+t \,{\mathrm e}^{-t} \]
i.c.

[_linear]

13015

\[ {}x^{\prime } = 2 t x \]

[_separable]

13018

\[ {}x^{\prime } = \left (t +x\right )^{2} \]

[[_homogeneous, ‘class C‘], _Riccati]

13019

\[ {}x^{\prime } = a x+b \]

[_quadrature]

13020

\[ {}x^{\prime }+p \left (t \right ) x = 0 \]

[_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]

13027

\[ {}x^{3}+3 t x^{2} x^{\prime } = 0 \]

[_separable]

13030

\[ {}x+3 t x^{2} x^{\prime } = 0 \]

[_separable]

13031

\[ {}x^{2}-t^{2} x^{\prime } = 0 \]

[_separable]

13032

\[ {}t \cot \left (x\right ) x^{\prime } = -2 \]

[_separable]

13167

\[ {}y^{\prime }+y = x +1 \]

[[_linear, ‘class A‘]]

13171

\[ {}2 x y y^{\prime }+x^{2}+y^{2} = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli]

13172

\[ {}x y^{\prime }+y = x^{3} y^{3} \]

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

13173

\[ {}y^{\prime }+3 y = 3 x^{2} {\mathrm e}^{-3 x} \]

[[_linear, ‘class A‘]]

13174

\[ {}y^{\prime }+4 x y = 8 x \]

[_separable]

13183

\[ {}y^{\prime }+y = 2 x \,{\mathrm e}^{-x} \]
i.c.

[[_linear, ‘class A‘]]

13184

\[ {}y^{\prime }+y = 2 x \,{\mathrm e}^{-x} \]
i.c.

[[_linear, ‘class A‘]]

13191

\[ {}y^{\prime } = \frac {y^{2}}{-2+x} \]
i.c.

[_separable]

13192

\[ {}y^{\prime } = y^{{1}/{3}} \]
i.c.

[_quadrature]

13193

\[ {}3 x +2 y+\left (2 x +y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

13200

\[ {}\frac {\left (2 s-1\right ) s^{\prime }}{t}+\frac {s-s^{2}}{t^{2}} = 0 \]

[_separable]

13206

\[ {}\frac {3-y}{x^{2}}+\frac {\left (y^{2}-2 x \right ) y^{\prime }}{x y^{2}} = 0 \]
i.c.

[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]

13207

\[ {}\frac {1+8 x y^{{2}/{3}}}{x^{{2}/{3}} y^{{1}/{3}}}+\frac {\left (2 x^{{4}/{3}} y^{{2}/{3}}-x^{{1}/{3}}\right ) y^{\prime }}{y^{{4}/{3}}} = 0 \]
i.c.

[[_homogeneous, ‘class G‘], _exact, _rational]

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]

13210

\[ {}y+x \left (x^{2}+y^{2}\right )^{2}+\left (y \left (x^{2}+y^{2}\right )^{2}-x \right ) y^{\prime } = 0 \]

[[_1st_order, _with_linear_symmetries], _rational]

13211

\[ {}4 x y+\left (x^{2}+1\right ) y^{\prime } = 0 \]

[_separable]

13212

\[ {}x y+2 x +y+2+\left (x^{2}+2 x \right ) y^{\prime } = 0 \]

[_separable]

13213

\[ {}2 r \left (s^{2}+1\right )+\left (r^{4}+1\right ) s^{\prime } = 0 \]

[_separable]

13215

\[ {}\tan \left (\theta \right )+2 r \theta ^{\prime } = 0 \]

[_separable]

13218

\[ {}x +y-x y^{\prime } = 0 \]

[_linear]

13219

\[ {}2 x y+3 y^{2}-\left (2 x y+x^{2}\right ) y^{\prime } = 0 \]

[[_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]

13225

\[ {}y+2+y \left (x +4\right ) y^{\prime } = 0 \]
i.c.

[_separable]

13228

\[ {}x^{2}+3 y^{2}-2 x y y^{\prime } = 0 \]
i.c.

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

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

\[ {}2 x^{2}+2 x y+y^{2}+\left (2 x y+x^{2}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

13235

\[ {}y^{\prime }+\frac {3 y}{x} = 6 x^{2} \]

[_linear]

13236

\[ {}x^{4} y^{\prime }+2 x^{3} y = 1 \]

[_linear]

13237

\[ {}y^{\prime }+3 y = 3 x^{2} {\mathrm e}^{-3 x} \]

[[_linear, ‘class A‘]]

13238

\[ {}y^{\prime }+4 x y = 8 x \]

[_separable]

13239

\[ {}x^{\prime }+\frac {x}{t^{2}} = \frac {1}{t^{2}} \]

[_separable]

13240

\[ {}\left (u^{2}+1\right ) v^{\prime }+4 v u = 3 u \]

[_separable]

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]

13253

\[ {}x y^{\prime }-2 y = 2 x^{4} \]
i.c.

[_linear]

13254

\[ {}y^{\prime }+3 x^{2} y = x^{2} \]
i.c.

[_separable]

13256

\[ {}2 x \left (y+1\right )-\left (x^{2}+1\right ) y^{\prime } = 0 \]
i.c.

[_separable]

13259

\[ {}y^{\prime }+\frac {y}{2 x} = \frac {x}{y^{3}} \]
i.c.

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

13265

\[ {}a y^{\prime }+b y = k \,{\mathrm e}^{-\lambda x} \]

[[_linear, ‘class A‘]]

13269

\[ {}y^{\prime } = \left (1-x \right ) y^{2}+\left (2 x -1\right ) y-x \]

[_Riccati]

13271

\[ {}y^{\prime } = -8 x y^{2}+4 x \left (1+4 x \right ) y-8 x^{3}-4 x^{2}+1 \]

[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]

13272

\[ {}6 x^{2} y-\left (x^{3}+1\right ) y^{\prime } = 0 \]

[_separable]

13273

\[ {}\left (3 y^{2} x^{2}-x \right ) y^{\prime }+2 x y^{3}-y = 0 \]

[[_homogeneous, ‘class G‘], _exact, _rational]

13274

\[ {}y-1+x \left (x +1\right ) y^{\prime } = 0 \]

[_separable]

13275

\[ {}x^{2}-2 y+x y^{\prime } = 0 \]

[_linear]

13276

\[ {}3 x -5 y+\left (x +y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

13277

\[ {}{\mathrm e}^{2 x} y^{2}+\left ({\mathrm e}^{2 x} y-2 y\right ) y^{\prime } = 0 \]

[_separable]

13278

\[ {}8 x^{3} y-12 x^{3}+\left (x^{4}+1\right ) y^{\prime } = 0 \]

[_separable]

13279

\[ {}2 x^{2}+x y+y^{2}+2 x^{2} y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Riccati]

13280

\[ {}y^{\prime } = \frac {4 x^{3} y^{2}-3 x^{2} y}{x^{3}-2 y x^{4}} \]

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

13281

\[ {}\left (x +1\right ) y^{\prime }+x y = {\mathrm e}^{-x} \]

[_linear]

13282

\[ {}y^{\prime } = \frac {2 x -7 y}{3 y-8 x} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

13283

\[ {}x^{2} y^{\prime }+x y = x y^{3} \]

[_separable]

13284

\[ {}\left (x^{3}+1\right ) y^{\prime }+6 x^{2} y = 6 x^{2} \]

[_separable]

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]

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]

13291

\[ {}y^{\prime } = \frac {2 x +7 y}{2 x -2 y} \]
i.c.

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

13292

\[ {}y^{\prime } = \frac {x y}{x^{2}+1} \]
i.c.

[_separable]

13295

\[ {}x^{2} y^{\prime }+x y = \frac {y^{3}}{x} \]
i.c.

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

13300

\[ {}4 x y^{2}+6 y+\left (5 x^{2} y+8 x \right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

13301

\[ {}8 y^{3} x^{2}-2 y^{4}+\left (5 x^{3} y^{2}-8 x y^{3}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

13302

\[ {}5 x +2 y+1+\left (2 x +y+1\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

13303

\[ {}3 x -y+1-\left (6 x -2 y-3\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

13304

\[ {}x -2 y-3+\left (2 x +y-1\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

13305

\[ {}10 x -4 y+12-\left (x +5 y+3\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

13306

\[ {}6 x +4 y+1+\left (4 x +2 y+2\right ) y^{\prime } = 0 \]
i.c.

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

13307

\[ {}3 x -y-6+\left (x +y+2\right ) y^{\prime } = 0 \]
i.c.

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

13308

\[ {}2 x +3 y+1+\left (4 x +6 y+1\right ) y^{\prime } = 0 \]
i.c.

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

13309

\[ {}4 x +3 y+1+\left (x +y+1\right ) y^{\prime } = 0 \]
i.c.

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

13634

\[ {}x^{\prime } {\mathrm e}^{3 t}+3 x \,{\mathrm e}^{3 t} = {\mathrm e}^{-t} \]
i.c.

[[_linear, ‘class A‘]]

13635

\[ {}x^{\prime } = -x+1 \]

[_quadrature]

13636

\[ {}x^{\prime } = x \left (2-x\right ) \]

[_quadrature]

13637

\[ {}x^{\prime } = \left (1+x\right ) \left (2-x\right ) \sin \left (x\right ) \]

[_quadrature]

13638

\[ {}x^{\prime } = -x \left (-x+1\right ) \left (2-x\right ) \]

[_quadrature]

13639

\[ {}x^{\prime } = x^{2}-x^{4} \]

[_quadrature]

13640

\[ {}x^{\prime } = t^{3} \left (-x+1\right ) \]
i.c.

[_separable]

13641

\[ {}y^{\prime } = \left (1+y^{2}\right ) \tan \left (x \right ) \]
i.c.

[_separable]

13642

\[ {}x^{\prime } = t^{2} x \]

[_separable]

13643

\[ {}x^{\prime } = -x^{2} \]

[_quadrature]

13644

\[ {}y^{\prime } = y^{2} {\mathrm e}^{-t^{2}} \]

[_separable]

13645

\[ {}x^{\prime }+p x = q \]

[_quadrature]

13646

\[ {}x y^{\prime } = k y \]

[_separable]

13647

\[ {}i^{\prime } = p \left (t \right ) i \]

[_separable]

13648

\[ {}x^{\prime } = \lambda x \]

[_quadrature]

13649

\[ {}m v^{\prime } = -m g +k v^{2} \]

[_quadrature]

13650

\[ {}x^{\prime } = k x-x^{2} \]
i.c.

[_quadrature]

13651

\[ {}x^{\prime } = -x \left (k^{2}+x^{2}\right ) \]
i.c.

[_quadrature]

13652

\[ {}y^{\prime }+\frac {y}{x} = x^{2} \]

[_linear]

13653

\[ {}x^{\prime }+t x = 4 t \]
i.c.

[_separable]

13658

\[ {}x^{\prime }+5 x = t \]

[[_linear, ‘class A‘]]

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]

13670

\[ {}x^{\prime } = k x-x^{2} \]

[_quadrature]

13770

\[ {}12 x +6 y-9+\left (5 x +2 y-3\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

13771

\[ {}x y^{\prime } = y+\sqrt {x^{2}+y^{2}} \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

13772

\[ {}x y^{\prime }+y = x^{3} \]

[_linear]

13773

\[ {}y-x y^{\prime } = x^{2} y y^{\prime } \]

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

13774

\[ {}x^{\prime }+3 x = {\mathrm e}^{2 t} \]

[[_linear, ‘class A‘]]

13776

\[ {}y^{\prime } = {\mathrm e}^{x -y} \]

[_separable]

13778

\[ {}x \left (\ln \left (x \right )-\ln \left (y\right )\right ) y^{\prime }-y = 0 \]

[[_homogeneous, ‘class A‘], _dAlembert]

13781

\[ {}x^{\prime } = {\mathrm e}^{\frac {x}{t}}+\frac {x}{t} \]

[[_homogeneous, ‘class A‘], _dAlembert]

13783

\[ {}y = x y^{\prime }+\frac {1}{y} \]

[_separable]

13785

\[ {}y^{\prime } = \frac {y}{x +y^{3}} \]

[[_homogeneous, ‘class G‘], _rational]

13788

\[ {}y^{\prime } = \frac {2 y-x -4}{2 x -y+5} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

13789

\[ {}y^{\prime }-\frac {y}{x +1}+y^{2} = 0 \]

[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli]

13793

\[ {}2 x +2 y-1+\left (x +y-2\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

13797

\[ {}y^{\prime } = \left (x -5 y\right )^{{1}/{3}}+2 \]

[[_homogeneous, ‘class C‘], _dAlembert]

13798

\[ {}\left (x -y\right ) y-x^{2} y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

13803

\[ {}y^{\prime } = \frac {3 x -4 y-2}{3 x -4 y-3} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

13806

\[ {}y^{\prime }-\frac {3 y}{x}+x^{3} y^{2} = 0 \]

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

13809

\[ {}3 y^{2}-x +2 y \left (y^{2}-3 x \right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _rational]

13810

\[ {}\left (x -y\right ) y-x^{2} y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

13811

\[ {}y^{\prime } = \frac {x +y-3}{1-x +y} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

13812

\[ {}x y^{\prime }+y-y^{2} \ln \left (x \right ) = 0 \]

[_Bernoulli]

13814

\[ {}\left (4 y+2 x +3\right ) y^{\prime }-2 y-x -1 = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

13816

\[ {}\left (y^{2}-x^{2}\right ) y^{\prime }+2 x y = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

13817

\[ {}3 x y^{2} y^{\prime }+y^{3}-2 x = 0 \]

[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli]

13870

\[ {}x^{2} y^{\prime } = 1+y^{2} \]

[_separable]

13873

\[ {}y^{\prime } = \cos \left (x +y\right ) \]

[[_homogeneous, ‘class C‘], _dAlembert]

13874

\[ {}x y^{\prime }+y = x y^{2} \]

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

13887

\[ {}y y^{\prime } = 1 \]

[_quadrature]

13889

\[ {}5 y^{\prime }-x y = 0 \]

[_separable]

14078

\[ {}x y \left (1-{y^{\prime }}^{2}\right ) = \left (x^{2}-y^{2}-a^{2}\right ) y^{\prime } \]

[_rational]

14083

\[ {}y-x y^{\prime } = 0 \]

[_separable]

14085

\[ {}1+y-\left (1-x \right ) y^{\prime } = 0 \]

[_separable]

14087

\[ {}y-a +x^{2} y^{\prime } = 0 \]

[_separable]

14088

\[ {}z-\left (-a^{2}+t^{2}\right ) z^{\prime } = 0 \]

[_separable]

14089

\[ {}y^{\prime } = \frac {1+y^{2}}{x^{2}+1} \]

[_separable]

14090

\[ {}1+s^{2}-\sqrt {t}\, s^{\prime } = 0 \]

[_separable]

14091

\[ {}r^{\prime }+r \tan \left (t \right ) = 0 \]

[_separable]

14092

\[ {}\left (x^{2}+1\right ) y^{\prime }-\sqrt {1-y^{2}} = 0 \]

[_separable]

14093

\[ {}\sqrt {-x^{2}+1}\, y^{\prime }-\sqrt {1-y^{2}} = 0 \]

[_separable]

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

\[ {}8 y+10 x +\left (5 y+7 x \right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

14101

\[ {}2 \sqrt {s t}-s+t s^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _dAlembert]

14102

\[ {}t -s+t s^{\prime } = 0 \]

[_linear]

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]

14105

\[ {}3 y-7 x +7-\left (3 x -7 y-3\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

14106

\[ {}x +2 y+1-\left (4 y+2 x +3\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

14107

\[ {}x +2 y+1-\left (2 x -3\right ) y^{\prime } = 0 \]

