2.3.1 first order ode linear

Table 2.395: first order ode linear

#

ODE

CAS classification

Solved?

19

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

[[_linear, ‘class A‘]]

20

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

[[_linear, ‘class A‘]]

21

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

[[_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‘]]

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]

43

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

[_separable]

44

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

[_separable]

49

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

[_separable]

57

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

[_separable]

59

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

[_separable]

62

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

[_separable]

64

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

[_separable]

65

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

[_separable]

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]

83

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

[_separable]

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]

89

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

[_linear]

90

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

[_linear]

91

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

[_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]

97

\[ {}\left (x^{2}+1\right ) y^{\prime }+3 x^{3} y = 6 x \,{\mathrm e}^{-\frac {3 x^{2}}{2}} \]
i.c.

[_linear]

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]

101

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

[_linear]

102

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

[_linear]

103

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

[_separable]

104

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

[_linear]

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]

179

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

[_linear]

183

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

[_separable]

185

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

[_linear]

193

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

[[_linear, ‘class A‘]]

198

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

[_linear]

199

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

[_linear]

203

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

[_linear]

206

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

[_linear]

207

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

[_linear]

209

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

[_separable]

213

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

[_separable]

661

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

[[_linear, ‘class A‘]]

662

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

[[_linear, ‘class A‘]]

663

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

[[_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‘]]

677

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

[_separable]

679

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

[_separable]

680

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

[_separable]

685

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

[_separable]

692

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

[_separable]

694

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

[_separable]

697

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

[_separable]

699

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

[_separable]

700

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

[_separable]

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]

714

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

[_separable]

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]

720

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

[_linear]

721

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

[_linear]

722

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

[_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]

728

\[ {}\left (x^{2}+1\right ) y^{\prime }+3 x^{3} y = 6 x \,{\mathrm e}^{-\frac {3 x^{2}}{2}} \]
i.c.

[_linear]

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]

775

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

[_separable]

777

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

[_linear]

785

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

[[_linear, ‘class A‘]]

790

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

[_linear]

791

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

[_linear]

795

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

[_linear]

798

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

[_linear]

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]

805

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

[_separable]

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‘]]

1101

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

[_linear]

1102

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

[[_linear, ‘class A‘]]

1103

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

[_linear]

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]

1108

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

[[_linear, ‘class A‘]]

1109

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

[[_linear, ‘class A‘]]

1110

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

[[_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]

1113

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

[_linear]

1114

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

[[_linear, ‘class A‘]]

1115

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

[_linear]

1116

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

[_linear]

1117

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

[_linear]

1118

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

1122

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

[_linear]

1123

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

[_linear]

1124

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

[[_linear, ‘class A‘]]

1125

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

[[_linear, ‘class A‘]]

1126

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

[[_linear, ‘class A‘]]

1127

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

[[_linear, ‘class A‘]]

1128

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

[[_linear, ‘class A‘]]

1166

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

[_linear]

1167

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

[_separable]

1168

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

[_linear]

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]

1171

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

[_linear]

1196

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

[_separable]

1202

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

[_linear]

1211

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

[[_linear, ‘class A‘]]

1218

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

[_linear]

1221

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

[_separable]

1223

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

[_linear]

1225

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

[_linear]

1229

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

[_linear]

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‘]]

1235

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

[[_linear, ‘class A‘]]

1240

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

[_linear]

1245

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

[_linear]

1520

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

[_linear]

1521

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

[_separable]

1530

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

[_linear]

1531

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

[_linear]

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]

1549

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

[_linear]

1550

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

[_linear]

1551

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

[_linear]

1552

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

[_linear]

1553

\[ {}y^{\prime }+\frac {4 y}{-1+x} = \frac {1}{\left (-1+x \right )^{5}}+\frac {\sin \left (x \right )}{\left (-1+x \right )^{4}} \]

[_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]

1556

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

[_linear]

1557

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

[_linear]

1558

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

[_linear]

1559

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

[_linear]

1560

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

[_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]

1563

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

[_linear]

1564

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

[_linear]

1565

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

[_linear]

1566

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

1570

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

[_linear]

1571

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

[_linear]

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]

1584

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

[_separable]

1591

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

[_separable]

1599

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

[_separable]

1613

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

[_separable]

1642

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

[_linear]

1680

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

[_separable]

1681

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

[_linear]

1700

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

[_linear]

1701

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

[_separable]

1713

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

[_separable]

1714

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

[_separable]

1716

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

[_linear]

1717

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

[_linear]

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]

1730

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

[_linear]

1731

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

[_separable]

2294

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

[_separable]

2295

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

[_separable]

2296

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

[_separable]

2297

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

[_separable]

2298

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

[_linear]

2299

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

[_separable]

2300

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

[_separable]

2301

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

[_linear]

2302

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

[[_linear, ‘class A‘]]

2303

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

[_linear]

2304

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

[_separable]

2305

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

[_linear]

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

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

[_separable]

2309

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

[_linear]

2310

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

[_linear]

2311

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

[_linear]

2312

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

[_linear]

2313

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

[_separable]

2314

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

[_linear]

2315

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

[_linear]

2316

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

[_linear]

2317

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

[_linear]

2319

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

[_separable]

2329

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

[_separable]

2342

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

[_separable]

2360

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

[_separable]

2472

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

[_separable]

2473

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

[_separable]

2474

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

[_linear]

2475

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

[[_linear, ‘class A‘]]

2476

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

[_linear]

2477

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

[_separable]

2478

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

[_linear]

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

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

[_separable]

2483

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

[_linear]

2484

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

[_linear]

2485

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

[_linear]

2486

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

[_linear]

2487

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

[_separable]

2488

\[ {}y^{\prime }+y = \left \{\begin {array}{cc} 2 & 0\le t \le 1 \\ 0 & 1<t \end {array}\right . \]
i.c.

[[_linear, ‘class A‘]]

2490

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

[_separable]

2500

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

[_separable]

2514

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

[_separable]

2519

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

[_separable]

2535

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

[_separable]

2841

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

[_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

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

[_separable]

2850

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

[_separable]

2857

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

[_separable]

2858

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

[_separable]

2861

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

[_separable]

2862

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

[_separable]

2871

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

[_linear]

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]

2937

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

[_linear]

2953

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

[_separable]

2958

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

[_linear]

2959

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

[_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‘]]

2963

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

[_linear]

2965

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

[_linear]

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]

2970

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

[_linear]

2973

\[ {}\cos \left (\theta \right ) r^{\prime } = 2+2 r \sin \left (\theta \right ) \]

[_linear]

2974

\[ {}\sin \left (\theta \right ) r^{\prime }+1+r \tan \left (\theta \right ) = \cos \left (\theta \right ) \]

[_linear]

2975

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

[_linear]

2977

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

[_linear]

2979

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

[_linear]

2981

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

[_linear]

3004

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

[_separable]

3007

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

[_linear]

3020

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

[_separable]

3027

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

[_linear]

3046

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

[_linear]

3051

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

[[_linear, ‘class A‘]]

3055

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

[_linear]

3169

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

[_linear]

3293

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

[_quadrature]

3334

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

[_separable]

3409

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

[_separable]

3431

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

[_separable]

3438

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

[_separable]

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‘]]

3443

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

[_linear]

3444

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

[_linear]

3445

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

[_linear]

3446

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

[_linear]

3449

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

[_linear]

3450

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

3454

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

[_linear]

3455

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

[_linear]

3456

\[ {}y^{\prime } = -\cot \left (t \right ) y+6 \cos \left (t \right )^{2} \]
i.c.

[_linear]

3458

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

[_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]

3464

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

[_linear]

3472

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

[_linear]

3474

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

[_linear]

3475

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

[_linear]

3478

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

[_linear]

3515

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

[_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]

3524

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

[_linear]

3525

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

[_separable]

3527

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

[_separable]

3530

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

[[_linear, ‘class A‘]]

3531

\[ {}x^{2} y^{\prime }-4 x y = x^{7} \sin \left (x \right ) \]

[_linear]

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]

3535

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

[_linear]

3536

\[ {}y^{\prime }+\frac {y}{\ln \left (x \right ) x} = 9 x^{2} \]

[_linear]

3537

\[ {}y^{\prime }-y \tan \left (x \right ) = 8 \sin \left (x \right )^{3} \]

[_linear]

3538

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

[_linear]

3539

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

[_linear]

3540

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

[_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‘]]

3562

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

[_separable]

3593

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

[_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]

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]

3605

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

[_separable]