[_linear]

14108

\[ {}\frac {y-x y^{\prime }}{\sqrt {x^{2}+y^{2}}} = m \]

[[_homogeneous, ‘class A‘], _dAlembert]

14109

\[ {}\frac {y y^{\prime }+x}{\sqrt {x^{2}+y^{2}}} = m \]

[[_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]

14112

\[ {}y^{\prime }-\frac {2 y}{x +1} = \left (x +1\right )^{3} \]

[_linear]

14113

\[ {}y^{\prime }-\frac {a y}{x} = \frac {x +1}{x} \]

[_linear]

14118

\[ {}y^{\prime }+\frac {n y}{x} = a \,x^{-n} \]

[_linear]

14119

\[ {}y^{\prime }+y = {\mathrm e}^{-x} \]

[[_linear, ‘class A‘]]

14120

\[ {}y^{\prime }+\frac {\left (1-2 x \right ) y}{x^{2}}-1 = 0 \]

[_linear]

14122

\[ {}\left (-x^{2}+1\right ) y^{\prime }-x y+a x y^{2} = 0 \]

[_separable]

14125

\[ {}x y^{\prime } = \left (y \ln \left (x \right )-2\right ) y \]

[_Bernoulli]

14129

\[ {}\left (y^{3}-x \right ) y^{\prime } = y \]

[[_homogeneous, ‘class G‘], _exact, _rational]

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]

14135

\[ {}y y^{\prime }+x = \frac {y}{x^{2}+y^{2}}-\frac {x y^{\prime }}{x^{2}+y^{2}} \]

[[_1st_order, _with_linear_symmetries], _exact, _rational]

14142

\[ {}y = x y^{\prime }+y^{\prime } \]

[_separable]

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]

14200

\[ {}\left (x^{2}+1\right ) y^{\prime }-x y-\alpha = 0 \]

[_linear]

14201

\[ {}x \cos \left (\frac {y}{x}\right ) y^{\prime } = y \cos \left (\frac {y}{x}\right )-x \]

[[_homogeneous, ‘class A‘], _dAlembert]

14203

\[ {}x y^{\prime }+y-y^{2} \ln \left (x \right ) = 0 \]

[_Bernoulli]

14204

\[ {}2 x +2 y-1+\left (x +y-2\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

14232

\[ {}-y+x y^{\prime } = 0 \]

[_separable]

14236

\[ {}y^{\prime }+\frac {1}{2 y} = 0 \]

[_quadrature]

14237

\[ {}y^{\prime }-\frac {y}{x} = 1 \]

[_linear]

14239

\[ {}x^{2} y^{\prime }+2 x y = 0 \]

[_separable]

14240

\[ {}y^{\prime }-y^{2} = 1 \]

[_quadrature]

14243

\[ {}y^{\prime }+3 y = 0 \]

[_quadrature]

14247

\[ {}2 x y^{\prime }-y = 0 \]

[_separable]

14254

\[ {}y^{\prime }-2 x y = 0 \]

[_separable]

14255

\[ {}y^{\prime }+y = x^{2}+2 x -1 \]

[[_linear, ‘class A‘]]

14257

\[ {}y^{\prime } = x \sqrt {y} \]

[_separable]

14260

\[ {}x \ln \left (x \right ) y^{\prime }-\left (1+\ln \left (x \right )\right ) y = 0 \]

[_separable]

14274

\[ {}y^{\prime } = 1-y \]

[_quadrature]

14275

\[ {}y^{\prime } = y+1 \]

[_quadrature]

14276

\[ {}y^{\prime } = y^{2}-4 \]

[_quadrature]

14277

\[ {}y^{\prime } = 4-y^{2} \]

[_quadrature]

14278

\[ {}y^{\prime } = x y \]

[_separable]

14279

\[ {}y^{\prime } = -x y \]

[_separable]

14282

\[ {}y^{\prime } = x +y \]

[[_linear, ‘class A‘]]

14283

\[ {}y^{\prime } = x y \]

[_separable]

14284

\[ {}y^{\prime } = \frac {x}{y} \]

[_separable]

14285

\[ {}y^{\prime } = \frac {y}{x} \]

[_separable]

14286

\[ {}y^{\prime } = 1+y^{2} \]

[_quadrature]

14287

\[ {}y^{\prime } = y^{2}-3 y \]

[_quadrature]

14290

\[ {}y^{\prime } = {\mathrm e}^{x -y} \]

[_separable]

14291

\[ {}y^{\prime } = \ln \left (x +y\right ) \]

[[_homogeneous, ‘class C‘], _dAlembert]

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]

14296

\[ {}y^{\prime } = \frac {1}{x y} \]

[_separable]

14297

\[ {}y^{\prime } = \ln \left (y-1\right ) \]

[_quadrature]

14298

\[ {}y^{\prime } = \sqrt {\left (y+2\right ) \left (y-1\right )} \]

[_quadrature]

14299

\[ {}y^{\prime } = \frac {y}{y-x} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

14300

\[ {}y^{\prime } = \frac {x}{y^{2}} \]

[_separable]

14301

\[ {}y^{\prime } = \frac {\sqrt {y}}{x} \]

[_separable]

14303

\[ {}y^{\prime } = \left (x y\right )^{{1}/{3}} \]

[[_homogeneous, ‘class G‘]]

14304

\[ {}y^{\prime } = \sqrt {\frac {y-4}{x}} \]

[[_homogeneous, ‘class C‘], _dAlembert]

14305

\[ {}y^{\prime } = -\frac {y}{x}+y^{{1}/{4}} \]

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

14306

\[ {}y^{\prime } = 4 y-5 \]
i.c.

[_quadrature]

14307

\[ {}y^{\prime }+3 y = 1 \]
i.c.

[_quadrature]

14308

\[ {}y^{\prime } = a y+b \]
i.c.

[_quadrature]

14311

\[ {}y^{\prime } = \frac {y}{x}+\cos \left (x \right ) \]
i.c.

[_linear]

14317

\[ {}y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2} \]
i.c.

[[_1st_order, _with_linear_symmetries], _Clairaut]

14328

\[ {}y^{\prime } = 3 y \]
i.c.

[_quadrature]

14329

\[ {}y^{\prime } = 1-y \]
i.c.

[_quadrature]

14330

\[ {}y^{\prime } = 1-y \]
i.c.

[_quadrature]

14332

\[ {}y^{\prime } = \frac {y}{x} \]
i.c.

[_separable]

14333

\[ {}y^{\prime } = \frac {2 x}{y} \]
i.c.

[_separable]

14334

\[ {}y^{\prime } = -2 y+y^{2} \]
i.c.

[_quadrature]

14335

\[ {}y^{\prime } = x y+x \]
i.c.

[_separable]

14336

\[ {}x \,{\mathrm e}^{y}+y^{\prime } = 0 \]
i.c.

[_separable]

14337

\[ {}y-x^{2} y^{\prime } = 0 \]
i.c.

[_separable]

14338

\[ {}2 y y^{\prime } = 1 \]

[_quadrature]

14339

\[ {}2 x y y^{\prime }+y^{2} = -1 \]

[_separable]

14340

\[ {}y^{\prime } = \frac {1-x y}{x^{2}} \]

[_linear]

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‘]]

14342

\[ {}y^{\prime } = \frac {y^{2}}{1-x y} \]

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

14343

\[ {}y^{\prime } = 4 y+1 \]
i.c.

[_quadrature]

14345

\[ {}y^{\prime } = \frac {y}{x} \]
i.c.

[_separable]

14346

\[ {}y^{\prime } = \frac {y}{-1+x}+x^{2} \]
i.c.

[_linear]

14347

\[ {}y^{\prime } = \frac {y}{x}+\sin \left (x^{2}\right ) \]
i.c.

[_linear]

14348

\[ {}y^{\prime } = \frac {2 y}{x}+{\mathrm e}^{x} \]
i.c.

[_linear]

14350

\[ {}x -y y^{\prime } = 0 \]

[_separable]

14351

\[ {}y-x y^{\prime } = 0 \]

[_separable]

14352

\[ {}x^{2}-y+x y^{\prime } = 0 \]

[_linear]

14353

\[ {}x y \left (1-y\right )-2 y^{\prime } = 0 \]

[_separable]

14355

\[ {}\left (2 x -1\right ) y+x \left (x +1\right ) y^{\prime } = 0 \]

[_separable]

14357

\[ {}y^{\prime } = x +y \]
i.c.

[[_linear, ‘class A‘]]

14358

\[ {}y^{\prime } = \frac {y}{x} \]
i.c.

[_separable]

14359

\[ {}y^{\prime } = \frac {y}{x} \]
i.c.

[_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]

14370

\[ {}y^{\prime } = -\frac {3 x^{2}}{2 y} \]
i.c.

[_separable]

14371

\[ {}y^{\prime } = -\frac {3 x^{2}}{2 y} \]
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]

14383

\[ {}y^{\prime } = \sqrt {\left (y+2\right ) \left (y-1\right )} \]
i.c.

[_quadrature]

14384

\[ {}y^{\prime } = \sqrt {\left (y+2\right ) \left (y-1\right )} \]
i.c.

[_quadrature]

14386

\[ {}y^{\prime } = \frac {y}{y-x} \]
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‘]]

14396

\[ {}y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2} \]
i.c.

[[_1st_order, _with_linear_symmetries], _Clairaut]

14397

\[ {}y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2} \]
i.c.

[[_1st_order, _with_linear_symmetries], _Clairaut]

14398

\[ {}y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2} \]
i.c.

[[_1st_order, _with_linear_symmetries], _Clairaut]

14399

\[ {}y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2} \]
i.c.

[[_1st_order, _with_linear_symmetries], _Clairaut]

14400

\[ {}y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2} \]
i.c.

[[_1st_order, _with_linear_symmetries], _Clairaut]

14430

\[ {}y^{\prime }-i y = 0 \]
i.c.

[_quadrature]

14522

\[ {}y^{\prime } = \frac {y+1}{t +1} \]

[_separable]

14523

\[ {}y^{\prime } = t^{2} y^{2} \]

[_separable]

14524

\[ {}y^{\prime } = t^{4} y \]

[_separable]

14525

\[ {}y^{\prime } = 2 y+1 \]

[_quadrature]

14526

\[ {}y^{\prime } = 2-y \]

[_quadrature]

14527

\[ {}y^{\prime } = {\mathrm e}^{-y} \]

[_quadrature]

14528

\[ {}x^{\prime } = 1+x^{2} \]

[_quadrature]

14529

\[ {}y^{\prime } = 2 t y^{2}+3 y^{2} \]

[_separable]

14530

\[ {}y^{\prime } = \frac {t}{y} \]

[_separable]

14532

\[ {}y^{\prime } = t y^{{1}/{3}} \]

[_separable]

14533

\[ {}y^{\prime } = \frac {1}{2 y+1} \]

[_quadrature]

14534

\[ {}y^{\prime } = \frac {2 y+1}{t} \]

[_separable]

14535

\[ {}y^{\prime } = y \left (1-y\right ) \]

[_quadrature]

14537

\[ {}v^{\prime } = t^{2} v-2-2 v+t^{2} \]

[_separable]

14538

\[ {}y^{\prime } = \frac {1}{t y+t +y+1} \]

[_separable]

14540

\[ {}y^{\prime } = y^{2}-4 \]

[_quadrature]

14541

\[ {}w^{\prime } = \frac {w}{t} \]

[_separable]

14542

\[ {}y^{\prime } = \sec \left (y\right ) \]

[_quadrature]

14543

\[ {}x^{\prime } = -t x \]
i.c.

[_separable]

14544

\[ {}y^{\prime } = t y \]
i.c.

[_separable]

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]

14549

\[ {}y^{\prime } = 2 y+1 \]
i.c.

[_quadrature]

14550

\[ {}y^{\prime } = t y^{2}+2 y^{2} \]
i.c.

[_separable]

14552

\[ {}y^{\prime } = \frac {1-y^{2}}{y} \]
i.c.

[_quadrature]

14553

\[ {}y^{\prime } = \left (y^{2}+1\right ) t \]
i.c.

[_separable]

14554

\[ {}y^{\prime } = \frac {1}{2 y+3} \]
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]

14559

\[ {}y^{\prime } = 1-2 y \]

[_quadrature]

14560

\[ {}y^{\prime } = 4 y^{2} \]

[_quadrature]

14561

\[ {}y^{\prime } = 2 y \left (1-y\right ) \]

[_quadrature]

14562

\[ {}y^{\prime } = y+t +1 \]

[[_linear, ‘class A‘]]

14563

\[ {}y^{\prime } = 3 y \left (1-y\right ) \]
i.c.

[_quadrature]

14564

\[ {}y^{\prime } = 2 y-t \]
i.c.

[[_linear, ‘class A‘]]

14566

\[ {}y^{\prime } = \left (t +1\right ) y \]
i.c.

[_separable]

14567

\[ {}S^{\prime } = S^{3}-2 S^{2}+S \]
i.c.

[_quadrature]

14568

\[ {}S^{\prime } = S^{3}-2 S^{2}+S \]
i.c.

[_quadrature]

14569

\[ {}S^{\prime } = S^{3}-2 S^{2}+S \]
i.c.

[_quadrature]

14570

\[ {}S^{\prime } = S^{3}-2 S^{2}+S \]
i.c.

[_quadrature]

14571

\[ {}S^{\prime } = S^{3}-2 S^{2}+S \]
i.c.

[_quadrature]

14572

\[ {}y^{\prime } = y^{2}+y \]

[_quadrature]

14573

\[ {}y^{\prime } = y^{2}-y \]

[_quadrature]

14574

\[ {}y^{\prime } = y^{3}+y^{2} \]

[_quadrature]

14576

\[ {}y^{\prime } = t y+t y^{2} \]

[_separable]

14577

\[ {}y^{\prime } = t^{2}+t^{2} y \]

[_separable]

14578

\[ {}y^{\prime } = t +t y \]

[_separable]

14580

\[ {}\theta ^{\prime } = \frac {9}{10}-\frac {11 \cos \left (\theta \right )}{10} \]

[_quadrature]

14582

\[ {}\theta ^{\prime } = \frac {11}{10}-\frac {9 \cos \left (\theta \right )}{10} \]

[_quadrature]

14583

\[ {}v^{\prime } = -\frac {v}{R C} \]

[_quadrature]

14584

\[ {}v^{\prime } = \frac {K -v}{R C} \]

[_quadrature]

14586

\[ {}y^{\prime } = 2 y+1 \]
i.c.

[_quadrature]

14590

\[ {}w^{\prime } = \left (3-w\right ) \left (w+1\right ) \]
i.c.

[_quadrature]

14591

\[ {}w^{\prime } = \left (3-w\right ) \left (w+1\right ) \]
i.c.

[_quadrature]

14592

\[ {}y^{\prime } = {\mathrm e}^{\frac {2}{y}} \]
i.c.

[_quadrature]

14593

\[ {}y^{\prime } = {\mathrm e}^{\frac {2}{y}} \]
i.c.

[_quadrature]

14594

\[ {}y^{\prime } = y^{2}-y^{3} \]
i.c.

[_quadrature]

14596

\[ {}y^{\prime } = \sqrt {y} \]
i.c.

[_quadrature]

14597

\[ {}y^{\prime } = 2-y \]
i.c.

[_quadrature]

14598

\[ {}\theta ^{\prime } = \frac {9}{10}-\frac {11 \cos \left (\theta \right )}{10} \]
i.c.

[_quadrature]

14599

\[ {}y^{\prime } = y \left (y-1\right ) \left (y-3\right ) \]
i.c.

[_quadrature]

14600

\[ {}y^{\prime } = y \left (y-1\right ) \left (y-3\right ) \]
i.c.