3610

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

[[_linear, ‘class A‘]]

3611

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

[_linear]

3612

\[ {}x^{2} y^{\prime }-4 x y = x^{7} \sin \left (x \right ) \]

[_linear]

3613

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

[_linear]

3614

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

[_linear]

3615

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

[_linear]

3616

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

[_linear]

3617

\[ {}y^{\prime }+\frac {y}{\ln \left (x \right ) x} = 9 x^{2} \]

[_linear]

3618

\[ {}y^{\prime }-y \tan \left (x \right ) = 8 \sin \left (x \right )^{3} \]

[_linear]

3619

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

[_linear]

3620

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

[_linear]

3621

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

[_linear]

3622

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

[_linear]

3623

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

[[_linear, ‘class A‘]]

3624

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

[_linear]

3625

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

[_linear]

3626

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

[_linear]

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‘]]

3629

\[ {}y^{\prime }-2 y = \left \{\begin {array}{cc} 1 & x \le 1 \\ 0 & 1<x \end {array}\right . \]
i.c.

[[_linear, ‘class A‘]]

3630

\[ {}y^{\prime }-2 y = \left \{\begin {array}{cc} 1-x & x <1 \\ 0 & 1\le x \end {array}\right . \]
i.c.

[[_linear, ‘class A‘]]

3632

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

[_linear]

3633

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

[[_linear, ‘class A‘]]

3634

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

[_linear]

3635

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

[_linear]

3642

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

[_separable]

3972

\[ {}-y+y^{\prime } = \left \{\begin {array}{cc} 2 & 0\le t <1 \\ -1 & 1\le t \end {array}\right . \]
i.c.

[[_linear, ‘class A‘]]

4093

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

[_linear]

4097

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

[_linear]

4100

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

[[_linear, ‘class A‘]]

4101

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

[_linear]

4104

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

[_linear]

4107

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

[[_linear, ‘class A‘]]

4109

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

[_linear]

4116

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

[_linear]

4191

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

[[_linear, ‘class A‘]]

4192

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

[_linear]

4193

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

[_linear]

4194

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

[_linear]

4195

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

[_linear]

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]

4201

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

[_linear]

4202

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

[_linear]

4203

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

[_linear]

4204

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

[_linear]

4205

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

[_linear]

4206

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

[_linear]

4207

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

[_linear]

4208

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

[_linear]

4209

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

[_linear]

4210

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

[_linear]

4211

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

[_linear]

4212

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

[_linear]

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]

4224

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

[_separable]

4225

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

[_separable]

4227

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

[_separable]

4228

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

[_separable]

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]

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]

4269

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

[_linear]

4270

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

[_linear]

4271

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

[_linear]

4272

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

[[_linear, ‘class A‘]]

4273

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

[_linear]

4274

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

[_linear]

4280

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

[_linear]

4283

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

[_linear]

4284

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

[_linear]

4289

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

[_linear]

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]

4297

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

[_linear]

4359

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

[_linear]

4367

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

[_linear]

4369

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

[_linear]

4370

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

[_linear]

4371

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

[_linear]

4372

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

[_linear]

4398

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

[_separable]

4404

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

[_linear]

4412

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

[_separable]

4437

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

[_linear]

4440

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

[_linear]

4609

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

[[_linear, ‘class A‘]]

4610

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

[[_linear, ‘class A‘]]

4611

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

[[_linear, ‘class A‘]]

4612

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

[[_linear, ‘class A‘]]

4613

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

[[_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]

4616

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

[_linear]

4617

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

[_linear]

4618

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

[_separable]

4619

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

[_linear]

4620

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

[_linear]

4621

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

[_separable]

4622

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

[_linear]

4623

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

[_linear]

4624

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

[_separable]

4625

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

[_linear]

4626

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

[_linear]

4627

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

[_linear]

4628

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

[_linear]

4629

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

[_linear]

4630

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

[_linear]

4631

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

[_linear]

4632

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

[_separable]

4633

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

[_linear]

4634

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

[_separable]

4635

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

[_linear]

4636

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

[_linear]

4637

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

[_linear]

4638

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

[_linear]

4639

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

[_linear]

4640

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

[_linear]

4641

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

[_linear]

4642

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

[_linear]

4643

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

[_separable]

4644

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

[_linear]

4645

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

[_linear]

4646

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

[_linear]

4679

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

[_linear]

4681

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

[_linear]

4738

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

[_linear]

4743

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

[_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]

4748

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

[_linear]

4749

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

[_linear]

4750

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

[_linear]

4751

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

[_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]

4757

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

[_linear]

4758

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

[_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]

4761

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

[_linear]

4762

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

[_linear]

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]

4823

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

[_linear]

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]

4836

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

[_linear]

4842

\[ {}\left (1-2 x \right ) y^{\prime } = 16+32 x -6 y \]

[_linear]

4844

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

[_linear]

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]

4855

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

[_linear]

4856

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

[_linear]

4877

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

[_linear]

4878

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

[_linear]

4879

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

[_linear]

4880

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

[_linear]

4881

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

[_linear]

4882

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

[_linear]

4883

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

[_separable]

4884

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

[_linear]

4885

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

[_linear]

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]

4889

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

[_linear]

4890

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

[_linear]

4891

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

[_linear]

4892

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

[_linear]

4893

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

[_linear]

4894

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

[_separable]

4903

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

[_linear]

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]

4910

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

[_linear]

4911

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

[_linear]

4912

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

[_linear]

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]

4916

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

[_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]

4918

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

[_linear]

4920

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

[_separable]

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]

4927

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

[_separable]

4928

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

[_linear]

4931

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

[_linear]

4932

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

[_linear]

4934

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

[_linear]

4936

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

[_linear]

4937

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

[_linear]

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]

4953

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

[_linear]

4954

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

[_linear]

4955

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

[_linear]

4956

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

[_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]

4961

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

[_linear]

4962

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

[_linear]

4973

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

[_linear]

4976

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

[_separable]

4978

\[ {}x^{5} y^{\prime } = 1-3 x^{4} y \]

[_linear]

4981

\[ {}x^{n} y^{\prime } = a +b \,x^{n -1} y \]

[_linear]

4987

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

[_linear]

4990

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

[_linear]

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]

5012

\[ {}\left (\operatorname {a0} +\operatorname {a1} \sin \left (x \right )^{2}\right ) y^{\prime }+\operatorname {a2} x \left (\operatorname {a3} +\operatorname {a1} \sin \left (x \right )^{2}\right )+\operatorname {a1} y \sin \left (2 x \right ) = 0 \]

[_linear]

5013

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

[_linear]

5014

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

[_linear]

5036

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

[[_linear, ‘class A‘]]

5134

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

[_separable]

5345

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

[_separable]

5391

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

[_quadrature]

5404

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

[_quadrature]

5406

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

[_separable]

5409

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

[_separable]

5411

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

[_separable]

5451

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

[_quadrature]

5455

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

[_quadrature]

5456

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

[_quadrature]

5476

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

[_separable]

5501

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

[_separable]

5503

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

[_linear]

5615

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

[_quadrature]

5616

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

[_quadrature]

5624

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

[_quadrature]

5685

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

[_separable]

5692

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

[_linear]

5712

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

[_linear]

5713

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

[_linear]

5714

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

[_linear]

5715

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

[_linear]

5716

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

[_linear]

5770

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

[_separable]

5791

\[ {}7 y-3+\left (2 x +1\right ) y^{\prime } = 0 \]

[_separable]

5839

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

[_linear]

5842

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

[_linear]

5843

\[ {}r^{\prime } = \left (r+{\mathrm e}^{-\theta }\right ) \tan \left (\theta \right ) \]

[_linear]

5844

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

[_linear]

5847

\[ {}\tan \left (\theta \right ) r^{\prime }-r = \tan \left (\theta \right )^{2} \]

[_linear]

5848

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

[[_linear, ‘class A‘]]

5849

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

[[_linear, ‘class A‘]]

5850

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

[[_linear, ‘class A‘]]

5851

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

[_linear]

5852

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

[_linear]

5853

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

[_linear]

5854

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

[_linear]

5858

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

[[_linear, ‘class A‘]]

5880

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

[_separable]

5881

\[ {}y^{\prime }+a y = k \,{\mathrm e}^{b x} \]

[[_linear, ‘class A‘]]

5885

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

[[_linear, ‘class A‘]]

5889

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

[_linear]

5892

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

[_linear]

5897

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

[_linear]

5902

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

[_linear]

6025

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

[_separable]