[_quadrature]

14601

\[ {}y^{\prime } = y \left (y-1\right ) \left (y-3\right ) \]
i.c.

[_quadrature]

14602

\[ {}y^{\prime } = y \left (y-1\right ) \left (y-3\right ) \]
i.c.

[_quadrature]

14603

\[ {}y^{\prime } = -y^{2} \]

[_quadrature]

14604

\[ {}y^{\prime } = y^{3} \]
i.c.

[_quadrature]

14605

\[ {}y^{\prime } = \frac {1}{\left (y+1\right ) \left (t -2\right )} \]
i.c.

[_separable]

14606

\[ {}y^{\prime } = \frac {1}{\left (2+y\right )^{2}} \]
i.c.

[_quadrature]

14607

\[ {}y^{\prime } = \frac {t}{y-2} \]
i.c.

[_separable]

14608

\[ {}y^{\prime } = 3 y \left (y-2\right ) \]
i.c.

[_quadrature]

14609

\[ {}y^{\prime } = 3 y \left (y-2\right ) \]
i.c.

[_quadrature]

14610

\[ {}y^{\prime } = 3 y \left (y-2\right ) \]
i.c.

[_quadrature]

14611

\[ {}y^{\prime } = 3 y \left (y-2\right ) \]
i.c.

[_quadrature]

14612

\[ {}y^{\prime } = y^{2}-4 y-12 \]
i.c.

[_quadrature]

14613

\[ {}y^{\prime } = y^{2}-4 y-12 \]
i.c.

[_quadrature]

14614

\[ {}y^{\prime } = y^{2}-4 y-12 \]
i.c.

[_quadrature]

14615

\[ {}y^{\prime } = y^{2}-4 y-12 \]
i.c.

[_quadrature]

14618

\[ {}y^{\prime } = \cos \left (y\right ) \]
i.c.

[_quadrature]

14620

\[ {}w^{\prime } = w \cos \left (w\right ) \]

[_quadrature]

14621

\[ {}w^{\prime } = w \cos \left (w\right ) \]
i.c.

[_quadrature]

14622

\[ {}w^{\prime } = w \cos \left (w\right ) \]
i.c.

[_quadrature]

14623

\[ {}w^{\prime } = w \cos \left (w\right ) \]
i.c.

[_quadrature]

14624

\[ {}w^{\prime } = w \cos \left (w\right ) \]
i.c.

[_quadrature]

14625

\[ {}w^{\prime } = \left (1-w\right ) \sin \left (w\right ) \]

[_quadrature]

14626

\[ {}y^{\prime } = \frac {1}{y-2} \]

[_quadrature]

14627

\[ {}v^{\prime } = -v^{2}-2 v-2 \]

[_quadrature]

14628

\[ {}w^{\prime } = 3 w^{3}-12 w^{2} \]

[_quadrature]

14629

\[ {}y^{\prime } = 1+\cos \left (y\right ) \]

[_quadrature]

14630

\[ {}y^{\prime } = \tan \left (y\right ) \]

[_quadrature]

14632

\[ {}w^{\prime } = \left (w^{2}-2\right ) \arctan \left (w\right ) \]

[_quadrature]

14633

\[ {}y^{\prime } = y^{2}-4 y+2 \]
i.c.

[_quadrature]

14634

\[ {}y^{\prime } = y^{2}-4 y+2 \]
i.c.

[_quadrature]

14635

\[ {}y^{\prime } = y^{2}-4 y+2 \]
i.c.

[_quadrature]

14636

\[ {}y^{\prime } = y^{2}-4 y+2 \]
i.c.

[_quadrature]

14637

\[ {}y^{\prime } = y^{2}-4 y+2 \]
i.c.

[_quadrature]

14638

\[ {}y^{\prime } = y^{2}-4 y+2 \]
i.c.

[_quadrature]

14639

\[ {}y^{\prime } = y \cos \left (\frac {\pi y}{2}\right ) \]

[_quadrature]

14640

\[ {}y^{\prime } = y-y^{2} \]

[_quadrature]

14641

\[ {}y^{\prime } = y \sin \left (\frac {\pi y}{2}\right ) \]

[_quadrature]

14642

\[ {}y^{\prime } = y^{3}-y^{2} \]

[_quadrature]

14643

\[ {}y^{\prime } = \cos \left (\frac {\pi y}{2}\right ) \]

[_quadrature]

14644

\[ {}y^{\prime } = y^{2}-y \]

[_quadrature]

14645

\[ {}y^{\prime } = y \sin \left (\frac {\pi y}{2}\right ) \]

[_quadrature]

14646

\[ {}y^{\prime } = y^{2}-y^{3} \]

[_quadrature]

14647

\[ {}y^{\prime } = -4 y+9 \,{\mathrm e}^{-t} \]

[[_linear, ‘class A‘]]

14648

\[ {}y^{\prime } = -4 y+3 \,{\mathrm e}^{-t} \]

[[_linear, ‘class A‘]]

14651

\[ {}y^{\prime } = 3 y-4 \,{\mathrm e}^{3 t} \]

[[_linear, ‘class A‘]]

14652

\[ {}y^{\prime } = \frac {y}{2}+4 \,{\mathrm e}^{\frac {t}{2}} \]

[[_linear, ‘class A‘]]

14653

\[ {}y^{\prime }+2 y = {\mathrm e}^{\frac {t}{3}} \]
i.c.

[[_linear, ‘class A‘]]

14654

\[ {}y^{\prime }-2 y = 3 \,{\mathrm e}^{-2 t} \]
i.c.

[[_linear, ‘class A‘]]

14657

\[ {}y^{\prime }-2 y = 7 \,{\mathrm e}^{2 t} \]
i.c.

[[_linear, ‘class A‘]]

14658

\[ {}y^{\prime }+2 y = 3 t^{2}+2 t -1 \]

[[_linear, ‘class A‘]]

14659

\[ {}y^{\prime }+2 y = t^{2}+2 t +1+{\mathrm e}^{4 t} \]

[[_linear, ‘class A‘]]

14661

\[ {}y^{\prime }-3 y = 2 t -{\mathrm e}^{4 t} \]

[[_linear, ‘class A‘]]

14663

\[ {}y^{\prime } = -\frac {y}{t}+2 \]

[_linear]

14664

\[ {}y^{\prime } = \frac {3 y}{t}+t^{5} \]

[_linear]

14665

\[ {}y^{\prime } = -\frac {y}{t +1}+t^{2} \]

[_linear]

14666

\[ {}y^{\prime } = -2 t y+4 \,{\mathrm e}^{-t^{2}} \]

[_linear]

14667

\[ {}y^{\prime }-\frac {2 t y}{t^{2}+1} = 3 \]

[_linear]

14668

\[ {}y^{\prime }-\frac {2 y}{t} = t^{3} {\mathrm e}^{t} \]

[_linear]

14669

\[ {}y^{\prime } = -\frac {y}{t +1}+2 \]
i.c.

[_linear]

14670

\[ {}y^{\prime } = \frac {y}{t +1}+4 t^{2}+4 t \]
i.c.

[_linear]

14671

\[ {}y^{\prime } = -\frac {y}{t}+2 \]
i.c.

[_linear]

14672

\[ {}y^{\prime } = -2 t y+4 \,{\mathrm e}^{-t^{2}} \]
i.c.

[_linear]

14673

\[ {}y^{\prime }-\frac {2 y}{t} = 2 t^{2} \]
i.c.

[_linear]

14674

\[ {}y^{\prime }-\frac {3 y}{t} = 2 t^{3} {\mathrm e}^{2 t} \]
i.c.

[_linear]

14684

\[ {}y^{\prime } = -2 t y+4 \,{\mathrm e}^{-t^{2}} \]

[_linear]

14685

\[ {}y^{\prime }+2 y = 3 \,{\mathrm e}^{-2 t} \]

[[_linear, ‘class A‘]]

14686

\[ {}y^{\prime } = 3 y \]

[_quadrature]

14688

\[ {}y^{\prime } = -\sin \left (y\right )^{5} \]

[_quadrature]

14690

\[ {}y^{\prime } = \sin \left (y\right )^{2} \]

[_quadrature]

14692

\[ {}y^{\prime } = y+{\mathrm e}^{-t} \]

[[_linear, ‘class A‘]]

14693

\[ {}y^{\prime } = 3-2 y \]

[_quadrature]

14694

\[ {}y^{\prime } = t y \]

[_separable]

14695

\[ {}y^{\prime } = 3 y+{\mathrm e}^{7 t} \]

[[_linear, ‘class A‘]]

14696

\[ {}y^{\prime } = \frac {t y}{t^{2}+1} \]

[_separable]

14698

\[ {}y^{\prime } = t +\frac {2 y}{t +1} \]

[_linear]

14699

\[ {}y^{\prime } = 3+y^{2} \]

[_quadrature]

14700

\[ {}y^{\prime } = 2 y-y^{2} \]

[_quadrature]

14701

\[ {}y^{\prime } = -3 y+{\mathrm e}^{-2 t}+t^{2} \]

[[_linear, ‘class A‘]]

14702

\[ {}x^{\prime } = -t x \]
i.c.

[_separable]

14704

\[ {}y^{\prime } = 3 y+2 \,{\mathrm e}^{3 t} \]
i.c.

[[_linear, ‘class A‘]]

14705

\[ {}y^{\prime } = t^{2} y^{3}+y^{3} \]
i.c.

[_separable]

14706

\[ {}y^{\prime }+5 y = 3 \,{\mathrm e}^{-5 t} \]
i.c.

[[_linear, ‘class A‘]]

14707

\[ {}y^{\prime } = 2 t y+3 t \,{\mathrm e}^{t^{2}} \]
i.c.

[_linear]

14709

\[ {}y^{\prime } = 2 t y^{2}+3 t^{2} y^{2} \]
i.c.

[_separable]

14710

\[ {}y^{\prime } = 1-y^{2} \]
i.c.

[_quadrature]

14712

\[ {}y^{\prime } = y^{2}-2 y+1 \]
i.c.

[_quadrature]

14715

\[ {}y^{\prime } = t^{2} y+1+y+t^{2} \]

[_separable]

14716

\[ {}y^{\prime } = \frac {2 y+1}{t} \]

[_separable]

14717

\[ {}y^{\prime } = 3-y^{2} \]
i.c.

[_quadrature]

14901

\[ {}y^{\prime } = 3-\sin \left (y\right ) \]

[_quadrature]

14902

\[ {}y^{\prime }+4 y = {\mathrm e}^{2 x} \]

[[_linear, ‘class A‘]]

14904

\[ {}y y^{\prime } = 2 x \]

[_separable]

14945

\[ {}y^{\prime }+3 x y = 6 x \]

[_separable]

14947

\[ {}y^{\prime }-y^{3} = 8 \]

[_quadrature]

14948

\[ {}x^{2} y^{\prime }+x y^{2} = x \]

[_separable]

14950

\[ {}y^{3}-25 y+y^{\prime } = 0 \]

[_quadrature]

14951

\[ {}\left (-2+x \right ) y^{\prime } = 3+y \]

[_separable]

14952

\[ {}\left (y-2\right ) y^{\prime } = x -3 \]

[_separable]

14953

\[ {}y^{\prime }+2 y-y^{2} = -2 \]

[_quadrature]

14955

\[ {}y^{\prime } = 2 \sqrt {y} \]
i.c.

[_quadrature]

14956

\[ {}y^{\prime } = 3 y^{2}-y^{2} \sin \left (x \right ) \]

[_separable]

14960

\[ {}y^{\prime }+4 y = 8 \]

[_quadrature]

14961

\[ {}y^{\prime }+x y = 4 x \]

[_separable]

14962

\[ {}y^{\prime }+4 y = x^{2} \]

[[_linear, ‘class A‘]]

14963

\[ {}y^{\prime } = x y-3 x -2 y+6 \]

[_separable]

14964

\[ {}y^{\prime } = \sin \left (x +y\right ) \]

[[_homogeneous, ‘class C‘], _dAlembert]

14966

\[ {}y^{\prime } = \frac {x}{y} \]

[_separable]

14967

\[ {}y^{\prime } = y^{2}+9 \]

[_quadrature]

14968

\[ {}x y y^{\prime } = y^{2}+9 \]

[_separable]

14969

\[ {}y^{\prime } = \frac {1+y^{2}}{x^{2}+1} \]

[_separable]

14971

\[ {}y^{\prime } = {\mathrm e}^{2 x -3 y} \]

[_separable]

14972

\[ {}y^{\prime } = \frac {x}{y} \]
i.c.

[_separable]

14973

\[ {}y^{\prime } = 2 x -1+2 x y-y \]
i.c.

[_separable]

14976

\[ {}y^{\prime } = x y-4 x \]

[_separable]

14977

\[ {}y^{\prime }-4 y = 2 \]

[_quadrature]

14979

\[ {}y^{\prime } = \sin \left (y\right ) \]

[_quadrature]

14981

\[ {}y^{\prime } = 200 y-2 y^{2} \]

[_quadrature]

14982

\[ {}y^{\prime } = x y-4 x \]

[_separable]

14983

\[ {}y^{\prime } = x y-3 x -2 y+6 \]

[_separable]

14984

\[ {}y^{\prime } = 3 y^{2}-y^{2} \sin \left (x \right ) \]

[_separable]

14985

\[ {}y^{\prime } = \tan \left (y\right ) \]

[_quadrature]

14986

\[ {}y^{\prime } = \frac {y}{x} \]

[_separable]

14988

\[ {}\left (x^{2}+1\right ) y^{\prime } = 1+y^{2} \]

[_separable]

14989

\[ {}\left (y^{2}-1\right ) y^{\prime } = 4 x y^{2} \]

[_separable]

14990

\[ {}y^{\prime } = {\mathrm e}^{-y} \]

[_quadrature]

14991

\[ {}y^{\prime } = {\mathrm e}^{-y}+1 \]

[_quadrature]

14992

\[ {}y^{\prime } = 3 x y^{3} \]

[_separable]

14994

\[ {}y^{\prime }-3 y^{2} x^{2} = -3 x^{2} \]

[_separable]

14995

\[ {}y^{\prime }-3 y^{2} x^{2} = 3 x^{2} \]

[_separable]

14996

\[ {}y^{\prime } = 200 y-2 y^{2} \]

[_quadrature]

14997

\[ {}y^{\prime }-2 y = -10 \]
i.c.

[_quadrature]

15001

\[ {}x y^{\prime } = y^{2}-y \]
i.c.

[_separable]

15002

\[ {}y^{\prime } = \frac {y^{2}-1}{x y} \]
i.c.

[_separable]

15009

\[ {}y^{\prime } = 4 y+8 \]

[_quadrature]

15011

\[ {}y^{\prime } = y \sin \left (x \right ) \]

[_separable]

15012

\[ {}y^{\prime }+4 y = y^{3} \]

[_quadrature]

15014

\[ {}y^{\prime }+2 y = 6 \]

[_quadrature]

15015

\[ {}y^{\prime }+2 y = 20 \,{\mathrm e}^{3 x} \]

[[_linear, ‘class A‘]]

15016

\[ {}y^{\prime } = 4 y+16 x \]

[[_linear, ‘class A‘]]

15017

\[ {}y^{\prime }-2 x y = x \]

[_separable]

15018

\[ {}x y^{\prime }+3 y-10 x^{2} = 0 \]

[_linear]

15020

\[ {}x y^{\prime } = \sqrt {x}+3 y \]

[_linear]

15022

\[ {}x y^{\prime }+\left (5 x +2\right ) y = \frac {20}{x} \]

[_linear]

15024

\[ {}y^{\prime }-3 y = 6 \]
i.c.