6029

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

[[_linear, ‘class A‘]]

6093

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

[_separable]

6102

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

[_separable]

6105

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

[[_linear, ‘class A‘]]

6106

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

[_linear]

6107

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

[_linear]

6108

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

[_linear]

6109

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

[_linear]

6110

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

[_linear]

6111

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

[_linear]

6112

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

[_linear]

6113

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

[_linear]

6114

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

[_linear]

6115

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

[_linear]

6116

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

[_linear]

6117

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

[[_linear, ‘class A‘]]

6118

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

[_linear]

6131

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

[_linear]

6208

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

[_linear]

6218

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

[_linear]

6226

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

[_linear]

6230

\[ {}\sin \left (\theta \right ) \cos \left (\theta \right ) r^{\prime }-\sin \left (\theta \right )^{2} = r \cos \left (\theta \right )^{2} \]

[_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]

6263

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

[_separable]

6273

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

[_separable]

6280

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

[_separable]

6285

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

[_separable]

6294

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

[_linear]

6296

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

[_separable]

6297

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

[_linear]

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]

6302

\[ {}r^{\prime }+r \tan \left (\theta \right ) = \sec \left (\theta \right ) \]

[_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]

6307

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

[_linear]

6308

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

[_separable]

6309

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

[_linear]

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‘]]

6312

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

[_linear]

6313

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

[_linear]

6314

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

[_linear]

6315

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

[_linear]

6319

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

[_linear]

6320

\[ {}x^{\prime } = \alpha -\beta \cos \left (\frac {\pi t}{12}\right )-k x \]
i.c.

[[_linear, ‘class A‘]]

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]

6340

\[ {}y^{\prime }-4 y = 32 x^{2} \]

[[_linear, ‘class A‘]]

6342

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

[_linear]

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‘]]

6401

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

[_linear]

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]

6415

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

[_linear]

6416

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

[_linear]

6420

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

[[_linear, ‘class A‘]]

6421

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

[_linear]

6425

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

[_separable]

6426

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

[_linear]

6427

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

[_linear]

6431

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

[_separable]

6440

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

[_linear]

6441

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

[_linear]

6442

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

[_linear]

6443

\[ {}\left (x^{2}+1\right ) y^{\prime }+3 x y = 5 x \]
i.c.

[_separable]

6444

\[ {}y^{\prime }+y \cot \left (x \right ) = 5 \,{\mathrm e}^{\cos \left (x \right )} \]
i.c.

[_linear]

6455

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

[_linear]

6459

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

[_separable]

6460

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

[_linear]

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]

6466

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

[_linear]

6470

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

[_linear]

6471

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

[_linear]

6473

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

[_linear]

6474

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

[_linear]

6477

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

[_linear]

6515

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

[[_linear, ‘class A‘]]

6516

\[ {}y^{\prime }-5 y = 3 \,{\mathrm e}^{x}-2 x +1 \]

[[_linear, ‘class A‘]]

6517

\[ {}y^{\prime }-5 y = x^{2} {\mathrm e}^{x}-x \,{\mathrm e}^{5 x} \]

[[_linear, ‘class A‘]]

6523

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

[[_linear, ‘class A‘]]

6524

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

[[_linear, ‘class A‘]]

6525

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

[[_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]

6579

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

[_separable]

6580

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

[_separable]

6582

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

[_separable]

6588

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

[_separable]

6589

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

[_separable]

6599

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

[_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]

6644

\[ {}i^{\prime }-6 i = 10 \sin \left (2 t \right ) \]

[[_linear, ‘class A‘]]

6649

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

[_linear]

6654

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

[_linear]

6659

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

[_linear]

6660

\[ {}L i^{\prime }+R i = E \sin \left (2 t \right ) \]
i.c.