[_quadrature]

15025

\[ {}y^{\prime }-3 y = 6 \]
i.c.

[_quadrature]

15026

\[ {}y^{\prime }+5 y = {\mathrm e}^{-3 x} \]
i.c.

[[_linear, ‘class A‘]]

15027

\[ {}3 y+x y^{\prime } = 20 x^{2} \]
i.c.

[_linear]

15028

\[ {}x y^{\prime } = y+x^{2} \cos \left (x \right ) \]
i.c.

[_linear]

15029

\[ {}\left (x^{2}+1\right ) y^{\prime } = x \left (3+3 x^{2}-y\right ) \]
i.c.

[_linear]

15032

\[ {}-y+x y^{\prime } = x^{2} {\mathrm e}^{-x^{2}} \]
i.c.

[_linear]

15033

\[ {}y^{\prime } = \frac {1}{\left (3 x +3 y+2\right )^{2}} \]

[[_homogeneous, ‘class C‘], _dAlembert]

15034

\[ {}y^{\prime } = \frac {\left (-2 y+3 x \right )^{2}+1}{-2 y+3 x}+\frac {3}{2} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

15035

\[ {}\cos \left (-4 y+8 x -3\right ) y^{\prime } = 2+2 \cos \left (-4 y+8 x -3\right ) \]

[[_homogeneous, ‘class C‘], _exact, _dAlembert]

15036

\[ {}y^{\prime } = 1+\left (y-x \right )^{2} \]
i.c.

[[_homogeneous, ‘class C‘], _Riccati]

15037

\[ {}x^{2} y^{\prime }-x y = y^{2} \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

15038

\[ {}y^{\prime } = \frac {y}{x}+\frac {x}{y} \]

[[_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‘]]

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]

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]

15046

\[ {}3 y^{\prime } = -2+\sqrt {2 x +3 y+4} \]

[[_homogeneous, ‘class C‘], _dAlembert]

15047

\[ {}3 y^{\prime }+\frac {2 y}{x} = 4 \sqrt {y} \]

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

15048

\[ {}y^{\prime } = 4+\frac {1}{\sin \left (4 x -y\right )} \]

[[_homogeneous, ‘class C‘], _dAlembert]

15049

\[ {}\left (y-x \right ) y^{\prime } = 1 \]

[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]

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‘]]

15052

\[ {}y^{\prime }+\frac {y}{x} = y^{3} x^{2} \]

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

15053

\[ {}y^{\prime } = 2 \sqrt {2 x +y-3}-2 \]

[[_homogeneous, ‘class C‘], _dAlembert]

15054

\[ {}y^{\prime } = 2 \sqrt {2 x +y-3} \]

[[_homogeneous, ‘class C‘], _dAlembert]

15055

\[ {}-y+x y^{\prime } = \sqrt {x y+x^{2}} \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

15056

\[ {}y^{\prime }+3 y = \frac {28 \,{\mathrm e}^{2 x}}{y^{3}} \]

[[_1st_order, _with_linear_symmetries], _Bernoulli]

15057

\[ {}y^{\prime } = \left (x -y+3\right )^{2} \]

[[_homogeneous, ‘class C‘], _Riccati]

15058

\[ {}y^{\prime }+2 x = 2 \sqrt {y+x^{2}} \]

[[_1st_order, _with_linear_symmetries], _Clairaut]

15060

\[ {}y^{\prime } = x \left (1+\frac {2 y}{x^{2}}+\frac {y^{2}}{x^{4}}\right ) \]

[[_homogeneous, ‘class G‘], _rational, _Riccati]

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]

15063

\[ {}2 x y+y^{2}+\left (2 x y+x^{2}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

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]

15067

\[ {}4 x^{3} y+\left (x^{4}-y^{4}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]

15068

\[ {}1+\ln \left (x y\right )+\frac {x y^{\prime }}{y} = 0 \]

[[_homogeneous, ‘class G‘], _exact]

15069

\[ {}1+{\mathrm e}^{y}+x \,{\mathrm e}^{y} y^{\prime } = 0 \]

[_separable]

15070

\[ {}{\mathrm e}^{y}+\left (x \,{\mathrm e}^{y}+1\right ) y^{\prime } = 0 \]

[[_1st_order, _with_exponential_symmetries], _exact]

15071

\[ {}1+y^{4}+x y^{3} y^{\prime } = 0 \]

[_separable]

15072

\[ {}y+\left (y^{4}-3 x \right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _rational]

15073

\[ {}\frac {2 y}{x}+\left (4 x^{2} y-3\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

15075

\[ {}3 y+3 y^{2}+\left (2 x +4 x y\right ) y^{\prime } = 0 \]

[_separable]

15076

\[ {}2 x \left (y+1\right )-y^{\prime } = 0 \]

[_separable]

15077

\[ {}2 y^{3}+\left (4 x^{3} y^{3}-3 x y^{2}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

15078

\[ {}4 x y+\left (3 x^{2}+5 y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

15079

\[ {}6+12 y^{2} x^{2}+\left (7 x^{3} y+\frac {x}{y}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _rational]

15080

\[ {}x y^{\prime } = 2 y-6 x^{3} \]

[_linear]

15081

\[ {}x y^{\prime } = 2 y^{2}-6 y \]

[_separable]

15082

\[ {}4 y^{2}-y^{2} x^{2}+y^{\prime } = 0 \]

[_separable]

15083

\[ {}y^{\prime } = \sqrt {x +y} \]

[[_homogeneous, ‘class C‘], _dAlembert]

15085

\[ {}x y y^{\prime }-y^{2} = \sqrt {x^{4}+y^{2} x^{2}} \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

15086

\[ {}y^{\prime } = y^{2}-2 x y+x^{2} \]

[[_homogeneous, ‘class C‘], _Riccati]

15087

\[ {}4 x y-6+x^{2} y^{\prime } = 0 \]

[_linear]

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]

15090

\[ {}3 y-x^{3}+x y^{\prime } = 0 \]

[_linear]

15092

\[ {}3 x y^{3}-y+x y^{\prime } = 0 \]

[[_homogeneous, ‘class D‘], _rational, _Bernoulli]

15093

\[ {}2+2 x^{2}-2 x y+\left (x^{2}+1\right ) y^{\prime } = 0 \]

[_linear]

15094

\[ {}\left (y^{2}-4\right ) y^{\prime } = y \]

[_quadrature]

15096

\[ {}y^{\prime } = \frac {1}{x y-3 x} \]

[_separable]

15097

\[ {}y^{\prime } = \frac {3 y}{x +1}-y^{2} \]

[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli]

15099

\[ {}\sin \left (y\right )+\left (x +1\right ) \cos \left (y\right ) y^{\prime } = 0 \]

[_separable]

15101

\[ {}x y y^{\prime } = 2 x^{2}+2 y^{2} \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

15102

\[ {}y^{\prime } = \frac {x +2 y}{x +2 y+3} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

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]

15105

\[ {}y^{\prime } = x y^{2}+3 y^{2}+x +3 \]

[_separable]

15106

\[ {}1-\left (x +2 y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]

15108

\[ {}y^{2}+1-y^{\prime } = 0 \]

[_quadrature]

15109

\[ {}y^{\prime }-3 y = 12 \,{\mathrm e}^{2 x} \]

[[_linear, ‘class A‘]]

15110

\[ {}x y y^{\prime } = y^{2}+x y+x^{2} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

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]

15114

\[ {}2 y-6 x +\left (x +1\right ) y^{\prime } = 0 \]

[_linear]

15115

\[ {}x y^{2}+\left (x^{2} y+10 y^{4}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _exact, _rational]

15117

\[ {}\left (y-x +3\right )^{2} \left (y^{\prime }-1\right ) = 1 \]

[[_homogeneous, ‘class C‘], _exact, _rational, _dAlembert]

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]

15124

\[ {}y^{\prime } = {\mathrm e}^{4 x +3 y} \]

[_separable]

15125

\[ {}y^{\prime } = \tan \left (6 x +3 y+1\right )-2 \]

[[_homogeneous, ‘class C‘], _dAlembert]

15126

\[ {}y^{\prime } = {\mathrm e}^{4 x +3 y} \]

[_separable]

15710

\[ {}2 x -y-y y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

15711

\[ {}y^{\prime }+2 y = 0 \]

[_quadrature]

15712

\[ {}y^{\prime }+x y = 0 \]

[_separable]

15723

\[ {}y^{\prime } = -\frac {x}{y} \]

[_separable]

15724

\[ {}3 y \left (t^{2}+y\right )+t \left (t^{2}+6 y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

15725

\[ {}y^{\prime } = -\frac {2 y}{x}-3 \]

[_linear]

15741

\[ {}y^{\prime }+2 y = 0 \]
i.c.

[_quadrature]

15753

\[ {}y^{\prime } = \frac {\left (x -4\right ) y^{3}}{x^{3} \left (y-2\right )} \]

[_separable]

15754

\[ {}y^{\prime } = \frac {y^{2}+2 x y}{x^{2}} \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

15763

\[ {}y^{\prime }+y \cos \left (x \right ) = 0 \]

[_separable]

15771

\[ {}2 x -3 y+\left (2 y-3 x \right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

15777

\[ {}y^{\prime }+2 y = x^{2} \]
i.c.

[[_linear, ‘class A‘]]

15785

\[ {}y^{\prime } = y^{{1}/{5}} \]
i.c.

[_quadrature]

15788

\[ {}y^{\prime } = y \sqrt {t} \]
i.c.

[_separable]

15790

\[ {}t y^{\prime } = y \]

[_separable]

15791

\[ {}y^{\prime } = y \tan \left (t \right ) \]
i.c.

[_separable]

15793

\[ {}y^{\prime } = \sqrt {-1+y^{2}} \]
i.c.

[_quadrature]

15794

\[ {}y^{\prime } = \sqrt {-1+y^{2}} \]
i.c.

[_quadrature]

15796

\[ {}y^{\prime } = \sqrt {-1+y^{2}} \]
i.c.

[_quadrature]

15798

\[ {}y^{\prime } = \sqrt {25-y^{2}} \]
i.c.

[_quadrature]

15800

\[ {}y^{\prime } = \sqrt {25-y^{2}} \]
i.c.

[_quadrature]

15801

\[ {}t y^{\prime }+y = t^{3} \]
i.c.

[_linear]

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

\[ {}y^{\prime } = \frac {y^{2}+1}{y} \]

[_quadrature]

15822

\[ {}y^{\prime } = \frac {y+1}{t +1} \]

[_separable]

15823

\[ {}y^{\prime } = \frac {2+y}{2 t +1} \]

[_separable]

15824

\[ {}\frac {3}{t^{2}} = \left (\frac {1}{\sqrt {y}}+\sqrt {y}\right ) y^{\prime } \]

[_separable]

15827

\[ {}y^{\prime }+k y = 0 \]

[_quadrature]

15830

\[ {}y^{\prime } = {\mathrm e}^{2 y+10 t} \]

[_separable]

15831

\[ {}y^{\prime } = {\mathrm e}^{3 y+2 t} \]

[_separable]

15844

\[ {}y^{\prime } = \frac {5^{-t}}{y^{2}} \]

[_separable]

15845

\[ {}y^{\prime } = t^{2} y^{2}+y^{2}-t^{2}-1 \]

[_separable]

15846

\[ {}y^{\prime } = y^{2}-3 y+2 \]

[_quadrature]

15847

\[ {}4 \left (-1+x \right )^{2} y^{\prime }-3 \left (3+y\right )^{2} = 0 \]

[_separable]

15849

\[ {}y^{\prime } = y^{3}+1 \]

[_quadrature]

15850

\[ {}y^{\prime } = y^{3}-1 \]

[_quadrature]

15851

\[ {}y^{\prime } = y^{3}+y \]

[_quadrature]

15852

\[ {}y^{\prime } = y^{3}-y^{2} \]

[_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]

15860

\[ {}y^{\prime } = \sqrt {\frac {y}{t}} \]
i.c.

[[_homogeneous, ‘class A‘], _dAlembert]

15861

\[ {}y^{\prime } = \frac {{\mathrm e}^{t}}{y+1} \]
i.c.

[_separable]

15863

\[ {}y^{\prime } = \frac {y}{\ln \left (y\right )} \]
i.c.

[_quadrature]

15867

\[ {}y^{\prime } = \frac {3+y}{3 x +1} \]
i.c.

[_separable]

15868

\[ {}y^{\prime } = {\mathrm e}^{x -y} \]
i.c.

[_separable]

15869

\[ {}y^{\prime } = {\mathrm e}^{2 x -y} \]
i.c.

[_separable]

15870

\[ {}y^{\prime } = \frac {3 y+1}{x +3} \]
i.c.

[_separable]

15871

\[ {}y^{\prime } = y \cos \left (t \right ) \]
i.c.

[_separable]

15872

\[ {}y^{\prime } = y^{2} \cos \left (t \right ) \]
i.c.

[_separable]

15874

\[ {}y^{\prime }+y f \left (t \right ) = 0 \]
i.c.

[_separable]

15875

\[ {}y^{\prime } = -\frac {y-2}{-2+x} \]
i.c.

[_separable]

15876

\[ {}y^{\prime } = \frac {x +y+3}{3 x +3 y+1} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

15877

\[ {}y^{\prime } = \frac {x -y+2}{2 x -2 y-1} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

15878

\[ {}y^{\prime } = \left (x +y-4\right )^{2} \]

[[_homogeneous, ‘class C‘], _Riccati]

15879

\[ {}y^{\prime } = \left (3 y+1\right )^{4} \]

[_quadrature]

15880

\[ {}y^{\prime } = 3 y \]

[_quadrature]

15881

\[ {}y^{\prime } = -y \]

[_quadrature]

15882

\[ {}y^{\prime } = y^{2}-y \]

[_quadrature]

15883

\[ {}y^{\prime } = 16 y-8 y^{2} \]

[_quadrature]

15884

\[ {}y^{\prime } = 12+4 y-y^{2} \]

[_quadrature]

15885

\[ {}y^{\prime } = y f \left (t \right ) \]
i.c.

[_separable]

15886

\[ {}y^{\prime }-y = 10 \]

[_quadrature]

15887

\[ {}y^{\prime }-y = 2 \,{\mathrm e}^{-t} \]

[[_linear, ‘class A‘]]

15889

\[ {}y^{\prime }-y = t^{2}-2 t \]

[[_linear, ‘class A‘]]

15891

\[ {}t y^{\prime }+y = t^{2} \]

[_linear]

15892

\[ {}t y^{\prime }+y = t \]

[_linear]

15895

\[ {}y^{\prime }-\frac {2 t y}{t^{2}+1} = 2 \]

[_linear]

15896

\[ {}y^{\prime }-\frac {4 t y}{4 t^{2}+1} = 4 t \]

[_linear]

15897

\[ {}y^{\prime } = 2 x +\frac {x y}{x^{2}-1} \]

[_linear]

15899

\[ {}y^{\prime }-\frac {3 t y}{t^{2}-4} = t \]

[_linear]

15900

\[ {}y^{\prime }-\frac {4 t y}{4 t^{2}-9} = t \]

[_linear]

15901

\[ {}y^{\prime }-\frac {9 x y}{9 x^{2}+49} = x \]

[_linear]

15903

\[ {}y^{\prime }+x y = x^{3} \]

[_linear]

15904

\[ {}y^{\prime }-x y = x \]

[_separable]

15905

\[ {}y^{\prime } = \frac {1}{x +y^{2}} \]

[[_1st_order, _with_exponential_symmetries]]

15906

\[ {}y^{\prime }-x = y \]

[[_linear, ‘class A‘]]

15907

\[ {}y-\left (x +3 y^{2}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _rational]

15908

\[ {}x^{\prime } = \frac {3 x t^{2}}{-t^{3}+1} \]

[_separable]

15909

\[ {}p^{\prime } = t^{3}+\frac {p}{t} \]

[_linear]

15910

\[ {}v^{\prime }+v = {\mathrm e}^{-s} \]

[[_linear, ‘class A‘]]

15911

\[ {}y^{\prime }-y = 4 \,{\mathrm e}^{t} \]
i.c.

[[_linear, ‘class A‘]]

15912

\[ {}y^{\prime }+y = {\mathrm e}^{-t} \]
i.c.

[[_linear, ‘class A‘]]

15913

\[ {}y^{\prime }+3 t^{2} y = {\mathrm e}^{-t^{3}} \]
i.c.

[_linear]

15914

\[ {}y^{\prime }+2 t y = 2 t \]
i.c.

[_separable]

15918

\[ {}\left (t^{2}+4\right ) y^{\prime }+2 t y = 2 t \]
i.c.

[_separable]

15919

\[ {}x^{\prime } = x+t +1 \]
i.c.

[[_linear, ‘class A‘]]

15920

\[ {}y^{\prime } = {\mathrm e}^{2 t}+2 y \]
i.c.

[[_linear, ‘class A‘]]

15921

\[ {}y^{\prime }-\frac {y}{t} = \ln \left (t \right ) \]

[_linear]

15926

\[ {}y^{\prime }+y = 5 \,{\mathrm e}^{2 t} \]

[[_linear, ‘class A‘]]

15927

\[ {}y^{\prime }+y = {\mathrm e}^{-t} \]

[[_linear, ‘class A‘]]

15928

\[ {}y^{\prime }+y = 2-{\mathrm e}^{2 t} \]

[[_linear, ‘class A‘]]

15929

\[ {}y^{\prime }-5 y = t \]

[[_linear, ‘class A‘]]

15930

\[ {}y^{\prime }+3 y = 27 t^{2}+9 \]

[[_linear, ‘class A‘]]

15933

\[ {}y^{\prime }+10 y = 2 \,{\mathrm e}^{t} \]

[[_linear, ‘class A‘]]

15934

\[ {}y^{\prime }-3 y = 27 t^{2} \]

[[_linear, ‘class A‘]]

15935

\[ {}y^{\prime }-y = 2 \,{\mathrm e}^{t} \]

[[_linear, ‘class A‘]]

15936

\[ {}y^{\prime }+y = 4+3 \,{\mathrm e}^{t} \]

[[_linear, ‘class A‘]]

15941

\[ {}y^{\prime }+y = t \]
i.c.

[[_linear, ‘class A‘]]

15944

\[ {}y^{\prime }+y = {\mathrm e}^{t} \]
i.c.

[[_linear, ‘class A‘]]

15945

\[ {}y^{2}-\frac {y}{2 \sqrt {t}}+\left (2 t y-\sqrt {t}+1\right ) y^{\prime } = 0 \]

[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

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]

15952

\[ {}\ln \left (t y\right )+\frac {t y^{\prime }}{y} = 0 \]

[[_homogeneous, ‘class G‘], _exact]

15953

\[ {}{\mathrm e}^{t y}+\frac {t \,{\mathrm e}^{t y} y^{\prime }}{y} = 0 \]

[_separable]

15955

\[ {}-1+3 y^{2} y^{\prime } = 0 \]

[_quadrature]

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]

15959

\[ {}-\frac {1}{y}+\left (\frac {t}{y^{2}}+3 y^{2}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _exact, _rational]

15960

\[ {}2 t y+\left (t^{2}+y^{2}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]

15961

\[ {}2 t y^{3}+\left (1+3 t^{2} y^{2}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _exact, _rational]

15962

\[ {}\sin \left (y\right )^{2}+t \sin \left (2 y\right ) y^{\prime } = 0 \]

[_separable]

15963

\[ {}3 t^{2}+3 y^{2}+6 t y y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli]

15966

\[ {}-2 t y^{2} \sin \left (t^{2}\right )+2 y \cos \left (t^{2}\right ) y^{\prime } = 0 \]

[_separable]

15970

\[ {}\left (3+t \right ) \cos \left (y+t \right )+\sin \left (y+t \right )+\left (3+t \right ) \cos \left (y+t \right ) y^{\prime } = 0 \]

[[_1st_order, _with_linear_symmetries], _exact]

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]

15975

\[ {}1+\frac {y}{t^{2}}-\frac {y^{\prime }}{t} = 0 \]
i.c.

[_linear]

15977

\[ {}1+5 t -y-\left (t +2 y\right ) y^{\prime } = 0 \]
i.c.

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

15986

\[ {}t^{2} y+t^{3} y^{\prime } = 0 \]

[_separable]

15987

\[ {}y \left (2 \,{\mathrm e}^{t}+4 t \right )+3 \left ({\mathrm e}^{t}+t^{2}\right ) y^{\prime } = 0 \]

[_separable]

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]

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‘]]

16000

\[ {}y^{\prime }+y = t y^{2} \]

[_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]

16009

\[ {}\cos \left (\frac {t}{y+t}\right )+{\mathrm e}^{\frac {2 y}{t}} y^{\prime } = 0 \]

[[_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‘]]

16021

\[ {}t -y+t y^{\prime } = 0 \]

[_linear]

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]

16034

\[ {}t +y-t y^{\prime } = 0 \]
i.c.

[_linear]

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]

16040

\[ {}t -2 y+1+\left (4 t -3 y-6\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

16041

\[ {}5 t +2 y+1+\left (2 t +y+1\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

16042

\[ {}3 t -y+1-\left (6 t -2 y-3\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

16043

\[ {}2 t +3 y+1+\left (4 t +6 y+1\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

16044

\[ {}y^{\prime }-\frac {2 y}{x} = -x^{2} y \]

[_separable]

16049

\[ {}1+y-t y^{\prime } = \ln \left (y^{\prime }\right ) \]

[[_1st_order, _with_linear_symmetries], _Clairaut]

16053

\[ {}y = t \left (y^{\prime }+1\right )+2 y^{\prime }+1 \]

[_linear]

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]

16058

\[ {}y^{\prime } = \frac {2 t^{5}}{5 y^{2}} \]

[_separable]

16060

\[ {}y^{\prime }-\frac {y}{t} = \frac {y^{2}}{t} \]

[_separable]

16061

\[ {}y^{\prime } = \frac {{\mathrm e}^{8 y}}{t} \]

[_separable]

16062

\[ {}y^{\prime } = \frac {{\mathrm e}^{5 t}}{y^{4}} \]

[_separable]

16065

\[ {}y^{\prime } = \frac {\left (4-7 x \right ) \left (2 y-3\right )}{\left (-1+x \right ) \left (2 x -5\right )} \]

[_separable]

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‘]]

16069

\[ {}y-x +y^{\prime } = 0 \]

[[_linear, ‘class A‘]]

16070

\[ {}y^{2}+\left (t y+t^{2}\right ) y^{\prime } = 0 \]

[[_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]

16077

\[ {}y^{\prime }+y = 5 \]

[_quadrature]

16078

\[ {}y^{\prime }+t y = t \]

[_separable]

16079

\[ {}x^{\prime }+\frac {x}{y} = y^{2} \]

[_linear]

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]

16087

\[ {}2 x -y-2+\left (2 y-x \right ) y^{\prime } = 0 \]
i.c.

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

16088

\[ {}\cos \left (-y+t \right )+\left (1-\cos \left (-y+t \right )\right ) y^{\prime } = 0 \]
i.c.

[[_homogeneous, ‘class C‘], _exact, _dAlembert]

16094

\[ {}y^{\prime } = \sqrt {x -y} \]
i.c.

[[_homogeneous, ‘class C‘], _dAlembert]

16221

\[ {}y^{\prime }-4 y = t^{2} \]

[[_linear, ‘class A‘]]

16223

\[ {}y^{\prime }-y = {\mathrm e}^{4 t} \]
i.c.

[[_linear, ‘class A‘]]

16224

\[ {}y^{\prime }+4 y = {\mathrm e}^{-4 t} \]
i.c.

[[_linear, ‘class A‘]]

16225

\[ {}y^{\prime }+4 y = t \,{\mathrm e}^{-4 t} \]

[[_linear, ‘class A‘]]

16586

\[ {}y^{\prime } = \frac {x}{y} \]

[_separable]

16587

\[ {}y^{\prime } = y+3 y^{{1}/{3}} \]

[_quadrature]

16588

\[ {}y^{\prime } = \sqrt {x -y} \]

[[_homogeneous, ‘class C‘], _dAlembert]

16589

\[ {}y^{\prime } = \sqrt {x^{2}-y}-x \]

[[_1st_order, _with_linear_symmetries], _dAlembert]

16590

\[ {}y^{\prime } = \sqrt {1-y^{2}} \]

[_quadrature]

16591

\[ {}y^{\prime } = \frac {y+1}{x -y} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

16593

\[ {}y^{\prime } = 1-\cot \left (y\right ) \]

[_quadrature]

16594

\[ {}y^{\prime } = \left (3 x -y\right )^{{1}/{3}}-1 \]

[[_homogeneous, ‘class C‘], _dAlembert]

16597

\[ {}y^{\prime }+2 y = {\mathrm e}^{x} \]

[[_linear, ‘class A‘]]

16598

\[ {}\left (-x^{2}+1\right ) y^{\prime }+x y = 2 x \]

[_separable]

16600

\[ {}y^{\prime } = x +y \]

[[_linear, ‘class A‘]]

16601

\[ {}y^{\prime } = y-x \]

[[_linear, ‘class A‘]]

16602

\[ {}y^{\prime } = \frac {x}{2}-y+\frac {3}{2} \]

[[_linear, ‘class A‘]]

16603

\[ {}y^{\prime } = \left (y-1\right )^{2} \]

[_quadrature]

16604

\[ {}y^{\prime } = \left (y-1\right ) x \]

[_separable]

16606

\[ {}y^{\prime } = \cos \left (x -y\right ) \]

[[_homogeneous, ‘class C‘], _dAlembert]

16607

\[ {}y^{\prime } = y-x^{2} \]

[[_linear, ‘class A‘]]

16608

\[ {}y^{\prime } = x^{2}+2 x -y \]

[[_linear, ‘class A‘]]

16609

\[ {}y^{\prime } = \frac {y+1}{-1+x} \]

[_separable]

16610

\[ {}y^{\prime } = \frac {x +y}{x -y} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

16612

\[ {}y^{\prime } = 2 x -y \]

[[_linear, ‘class A‘]]

16613

\[ {}y^{\prime } = y+x^{2} \]

[[_linear, ‘class A‘]]

16614

\[ {}y^{\prime } = -\frac {y}{x} \]

[_separable]

16617

\[ {}y^{\prime } = y \]

[_quadrature]

16618

\[ {}y^{\prime } = y^{2} \]

[_quadrature]

16621

\[ {}y^{\prime } = x +y \]
i.c.

[[_linear, ‘class A‘]]

16623

\[ {}x y^{\prime } = 2 x -y \]
i.c.

[_linear]

16624

\[ {}1+y^{2}+\left (x^{2}+1\right ) y^{\prime } = 0 \]

[_separable]

16625

\[ {}1+y^{2}+x y y^{\prime } = 0 \]

[_separable]

16626

\[ {}y^{\prime } \sin \left (x \right )-y \cos \left (x \right ) = 0 \]
i.c.

[_separable]

16627

\[ {}1+y^{2} = x y^{\prime } \]

[_separable]

16630

\[ {}{\mathrm e}^{-y} y^{\prime } = 1 \]

[_quadrature]

16631

\[ {}y \ln \left (y\right )+x y^{\prime } = 1 \]
i.c.

[_separable]

16632

\[ {}y^{\prime } = a^{x +y} \]

[_separable]

16633

\[ {}{\mathrm e}^{y} \left (x^{2}+1\right ) y^{\prime }-2 x \left (1+{\mathrm e}^{y}\right ) = 0 \]

[_separable]

16637

\[ {}y^{\prime } = \sin \left (x -y\right ) \]

[[_homogeneous, ‘class C‘], _dAlembert]

16638

\[ {}y^{\prime } = a x +b y+c \]

[[_linear, ‘class A‘]]

16639

\[ {}\left (x +y\right )^{2} y^{\prime } = a^{2} \]

[[_homogeneous, ‘class C‘], _dAlembert]

16641

\[ {}a^{2}+y^{2}+2 x \sqrt {a x -x^{2}}\, y^{\prime } = 0 \]
i.c.

[_separable]

16642

\[ {}y^{\prime } = \frac {y}{x} \]
i.c.

[_separable]

16654

\[ {}{\mathrm e}^{y} = {\mathrm e}^{4 y} y^{\prime }+1 \]

[_quadrature]

16655

\[ {}\left (x +1\right ) y^{\prime } = y-1 \]

[_separable]

16656

\[ {}y^{\prime } = 2 x \left (\pi +y\right ) \]

[_separable]

16658

\[ {}x y^{\prime } = y+x \cos \left (\frac {y}{x}\right )^{2} \]

[[_homogeneous, ‘class A‘], _dAlembert]

16659

\[ {}x -y+x y^{\prime } = 0 \]

[_linear]

16660

\[ {}x y^{\prime } = y \left (\ln \left (y\right )-\ln \left (x \right )\right ) \]

[[_homogeneous, ‘class A‘], _dAlembert]

16661

\[ {}x^{2} y^{\prime } = y^{2}-x y+x^{2} \]

[[_homogeneous, ‘class A‘], _rational, _Riccati]

16662

\[ {}x y^{\prime } = y+\sqrt {y^{2}-x^{2}} \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

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‘]]

16666

\[ {}x +y-2+\left (1-x \right ) y^{\prime } = 0 \]

[_linear]

16667

\[ {}3 y-7 x +7-\left (3 x -7 y-3\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

16668

\[ {}x +y-2+\left (x -y+4\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

16669

\[ {}x +y+\left (x -y-2\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

16670

\[ {}2 x +3 y-5+\left (3 x +2 y-5\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

16671

\[ {}8 x +4 y+1+\left (4 x +2 y+1\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

16672

\[ {}x -2 y-1+\left (3 x -6 y+2\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

16673

\[ {}x +y+\left (x +y-1\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

16674

\[ {}2 x y^{\prime } \left (x -y^{2}\right )+y^{3} = 0 \]

[[_homogeneous, ‘class G‘], _rational]

16675

\[ {}4 y^{6}+x^{3} = 6 x y^{5} y^{\prime } \]

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

16676

\[ {}y \left (1+\sqrt {x^{2} y^{4}+1}\right )+2 x y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘]]

16677

\[ {}x +y^{3}+3 \left (y^{3}-x \right ) y^{2} y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _rational]

16678

\[ {}y^{\prime }+2 y = {\mathrm e}^{-x} \]

[[_linear, ‘class A‘]]

16679

\[ {}x^{2}-x y^{\prime } = y \]
i.c.

[_linear]

16680

\[ {}y^{\prime }-2 x y = 2 x \,{\mathrm e}^{x^{2}} \]

[_linear]

16681

\[ {}y^{\prime }+2 x y = {\mathrm e}^{-x^{2}} \]

[_linear]

16683

\[ {}x y^{\prime }-2 y = x^{3} \cos \left (x \right ) \]

[_linear]

16686

\[ {}\left (2 x -y^{2}\right ) y^{\prime } = 2 y \]

[[_homogeneous, ‘class G‘], _rational]

16688

\[ {}y^{\prime } = \frac {y}{2 y \ln \left (y\right )+y-x} \]

[[_1st_order, _with_linear_symmetries]]

16698

\[ {}x y^{\prime }+y = 2 x \]

[_linear]

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]

16703

\[ {}\left (x^{3}+{\mathrm e}^{y}\right ) y^{\prime } = 3 x^{2} \]

[[_1st_order, _with_linear_symmetries]]

16704

\[ {}y^{\prime }+3 x y = y \,{\mathrm e}^{x^{2}} \]

[_separable]

16709

\[ {}y^{\prime }-y \cos \left (x \right ) = y^{2} \cos \left (x \right ) \]

[_separable]

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]

16722

\[ {}\frac {x y}{\sqrt {x^{2}+1}}+2 x y-\frac {y}{x}+\left (\sqrt {x^{2}+1}+x^{2}-\ln \left (x \right )\right ) y^{\prime } = 0 \]

[_separable]

16727

\[ {}3 x^{2} y+y^{3}+\left (x^{3}+3 x y^{2}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]

16729

\[ {}x^{2}+y-x y^{\prime } = 0 \]

[_linear]

16730

\[ {}x +y^{2}-2 x y y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

16735

\[ {}3 y^{2}-x +\left (2 y^{3}-6 x y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _rational]

16736

\[ {}x^{2}+y^{2}+1-2 x y y^{\prime } = 0 \]

[_rational, _Bernoulli]

16737

\[ {}x -x y+\left (y+x^{2}\right ) y^{\prime } = 0 \]

[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class A‘]]

16745

\[ {}{y^{\prime }}^{2}-y y^{\prime }+{\mathrm e}^{x} = 0 \]

[[_1st_order, _with_linear_symmetries]]

16748

\[ {}y^{\prime } = {\mathrm e}^{\frac {y^{\prime }}{y}} \]

[_quadrature]

16751

\[ {}y = y^{\prime } \ln \left (y^{\prime }\right ) \]

[_quadrature]

16752

\[ {}y = \left (y^{\prime }-1\right ) {\mathrm e}^{y^{\prime }} \]

[_quadrature]

16755

\[ {}y^{{2}/{5}}+{y^{\prime }}^{{2}/{5}} = a^{{2}/{5}} \]

[_quadrature]

16757

\[ {}y = y^{\prime } \left (1+y^{\prime } \cos \left (y^{\prime }\right )\right ) \]

[_quadrature]

16758

\[ {}y = \arcsin \left (y^{\prime }\right )+\ln \left (1+{y^{\prime }}^{2}\right ) \]

[_quadrature]

16759

\[ {}y = 2 x y^{\prime }+\ln \left (y^{\prime }\right ) \]

[[_1st_order, _with_linear_symmetries], _dAlembert]

16771

\[ {}x y^{\prime }-y^{2}+\left (2 x +1\right ) y = x^{2}+2 x \]

[[_1st_order, _with_linear_symmetries], _rational, _Riccati]

16772

\[ {}x^{2} y^{\prime } = y^{2} x^{2}+x y+1 \]

[[_homogeneous, ‘class G‘], _rational, _Riccati]

16775

\[ {}{y^{\prime }}^{3}-4 x y y^{\prime }+8 y^{2} = 0 \]

[[_1st_order, _with_linear_symmetries]]

16777

\[ {}y^{\prime } = y^{{2}/{3}}+a \]

[_quadrature]

16785

\[ {}{y^{\prime }}^{2}-y y^{\prime }+{\mathrm e}^{x} = 0 \]

[[_1st_order, _with_linear_symmetries]]

16788

\[ {}y^{\prime } = \left (x -y\right )^{2}+1 \]

[[_homogeneous, ‘class C‘], _Riccati]

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]

16794

\[ {}y-x y^{2} \ln \left (x \right )+x y^{\prime } = 0 \]

[_Bernoulli]

16796

\[ {}y^{\prime } = \frac {1}{2 x -y^{2}} \]

[[_1st_order, _with_exponential_symmetries]]

16798

\[ {}x y y^{\prime }-y^{2} = x^{4} \]

[[_homogeneous, ‘class D‘], _rational, _Bernoulli]

16799

\[ {}\frac {1}{y^{2}-x y+x^{2}} = \frac {y^{\prime }}{2 y^{2}-x y} \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

16800

\[ {}\left (2 x -1\right ) y^{\prime }-2 y = \frac {1-4 x}{x^{2}} \]

[_linear]

16801

\[ {}x -y+3+\left (3 x +y+1\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

16803

\[ {}y^{\prime } \left (3 x^{2}-2 x \right )-y \left (6 x -2\right ) = 0 \]

[_separable]

16804

\[ {}x y^{2} y^{\prime }-y^{3} = \frac {x^{4}}{3} \]

[[_homogeneous, ‘class D‘], _rational, _Bernoulli]

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]

16807

\[ {}x -y+2+\left (x -y+3\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

16808

\[ {}x y^{2}+y-x y^{\prime } = 0 \]

[[_homogeneous, ‘class D‘], _rational, _Bernoulli]

16811

\[ {}\left (x -2 x y-y^{2}\right ) y^{\prime }+y^{2} = 0 \]

[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]

16813

\[ {}y^{\prime }-1 = {\mathrm e}^{x +2 y} \]

[[_homogeneous, ‘class C‘], _dAlembert]

16814

\[ {}2 x^{5}+4 x^{3} y-2 x y^{2}+\left (y^{2}+2 x^{2} y-x^{4}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _rational]

16815

\[ {}x^{2} y^{n} y^{\prime } = 2 x y^{\prime }-y \]

[[_homogeneous, ‘class G‘], _rational]

16816

\[ {}\left (3 x +3 y+a^{2}\right ) y^{\prime } = 4 x +4 y+b^{2} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

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]

16821

\[ {}\left (5 x -7 y+1\right ) y^{\prime }+x +y-1 = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

16822

\[ {}x +y+1+\left (2 x +2 y-1\right ) y^{\prime } = 0 \]
i.c.

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

16823

\[ {}y^{3}+2 \left (x^{2}-x y^{2}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _rational]

16824

\[ {}y^{\prime } = \frac {2 \left (y+2\right )^{2}}{\left (x +y-1\right )^{2}} \]

[[_homogeneous, ‘class C‘], _rational]

17221

\[ {}y^{\prime } = \frac {x^{4}}{y} \]

[_separable]

17223

\[ {}y^{\prime }+y^{3} \sin \left (x \right ) = 0 \]

[_separable]

17226

\[ {}x y^{\prime } = \sqrt {1-y^{2}} \]

[_separable]

17231

\[ {}y^{\prime } = 4 \sqrt {x y} \]

[[_homogeneous, ‘class G‘]]

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]

17236

\[ {}r^{\prime } = \frac {r^{2}}{\theta } \]
i.c.

[_separable]

17238

\[ {}y^{\prime } = \frac {2 x}{2 y+1} \]
i.c.

[_separable]

17239

\[ {}y^{\prime } = 2 x y^{2}+4 x^{3} y^{2} \]
i.c.

[_separable]

17240

\[ {}y^{\prime } = x^{2} {\mathrm e}^{-3 y} \]
i.c.

[_separable]

17241

\[ {}y^{\prime } = \left (1+y^{2}\right ) \tan \left (2 x \right ) \]
i.c.

[_separable]

17244

\[ {}x^{2} y^{\prime } = y-x y \]
i.c.

[_separable]

17251

\[ {}y^{\prime } = 2 y^{2}+x y^{2} \]
i.c.

[_separable]

17254

\[ {}y^{\prime } = 2 \left (x +1\right ) \left (1+y^{2}\right ) \]
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]

17257

\[ {}y^{\prime } = \frac {a y+b}{c y+d} \]

[_quadrature]

17258

\[ {}y^{\prime }+4 y = t +{\mathrm e}^{-2 t} \]

[[_linear, ‘class A‘]]

17259

\[ {}y^{\prime }-2 y = t^{2} {\mathrm e}^{2 t} \]

[[_linear, ‘class A‘]]

17260

\[ {}y^{\prime }+y = t \,{\mathrm e}^{-t}+1 \]

[[_linear, ‘class A‘]]

17262

\[ {}y^{\prime }-2 y = 3 \,{\mathrm e}^{t} \]

[[_linear, ‘class A‘]]

17264

\[ {}y^{\prime }+2 t y = 16 t \,{\mathrm e}^{-t^{2}} \]

[_linear]

17265

\[ {}\left (t^{2}+1\right ) y^{\prime }+4 t y = \frac {1}{\left (t^{2}+1\right )^{2}} \]

[_linear]

17266

\[ {}2 y^{\prime }+y = 3 t \]

[[_linear, ‘class A‘]]

17267

\[ {}t y^{\prime }-y = t^{3} {\mathrm e}^{-t} \]

[_linear]

17269

\[ {}2 y^{\prime }+y = 3 t^{2} \]

[[_linear, ‘class A‘]]

17271

\[ {}y^{\prime }+2 y = t \,{\mathrm e}^{-2 t} \]
i.c.

[[_linear, ‘class A‘]]

17272

\[ {}t y^{\prime }+4 y = t^{2}-t +1 \]
i.c.

[_linear]

17274

\[ {}y^{\prime }-2 y = {\mathrm e}^{2 t} \]
i.c.

[[_linear, ‘class A‘]]

17279

\[ {}2 y^{\prime }-y = {\mathrm e}^{\frac {t}{3}} \]
i.c.

[[_linear, ‘class A‘]]

17280

\[ {}3 y^{\prime }-2 y = {\mathrm e}^{-\frac {\pi t}{2}} \]
i.c.

[[_linear, ‘class A‘]]

17281

\[ {}t y^{\prime }+\left (t +1\right ) y = 2 t \,{\mathrm e}^{-t} \]
i.c.

[_linear]

17285

\[ {}y^{\prime }+\frac {4 y}{3} = 1-\frac {t}{4} \]
i.c.

[[_linear, ‘class A‘]]

17288

\[ {}y^{\prime }-\frac {3 y}{2} = 3 t +3 \,{\mathrm e}^{t} \]
i.c.

[[_linear, ‘class A‘]]

17289

\[ {}y^{\prime }-6 y = t^{6} {\mathrm e}^{6 t} \]

[[_linear, ‘class A‘]]

17292

\[ {}2 y^{\prime }+y = 3 t^{2} \]

[[_linear, ‘class A‘]]

17294

\[ {}t \left (-4+t \right ) y^{\prime }+y = 0 \]
i.c.

[_separable]

17296

\[ {}\left (-t^{2}+4\right ) y^{\prime }+2 t y = 3 t^{2} \]
i.c.

[_linear]

17297

\[ {}\left (-t^{2}+4\right ) y^{\prime }+2 t y = 3 t^{2} \]
i.c.

[_linear]

17299

\[ {}y^{\prime } = \frac {-y+t}{2 t +5 y} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

17305

\[ {}y^{\prime } = y^{{1}/{3}} \]
i.c.

[_quadrature]

17306

\[ {}y^{\prime } = -\frac {t}{2}+\frac {\sqrt {t^{2}+4 y}}{2} \]
i.c.

[[_1st_order, _with_linear_symmetries], _Clairaut]

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]

17311

\[ {}y^{\prime } = t y \left (3-y\right ) \]

[_separable]

17312

\[ {}y^{\prime } = y \left (3-t y\right ) \]

[_Bernoulli]

17313

\[ {}y^{\prime } = -y \left (3-t y\right ) \]

[_Bernoulli]

17316

\[ {}2 x +3+\left (2 y-2\right ) y^{\prime } = 0 \]

[_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

\[ {}2 x -y+\left (2 y-x \right ) y^{\prime } = 0 \]
i.c.

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

17335

\[ {}y^{\prime } = {\mathrm e}^{2 x}+y-1 \]

[[_linear, ‘class A‘]]

17337

\[ {}y+\left (2 x y-{\mathrm e}^{-2 y}\right ) y^{\prime } = 0 \]

[[_1st_order, _with_exponential_symmetries]]

17341

\[ {}3 x y+y^{2}+\left (x y+x^{2}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

17342

\[ {}y y^{\prime } = x +1 \]

[_separable]

17344

\[ {}\frac {\left (3 x^{3}-x y^{2}\right ) y^{\prime }}{3 x^{2} y+y^{3}} = 1 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

17345

\[ {}x \left (-1+x \right ) y^{\prime } = y \left (y+1\right ) \]

[_separable]

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‘]]

17349

\[ {}x y^{\prime }-4 \sqrt {y^{2}-x^{2}} = y \]

[[_homogeneous, ‘class A‘], _dAlembert]

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]

17354

\[ {}t y^{\prime }+y = t^{2} y^{2} \]

[[_homogeneous, ‘class G‘], _rational, _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]

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]

17364

\[ {}\left (3 x-y \right ) x^{\prime }+9 y -2 x = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

17365

\[ {}1 = \left (3 \,{\mathrm e}^{y}-2 x \right ) y^{\prime } \]

[[_1st_order, _with_exponential_symmetries]]

17366

\[ {}y^{\prime }-4 \,{\mathrm e}^{x} y^{2} = y \]

[[_1st_order, _with_linear_symmetries], _Bernoulli]

17369

\[ {}\frac {\sqrt {x}\, y^{\prime }}{y} = 1 \]

[_separable]

17370

\[ {}5 x y^{2}+5 y+\left (5 x^{2} y+5 x \right ) y^{\prime } = 0 \]

[_separable]

17372

\[ {}\left (2-x \right ) y^{\prime } = y+2 \left (2-x \right )^{5} \]

[_linear]

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]

17376

\[ {}y^{\prime }+y-y^{{1}/{4}} = 0 \]

[_quadrature]

17817

\[ {}\sqrt {-x^{2}+1}\, y^{\prime }+\sqrt {1-y^{2}} = 0 \]

[_separable]

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

\[ {}y^{2}+x^{2} y^{\prime } = x y y^{\prime } \]

[[_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]

17823

\[ {}3 y-7 x +7 = \left (3 x -7 y-3\right ) y^{\prime } \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

17824

\[ {}\left (x +2 y+1\right ) y^{\prime } = 4 y+2 x +3 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

17825

\[ {}y^{\prime } = \frac {2 \left (y+2\right )^{2}}{\left (x +y-1\right )^{2}} \]

[[_homogeneous, ‘class C‘], _rational]

17826

\[ {}\left (x +y\right )^{2} y^{\prime } = a^{2} \]

[[_homogeneous, ‘class C‘], _dAlembert]

17827

\[ {}x y^{\prime }-4 y = \sqrt {y}\, x^{2} \]

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

17829

\[ {}y^{\prime } = 2 x y-x^{3}+x \]

[_linear]

17831

\[ {}\left (x -2 x y-y^{2}\right ) y^{\prime }+y^{2} = 0 \]

[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]

17832

\[ {}x y^{\prime }+y = x y^{2} \ln \left (x \right ) \]

[_Bernoulli]

17835

\[ {}x -y^{2}+2 x y y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

17836

\[ {}y^{\prime } = \frac {y^{2}}{3}+\frac {2}{3 x^{2}} \]

[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]]

17837

\[ {}y^{\prime }+y^{2}+\frac {y}{x}-\frac {4}{x^{2}} = 0 \]

[[_homogeneous, ‘class G‘], _rational, _Riccati]

17839

\[ {}y^{\prime } = y^{2}+\frac {1}{x^{4}} \]

[_rational, [_Riccati, _special]]

17842

\[ {}y^{\prime } = \frac {x -y^{2}}{2 y \left (x +y^{2}\right )} \]

[[_homogeneous, ‘class G‘], _rational]

17843

\[ {}\left (\left (x +y\right ) x +a^{2}\right ) y^{\prime } = y \left (x +y\right )+b^{2} \]

[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

17846

\[ {}\frac {y y^{\prime }+x}{\sqrt {1+x^{2}+y^{2}}}+\frac {y-x y^{\prime }}{x^{2}+y^{2}} = 0 \]

[[_1st_order, _with_linear_symmetries], _exact]

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]

17850

\[ {}y^{3}+2 \left (x^{2}-x y^{2}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _rational]

17851

\[ {}\left (y^{2} x^{2}-1\right ) y^{\prime }+2 x y^{3} = 0 \]

[[_homogeneous, ‘class G‘], _rational]

17852

\[ {}a x y^{\prime }+b y+x^{m} y^{n} \left (\alpha x y^{\prime }+\beta y\right ) = 0 \]

[[_homogeneous, ‘class G‘], _rational]

17854

\[ {}y^{\prime } = 2 x y-x^{3}+x \]

[_linear]

17855

\[ {}y-x y^{2} \ln \left (x \right )+x y^{\prime } = 0 \]

[_Bernoulli]

17873

\[ {}y = 2 x y^{\prime }+y^{2} {y^{\prime }}^{3} \]

[[_1st_order, _with_linear_symmetries]]

17876

\[ {}y^{\prime } = \sqrt {y-x} \]

[[_homogeneous, ‘class C‘], _dAlembert]

17877

\[ {}y^{\prime } = \sqrt {y-x}+1 \]

[[_homogeneous, ‘class C‘], _dAlembert]

17878

\[ {}y^{\prime } = \sqrt {y} \]

[_quadrature]

17879

\[ {}y^{\prime } = y \ln \left (y\right ) \]

[_quadrature]

17880

\[ {}y^{\prime } = y \ln \left (y\right )^{2} \]

[_quadrature]

17881

\[ {}y^{\prime } = -x +\sqrt {x^{2}+2 y} \]

[[_1st_order, _with_linear_symmetries], _Clairaut]

17882

\[ {}y^{\prime } = -x -\sqrt {x^{2}+2 y} \]

[[_1st_order, _with_linear_symmetries], _Clairaut]

17890

\[ {}{y^{\prime }}^{2}-y y^{\prime }+{\mathrm e}^{x} = 0 \]

[[_1st_order, _with_linear_symmetries]]

17978

\[ {}x y^{\prime } = 2 y \]

[_separable]

17979

\[ {}y y^{\prime } = {\mathrm e}^{2 x} \]

[_separable]

17980

\[ {}y^{\prime } = k y \]

[_quadrature]

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‘]]

17989

\[ {}\left (y \cos \left (y\right )-\sin \left (y\right )+x \right ) y^{\prime } = y \]

[[_1st_order, _with_linear_symmetries]]

17990

\[ {}1+y^{2}+y^{2} y^{\prime } = 0 \]

[_quadrature]

17999

\[ {}x y y^{\prime } = y-1 \]

[_separable]

18000

\[ {}x^{5} y^{\prime }+y^{5} = 0 \]

[_separable]

18002

\[ {}y^{\prime } = 2 x y \]

[_separable]

18005

\[ {}y^{\prime }+y \tan \left (x \right ) = 0 \]

[_separable]

18006

\[ {}y^{\prime }-y \tan \left (x \right ) = 0 \]

[_separable]

18007

\[ {}\left (x^{2}+1\right ) y^{\prime }+1+y^{2} = 0 \]

[_separable]

18008

\[ {}y \ln \left (y\right )-x y^{\prime } = 0 \]

[_separable]

18015

\[ {}y^{\prime } = {\mathrm e}^{-2 y+3 x} \]
i.c.

[_separable]

18017

\[ {}{\mathrm e}^{-y}+\left (x^{2}+1\right ) y^{\prime } = 0 \]
i.c.

[_separable]

18024

\[ {}v^{\prime } = g -\frac {k v^{2}}{m} \]

[_quadrature]

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]

18028

\[ {}x \sin \left (\frac {y}{x}\right ) y^{\prime } = y \sin \left (\frac {y}{x}\right )+x \]

[[_homogeneous, ‘class A‘], _dAlembert]

18029

\[ {}x y^{\prime } = y+2 \,{\mathrm e}^{-\frac {y}{x}} x \]

[[_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

\[ {}x^{2} y^{\prime } = y^{2}+2 x y \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

18034

\[ {}x^{3}+y^{3}-x y^{2} y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

18035

\[ {}y^{\prime } = \left (x +y\right )^{2} \]

[[_homogeneous, ‘class C‘], _Riccati]

18036

\[ {}y^{\prime } = \sin \left (x -y+1\right )^{2} \]

[[_homogeneous, ‘class C‘], _dAlembert]

18037

\[ {}y^{\prime } = \frac {x +y+4}{x -y-6} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18038

\[ {}y^{\prime } = \frac {x +y+4}{x +y-6} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18039

\[ {}2 x -2 y+\left (y-1\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18040

\[ {}y^{\prime } = \frac {x +y-1}{x +4 y+2} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18041

\[ {}2 x +3 y-1-4 \left (x +1\right ) y^{\prime } = 0 \]

[_linear]

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]

18044

\[ {}y^{\prime } = \frac {y-x y^{2}}{x +x^{2} y} \]

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

18045

\[ {}\left (x +\frac {2}{y}\right ) y^{\prime }+y = 0 \]

[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

18048

\[ {}y+y \cos \left (x y\right )+\left (x +x \cos \left (x y\right )\right ) y^{\prime } = 0 \]

[_separable]

18051

\[ {}-\frac {\sin \left (\frac {x}{y}\right )}{y}+\frac {x \sin \left (\frac {x}{y}\right ) y^{\prime }}{y^{2}} = 0 \]

[_separable]

18052

\[ {}1+y+\left (1-x \right ) y^{\prime } = 0 \]

[_separable]

18057

\[ {}2 x \left (1+\sqrt {x^{2}-y}\right ) = \sqrt {x^{2}-y}\, y^{\prime } \]

[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]

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]

18063

\[ {}\frac {y-x y^{\prime }}{\left (x +y\right )^{2}}+y^{\prime } = 1 \]

[[_1st_order, _with_linear_symmetries], _exact, _rational]

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]

18067

\[ {}x y^{\prime }+y+3 x^{3} y^{4} y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _rational]

18070

\[ {}y+\left (x -2 y^{3} x^{2}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _rational]

18071

\[ {}x +3 y^{2}+2 x y y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

18076

\[ {}-y+x y^{\prime } = \left (1+y^{2}\right ) y^{\prime } \]

[[_1st_order, _with_linear_symmetries], _rational]

18077

\[ {}y-x y^{\prime } = x y^{3} y^{\prime } \]

[_separable]

18079

\[ {}\left (x +y\right ) y^{\prime } = y-x \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18081

\[ {}y^{2}-y+x y^{\prime } = 0 \]

[_separable]

18082

\[ {}-y+x y^{\prime } = 2 x^{2}-3 \]

[_linear]

18083

\[ {}x y^{\prime }+y = \sqrt {x y}\, y^{\prime } \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

18085

\[ {}-y+x y^{\prime } = x^{2} y^{4} \left (x y^{\prime }+y\right ) \]

[[_homogeneous, ‘class G‘], _rational]

18086

\[ {}x y^{\prime }+y+x^{2} y^{5} y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _rational]

18087

\[ {}2 x y^{2}-y+x y^{\prime } = 0 \]

[[_homogeneous, ‘class D‘], _rational, _Bernoulli]

18089

\[ {}y^{\prime } = \frac {2 y}{x}+\frac {x^{3}}{y}+x \tan \left (\frac {y}{x^{2}}\right ) \]

[[_homogeneous, ‘class G‘]]

18090

\[ {}x y^{\prime }-3 y = x^{4} \]

[_linear]

18093

\[ {}y^{\prime }+y = 2 x \,{\mathrm e}^{-x}+x^{2} \]

[[_linear, ‘class A‘]]

18095

\[ {}2 y-x^{3} = x y^{\prime } \]

[_linear]

18097

\[ {}y^{\prime }-2 x y = 6 x \,{\mathrm e}^{x^{2}} \]

[_linear]

18099

\[ {}y-2 x y-x^{2}+x^{2} y^{\prime } = 0 \]

[_linear]

18100

\[ {}x y^{\prime }+y = x^{4} y^{3} \]

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

18102

\[ {}x y^{\prime }+y = x y^{2} \]

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

18104

\[ {}y-x y^{\prime } = y^{\prime } y^{2} {\mathrm e}^{y} \]

[[_1st_order, _with_linear_symmetries]]

18105

\[ {}x y^{\prime }+2 = x^{3} \left (y-1\right ) y^{\prime } \]

[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]]

18106

\[ {}x y^{\prime } = 2 x^{2} y+y \ln \left (y\right ) \]

[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]

18121

\[ {}\left (1-x y\right ) y^{\prime } = y^{2} \]

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

18122

\[ {}2 x +3 y+1+\left (2 y-3 x +5\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18123

\[ {}x y^{\prime } = \sqrt {x^{2}+y^{2}} \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

18124

\[ {}y^{2} = \left (x^{3}-x y\right ) y^{\prime } \]

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

18125

\[ {}y^{3} x^{2}+y = \left (x^{3} y^{2}-x \right ) y^{\prime } \]

[[_homogeneous, ‘class G‘], _rational]

18127

\[ {}x y^{\prime }+y = y^{2}+x^{2} y^{\prime } \]

[_separable]

18128

\[ {}x y y^{\prime } = y^{2}+x^{2} y^{\prime } \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

18131

\[ {}y+x^{2} = x y^{\prime } \]

[_linear]

18133

\[ {}6 x +4 y+3+\left (3 x +2 y+2\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18134

\[ {}\cos \left (x +y\right ) = x \sin \left (x +y\right )+x \sin \left (x +y\right ) y^{\prime } \]

[[_1st_order, _with_linear_symmetries], _exact]

18137

\[ {}y^{\prime } \ln \left (x -y\right ) = 1+\ln \left (x -y\right ) \]

[[_homogeneous, ‘class C‘], _exact, _dAlembert]

18138

\[ {}y^{\prime }+2 x y = {\mathrm e}^{-x^{2}} \]

[_linear]

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‘]]

18140

\[ {}\left (x^{2}+1\right ) y^{\prime }+2 x y = 4 x^{3} \]

[_linear]

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]

18149

\[ {}y^{\prime } = \frac {x +2 y+2}{-2 x +y} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18150

\[ {}3 x^{2} \ln \left (y\right )+\frac {x^{3} y^{\prime }}{y} = 0 \]

[_separable]

18152

\[ {}\frac {y-x}{\left (x +y\right )^{3}}-\frac {2 x y^{\prime }}{\left (x +y\right )^{3}} = 0 \]

[_linear]

18153

\[ {}x y^{2}+y+x y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

18155

\[ {}3 x^{2} y-y^{3}-\left (3 x y^{2}-x^{3}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]

18157

\[ {}y^{\prime } = \frac {-3 x -2 y-1}{2 x +3 y-1} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18158

\[ {}{\mathrm e}^{x^{2} y} \left (1+2 x^{2} y\right )+x^{3} {\mathrm e}^{x^{2} y} y^{\prime } = 0 \]

[_linear]

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]

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]

18415

\[ {}x^{\prime } = x^{2}-3 x+2 \]
i.c.

[_quadrature]

18416

\[ {}x^{\prime } = b \,{\mathrm e}^{x} \]
i.c.

[_quadrature]

18417

\[ {}x^{\prime } = \left (x-1\right )^{2} \]
i.c.

[_quadrature]

18418

\[ {}x^{\prime } = \sqrt {x^{2}-1} \]
i.c.

[_quadrature]

18419

\[ {}x^{\prime } = 2 \sqrt {x} \]
i.c.

[_quadrature]

18420

\[ {}x^{\prime } = \tan \left (x\right ) \]
i.c.

[_quadrature]

18422

\[ {}1+2 x+\left (-t^{2}+4\right ) x^{\prime } = 0 \]

[_separable]

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]

18425

\[ {}{\mathrm e}^{3 t} x^{\prime }+3 x \,{\mathrm e}^{3 t} = 2 t \]

[[_linear, ‘class A‘]]

18427

\[ {}x^{\prime }+2 x = {\mathrm e}^{t} \]

[[_linear, ‘class A‘]]

18428

\[ {}x^{\prime }+x \tan \left (t \right ) = 0 \]

[_separable]

18430

\[ {}t^{3} x^{\prime }+\left (-3 t^{2}+2\right ) x = t^{3} \]

[_linear]

18435

\[ {}x^{\prime } = -\lambda x \]

[_quadrature]

18453

\[ {}y^{\prime }+c y = a \]

[_quadrature]

18460

\[ {}v^{\prime }+\frac {2 v}{u} = 3 \]

[_linear]

18463

\[ {}y-x y^{\prime } = b \left (1+x^{2} y^{\prime }\right ) \]

[_separable]

18464

\[ {}x^{\prime } = k \left (A -n x\right ) \left (M -m x\right ) \]

[_quadrature]

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]

18468

\[ {}2 a x +b y+\left (2 c y+b x +e \right ) y^{\prime } = g \]

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18470

\[ {}y y^{\prime }+x = m y \]

[[_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]

18473

\[ {}y^{\prime }+x y = x \]

[_separable]

18476

\[ {}p^{\prime } = \frac {p+a \,t^{3}-2 p t^{2}}{t \left (-t^{2}+1\right )} \]

[_linear]

18477

\[ {}\left (T \ln \left (t \right )-1\right ) T = t T^{\prime } \]

[_Bernoulli]

18483

\[ {}\sqrt {t^{2}+T} = T^{\prime } \]

[[_homogeneous, ‘class G‘]]

18485

\[ {}y^{\prime } = \left (x +y\right )^{2} \]

[[_homogeneous, ‘class C‘], _Riccati]

18490

\[ {}y^{\prime } = x \left (a y^{2}+b \right ) \]

[_separable]

18491

\[ {}n^{\prime } = \left (n^{2}+1\right ) x \]

[_separable]

18492

\[ {}v^{\prime }+\frac {2 v}{u} = 3 v \]

[_separable]

18495

\[ {}\frac {y^{\prime }}{x} = y \sin \left (x^{2}-1\right )-\frac {2 y}{\sqrt {x}} \]

[_separable]

18496

\[ {}y^{\prime } = 1+\frac {2 y}{x -y} \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18497

\[ {}v^{\prime }+2 u v = 2 u \]

[_separable]

18498

\[ {}1+v^{2}+\left (u^{2}+1\right ) v v^{\prime } = 0 \]

[_separable]

18500

\[ {}4 y {y^{\prime }}^{3}-2 x^{2} {y^{\prime }}^{2}+4 x y y^{\prime }+x^{3} = 16 y^{2} \]

[[_1st_order, _with_linear_symmetries]]

18540

\[ {}y^{\prime }+\frac {y}{x} = -x^{2}+1 \]

[_linear]

18542

\[ {}y^{\prime } = x -y \]

[[_linear, ‘class A‘]]

18545

\[ {}x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}-1\right ) y = x^{3} \]

[_linear]

18547

\[ {}x \left (-x^{2}+1\right ) y^{\prime }+\left (2 x^{2}-1\right ) y = a \,x^{3} \]

[_linear]

18548

\[ {}y^{\prime }+\sin \left (x \right ) y = y^{2} \sin \left (x \right ) \]

[_separable]

18549

\[ {}\left (-x^{2}+1\right ) y^{\prime }-x y = a x y^{2} \]

[_separable]

18560

\[ {}x^{2}+\ln \left (y\right )+\frac {x y^{\prime }}{y} = 0 \]

[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]

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

\[ {}\left (2 x y+x^{2}\right ) y^{\prime }-3 x^{2}+2 x y-y^{2} = 0 \]

[[_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]

18566

\[ {}\left (x^{2}-2 x y\right ) y^{\prime }+x^{2}-3 x y+2 y^{2} = 0 \]

[_linear]

18567

\[ {}3 x^{2} y^{\prime }+2 x^{2}-3 y^{2} = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Riccati]

18568

\[ {}\left (3 x +2 y-7\right ) y^{\prime } = 2 x -3 y+6 \]

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18569

\[ {}\left (6 x -5 y+4\right ) y^{\prime } = 1+2 x -y \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18570

\[ {}\left (5 x -2 y+7\right ) y^{\prime } = x -3 y+2 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18571

\[ {}\left (x -3 y+4\right ) y^{\prime } = 5 x -7 y \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18572

\[ {}\left (x -3 y+4\right ) y^{\prime } = 2 x -6 y+7 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18573

\[ {}\left (5 x -2 y+7\right ) y^{\prime } = 10 x -4 y+6 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18574

\[ {}\left (2 x -2 y+5\right ) y^{\prime } = x -y+3 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18575

\[ {}\left (6 x -4 y+1\right ) y^{\prime } = 3 x -2 y+1 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18648

\[ {}\left (1-x \right ) y^{\prime }-y-1 = 0 \]

[_separable]

18650

\[ {}y-x y^{\prime } = a \left (y^{2}+y^{\prime }\right ) \]

[_separable]

18652

\[ {}x^{2}+y^{2}-2 x y y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

18653

\[ {}y^{2}+\left (x y+x^{2}\right ) y^{\prime } = 0 \]

[[_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‘]]

18656

\[ {}3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18657

\[ {}\left (y-3 x +3\right ) y^{\prime } = 2 y-x -4 \]

[[_homogeneous, ‘class C‘], _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]

18659

\[ {}x +y y^{\prime }+\frac {-y+x y^{\prime }}{x^{2}+y^{2}} = 0 \]

[[_1st_order, _with_linear_symmetries], _exact, _rational]

18661

\[ {}2 a x +b y+g +\left (2 c y+b x +e \right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18663

\[ {}y-x y^{\prime }+\ln \left (x \right ) = 0 \]

[_linear]

18664

\[ {}\left (1+x y\right ) y-\left (1-x y\right ) x y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

18665

\[ {}a \left (x y^{\prime }+2 y\right ) = x y y^{\prime } \]

[_separable]

18667

\[ {}y \left (2 x y+{\mathrm e}^{x}\right )-{\mathrm e}^{x} y^{\prime } = 0 \]

[_Bernoulli]

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‘]]

18669

\[ {}y \left (x y+2 y^{2} x^{2}\right )+x \left (x y-y^{2} x^{2}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

18672

\[ {}3 x^{2} y^{4}+2 x y+\left (2 x^{3} y^{3}-x^{2}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _rational]

18674

\[ {}y^{3}-2 x^{2} y+\left (2 x y^{2}-x^{3}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

18675

\[ {}2 x^{2} y-3 y^{4}+\left (3 x^{3}+2 x y^{3}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _rational]

18676

\[ {}y^{2}+2 x^{2} y+\left (2 x^{3}-x y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

18677

\[ {}x y^{\prime }-a y = x +1 \]

[_linear]

18678

\[ {}y^{\prime }+y = {\mathrm e}^{-x} \]

[[_linear, ‘class A‘]]

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]

18687

\[ {}\left (x +y\right )^{2} y^{\prime } = a^{2} \]

[[_homogeneous, ‘class C‘], _dAlembert]

18688

\[ {}-y+x y^{\prime } = \sqrt {x^{2}+y^{2}} \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

18692

\[ {}y^{\prime }+\frac {\left (1-2 x \right ) y}{x^{2}} = 1 \]

[_linear]

18694

\[ {}2 x -y+1+\left (2 y-x -1\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18696

\[ {}x y^{\prime }+\frac {y^{2}}{x} = y \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

18698

\[ {}y^{\prime }+\frac {4 x y}{x^{2}+1} = \frac {1}{\left (x^{2}+1\right )^{3}} \]

[_linear]

18699

\[ {}x^{2} y-\left (x^{3}+y^{3}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

18700

\[ {}x \left (-x^{2}+1\right ) y^{\prime }+\left (2 x^{2}-1\right ) y = a \,x^{3} \]

[_linear]

18701

\[ {}x^{2}+y^{2}+1-2 x y y^{\prime } = 0 \]

[_rational, _Bernoulli]

18702

\[ {}y y^{\prime }+x = m \left (-y+x y^{\prime }\right ) \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18704

\[ {}\left (x +1\right ) y^{\prime }+1 = 2 \,{\mathrm e}^{y} \]

[_separable]

18706

\[ {}y+\left (a \,x^{2} y^{n}-2 x \right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _rational]

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

\[ {}2 x y+\left (y^{2}-x^{2}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

18715

\[ {}y-x y^{\prime } = b \left (1+x^{2} y^{\prime }\right ) \]

[_separable]

18716

\[ {}3 y+2 x +4-\left (4 x +6 y+5\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18717

\[ {}\left (x^{3} y^{3}+y^{2} x^{2}+x y+1\right ) y+\left (x^{3} y^{3}-y^{2} x^{2}-x y+1\right ) x y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _rational]

18718

\[ {}2 y^{2} x^{2}+y-\left (x^{3} y-3 x \right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

18719

\[ {}y^{2}+x^{2} y^{\prime } = x y y^{\prime } \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

18720

\[ {}y^{\prime }+\frac {n y}{x} = a \,x^{-n} \]

[_linear]

18721

\[ {}\left (x -y\right )^{2} y^{\prime } = a^{2} \]

[[_homogeneous, ‘class C‘], _dAlembert]

18729

\[ {}y = -a y^{\prime }+\frac {c +a \arcsin \left (y^{\prime }\right )}{\sqrt {1-{y^{\prime }}^{2}}} \]

[_quadrature]

18742

\[ {}x y \left (y-x y^{\prime }\right ) = y y^{\prime }+x \]

[_separable]

18743

\[ {}y^{\prime }+2 x y = x^{2}+y^{2} \]

[[_homogeneous, ‘class C‘], _Riccati]

18756

\[ {}\left (-y+x y^{\prime }\right ) \left (y y^{\prime }+x \right ) = h^{2} y^{\prime } \]

[_rational]

18761

\[ {}{y^{\prime }}^{3}-4 x y y^{\prime }+8 y^{2} = 0 \]

[[_1st_order, _with_linear_symmetries]]

18768

\[ {}y = 2 x y^{\prime }+y^{2} {y^{\prime }}^{3} \]

[[_1st_order, _with_linear_symmetries]]

18771

\[ {}y^{\prime } \sqrt {x} = \sqrt {y} \]

[_separable]

18968

\[ {}y+x +x y^{\prime } = 0 \]

[_linear]

18969

\[ {}\left (1+x y\right ) y-x y^{\prime } = 0 \]

[[_homogeneous, ‘class D‘], _rational, _Bernoulli]

18971

\[ {}y-x +\left (x +y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18972

\[ {}x +y y^{\prime }+\frac {-y+x y^{\prime }}{x^{2}+y^{2}} = 0 \]

[[_1st_order, _with_linear_symmetries], _exact, _rational]

18973

\[ {}x^{3}+3 x y^{2}+\left (y^{3}+3 x^{2} y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]

18974

\[ {}x y^{\prime }+y = y^{2} \ln \left (x \right ) \]

[_Bernoulli]

18975

\[ {}\left (-x^{2}+1\right ) y^{\prime }-2 x y = -x^{3}+x \]

[_linear]

18976

\[ {}x y^{\prime }-y-\cos \left (\frac {1}{x}\right ) = 0 \]

[_linear]

18977

\[ {}y y^{\prime }+x = m \left (-y+x y^{\prime }\right ) \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18980

\[ {}x^{2} y^{\prime }+y = 1 \]

[_separable]

18981

\[ {}2 y+\left (x^{2}+1\right ) \arctan \left (x \right ) y^{\prime } = 0 \]

[_separable]

18993

\[ {}y-x y^{\prime } = a \left (y^{2}+y^{\prime }\right ) \]

[_separable]

18994

\[ {}\left (x +y-1\right ) y^{\prime } = x +y+1 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18995

\[ {}\left (2 x +2 y+1\right ) y^{\prime } = x +y+1 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18996

\[ {}\left (2 x +3 y-5\right ) y^{\prime }+2 x +3 y-1 = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

18997

\[ {}\left (x^{2}+y^{2}\right ) y^{\prime } = x y+x^{2} \]

[[_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]

19001

\[ {}\left (2 x -2 y+5\right ) y^{\prime }-x +y-3 = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

19002

\[ {}x +y+1-\left (2 x +2 y+1\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

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]

19008

\[ {}\left (6 x -5 y+4\right ) y^{\prime }+y-2 x -1 = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

19009

\[ {}\left (x -3 y+4\right ) y^{\prime }+7 y-5 x = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

19010

\[ {}\left (2 x +4 y+3\right ) y^{\prime } = x +2 y+1 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

19011

\[ {}-y+x y^{\prime } = \sqrt {x^{2}+y^{2}} \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

19012

\[ {}x \left (x^{2}+3 y^{2}\right )+y \left (y^{2}+3 x^{2}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]

19013

\[ {}x^{2}+3 y^{2}-2 x y y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

19014

\[ {}y^{\prime } = \frac {1+2 x -y}{x +2 y-3} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

19015

\[ {}\left (x -y\right ) y^{\prime } = x +y+1 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

19016

\[ {}x -y-2-\left (2 x -2 y-3\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

19024

\[ {}y^{2}+\left (x -\frac {1}{y}\right ) y^{\prime } = 0 \]

[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]]

19027

\[ {}y^{\prime }+\frac {\left (1-2 x \right ) y}{x^{2}} = 1 \]

[_linear]

19035

\[ {}y \left (2 x y+{\mathrm e}^{x}\right )-{\mathrm e}^{x} y^{\prime } = 0 \]

[_Bernoulli]

19038

\[ {}y y^{\prime }+x = \frac {a^{2} \left (-y+x y^{\prime }\right )}{x^{2}+y^{2}} \]

[[_1st_order, _with_linear_symmetries], _exact, _rational]

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‘]]

19041

\[ {}\left (x^{4} y^{4}+y^{2} x^{2}+x y\right ) y+\left (x^{4} y^{4}-y^{2} x^{2}+x y\right ) x y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _rational]

19042

\[ {}y \left (x y+2 y^{2} x^{2}\right )+x \left (x y-y^{2} x^{2}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

19044

\[ {}x^{2}+y^{2}-2 x y y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

19046

\[ {}y^{2}+2 x^{2} y+\left (2 x^{3}-x y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

19047

\[ {}2 y+3 x y^{\prime }+2 x y \left (3 y+4 x y^{\prime }\right ) = 0 \]

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

19049

\[ {}\frac {\left (y+x -a \right ) y^{\prime }}{y+x -b} = \frac {x +y+a}{x +y+b} \]

[[_homogeneous, ‘class C‘], _rational, _dAlembert]

19050

\[ {}\left (x -y\right )^{2} y^{\prime } = a^{2} \]

[[_homogeneous, ‘class C‘], _dAlembert]

19051

\[ {}\left (x +y\right )^{2} y^{\prime } = a^{2} \]

[[_homogeneous, ‘class C‘], _dAlembert]

19052

\[ {}y^{\prime } = \left (4 x +y+1\right )^{2} \]

[[_homogeneous, ‘class C‘], _Riccati]

19055

\[ {}-y+x y^{\prime } = \sqrt {x^{2}+y^{2}} \]

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

19057

\[ {}y^{\prime } = \frac {1+x^{2}+y^{2}}{2 x y} \]

[_rational, _Bernoulli]

19058

\[ {}y y^{\prime }+x = m \left (-y+x y^{\prime }\right ) \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

19059

\[ {}y+\left (a \,x^{2} y^{n}-2 x \right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _rational]

19065

\[ {}2 y+3 x y^{\prime }+2 x y \left (3 y+4 x y^{\prime }\right ) = 0 \]

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

19067

\[ {}\left (2 x +2 y+3\right ) y^{\prime } = x +y+1 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

19071

\[ {}y^{\prime } = \sin \left (x +y\right )+\cos \left (x +y\right ) \]

[[_homogeneous, ‘class C‘], _dAlembert]

19074

\[ {}y \left (2 x y+{\mathrm e}^{x}\right )-{\mathrm e}^{x} y^{\prime } = 0 \]

[_Bernoulli]

19075

\[ {}y^{2}+x^{2} y^{\prime } = x y y^{\prime } \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

19079

\[ {}y^{\prime }+\frac {a x +b y+c}{b x +f y+e} = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

19150

\[ {}y = 3 x +a \ln \left (y^{\prime }\right ) \]

[_separable]

19152

\[ {}y = x +a \arctan \left (y^{\prime }\right ) \]

[[_homogeneous, ‘class C‘], _dAlembert]

19157

\[ {}y = \sin \left (y^{\prime }\right )-y^{\prime } \cos \left (y^{\prime }\right ) \]

[_quadrature]

19162

\[ {}x = y+a \ln \left (y^{\prime }\right ) \]

[_separable]

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

\[ {}y-x y^{\prime } = y y^{\prime }+x \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

19200

\[ {}\left (x^{3} y^{3}+y^{2} x^{2}+x y+1\right ) y+\left (x^{3} y^{3}-y^{2} x^{2}-x y+1\right ) x y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _rational]

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]

19202

\[ {}\left (-y+x y^{\prime }\right ) \left (y y^{\prime }+x \right ) = h^{2} y^{\prime } \]

[_rational]

19223

\[ {}{y^{\prime }}^{3} = y^{4} \left (x y^{\prime }+y\right ) \]

[[_1st_order, _with_linear_symmetries]]

19225

\[ {}a x y {y^{\prime }}^{2}+\left (x^{2}-a y^{2}-b \right ) y^{\prime }-x y = 0 \]

[_rational]

19233

\[ {}y-x y^{\prime } = a \left (y^{2}+y^{\prime }\right ) \]

[_separable]

19234

\[ {}y-x y^{\prime } = b \left (1+x^{2} y^{\prime }\right ) \]

[_separable]

19430

\[ {}y-x y^{\prime } = 0 \]

[_separable]

19432

\[ {}x^{3}+x y^{2}+a^{2} y+\left (y^{3}+x^{2} y-a^{2} x \right ) y^{\prime } = 0 \]

[[_1st_order, _with_linear_symmetries], _rational]

19433

\[ {}\left (x +2 y^{3}\right ) y^{\prime } = y \]

[[_homogeneous, ‘class G‘], _rational]

19435

\[ {}1+y^{2}-x y y^{\prime } = 0 \]

[_separable]

19436

\[ {}y^{2}+\left (x y+x^{2}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

19437

\[ {}y^{\prime } = \frac {6 x -2 y-7}{2 x +3 y-6} \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

19438

\[ {}2 x +y+1+\left (4 x +2 y-1\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

19440

\[ {}y^{\prime }+2 x y = {\mathrm e}^{-x^{2}} \]

[_linear]

19441

\[ {}\left (x +2 y^{3}\right ) y^{\prime } = y \]

[[_homogeneous, ‘class G‘], _rational]

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]

19477

\[ {}y = 2 x y^{\prime }+y^{2} {y^{\prime }}^{3} \]

[[_1st_order, _with_linear_symmetries]]

19481

\[ {}x y \left (y-x y^{\prime }\right ) = y y^{\prime }+x \]

[_separable]

19492

\[ {}{y^{\prime }}^{3}-4 x y y^{\prime }+8 y^{2} = 0 \]

[[_1st_order, _with_linear_symmetries]]