[[_linear, ‘class A‘]]

6667

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

[_quadrature]

6794

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

[_linear]

6842

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

[_linear]

6897

\[ {}y^{\prime }+4 x y = 8 x^{3} \]

[_linear]

6900

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

[[_linear, ‘class A‘]]

6901

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

[_linear]

6902

\[ {}x y+x^{2} y^{\prime } = 10 \sin \left (x \right ) \]

[_linear]

6903

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

[_linear]

6904

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

[_separable]

6914

\[ {}3 x y^{\prime }+5 y = 10 \]

[_separable]

6948

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

[_separable]

6951

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

[_separable]

6952

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

[[_linear, ‘class A‘]]

6961

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

[_separable]

6977

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

[[_linear, ‘class A‘]]

6980

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

[[_linear, ‘class A‘]]

6985

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

[_separable]

6990

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

[_separable]

6992

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

[_linear]

7000

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

[_linear]

7001

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

[_linear]

7009

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

[[_linear, ‘class A‘]]

7022

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

[_linear]

7023

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

[_linear]

7024

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

[_linear]

7025

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

[_linear]

7032

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

[[_linear, ‘class A‘]]

7033

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

[[_linear, ‘class A‘]]

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‘]]

7042

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

[[_linear, ‘class A‘]]

7043

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

[[_linear, ‘class A‘]]

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‘]]

7067

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

[_separable]

7080

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

[_separable]

7087

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

[_separable]

7093

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

[_separable]

7131

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

[_separable]

7147

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

[[_linear, ‘class A‘]]

7149

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

[_separable]

7150

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

[_linear]

7151

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

[_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]

7156

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

[_linear]

7157

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

[_linear]

7158

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

[_linear]

7161

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

[_linear]

7162

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

[_linear]

7163

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

[_linear]

7164

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

[_linear]

7165

\[ {}r^{\prime }+r \sec \left (t \right ) = \cos \left (t \right ) \]

[_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‘]]

7171

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

[_linear]

7175

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

[_linear]

7176

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

[_linear]

7177

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

[_linear]

7178

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

[_linear]

7179

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

[_separable]

7180

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

[_linear]

7181

\[ {}2 y+y^{\prime } = \left \{\begin {array}{cc} 1 & 0\le x \le 3 \\ 0 & 3<x \end {array}\right . \]
i.c.

[[_linear, ‘class A‘]]

7182

\[ {}y^{\prime }+y = \left \{\begin {array}{cc} 1 & 0\le x \le 1 \\ -1 & 1<x \end {array}\right . \]
i.c.

[[_linear, ‘class A‘]]

7183

\[ {}y^{\prime }+2 x y = \left \{\begin {array}{cc} x & 0\le x <1 \\ 0 & 1\le x \end {array}\right . \]
i.c.

[_linear]

7184

\[ {}\left (x^{2}+1\right ) y^{\prime }+2 x y = \left \{\begin {array}{cc} x & 0\le x <1 \\ -x & 1\le x \end {array}\right . \]
i.c.

[_linear]

7185

\[ {}y^{\prime }+\left (\left \{\begin {array}{cc} 2 & 0\le x \le 1 \\ -\frac {2}{x} & 1<x \end {array}\right .\right ) y = 4 x \]
i.c.

[_linear]

7186

\[ {}y^{\prime }+\left (\left \{\begin {array}{cc} 1 & 0\le x \le 2 \\ 5 & 2<x \end {array}\right .\right ) y = 0 \]
i.c.

[_separable]

7187

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

[_linear]

7188

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

[_linear]

7189

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

[_linear]

7190

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

[_linear]

7191

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

[_linear]

7192

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

[_separable]

7195

\[ {}x y^{\prime }-4 y = x^{6} {\mathrm e}^{x} \]
i.c.

[_linear]

7197

\[ {}x y^{\prime }-4 y = x^{6} {\mathrm e}^{x} \]
i.c.

[_linear]

7384

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

[_separable]

7401

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

[_separable]

7408

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

[[_linear, ‘class A‘]]

7410

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

[[_linear, ‘class A‘]]

7418

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

[_separable]

7439

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

[_quadrature]

7444

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

[_linear]

7446

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

[_linear]

7555

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

[_separable]

7583

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

[_separable]

7584

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

[_linear]

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‘]]

7598

\[ {}L y^{\prime }+R y = E \sin \left (\omega x \right ) \]
i.c.

[[_linear, ‘class A‘]]

7599

\[ {}L y^{\prime }+R y = E \,{\mathrm e}^{i \omega x} \]
i.c.

[[_linear, ‘class A‘]]

7600

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

[[_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]

7604

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

[_linear]

7605

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

[_linear]

7606

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

[_linear]

7607

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

[_linear]

7608

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

[[_linear, ‘class A‘]]

7731

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

[_separable]

7774

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

[_separable]

7803

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

[_linear]

7808

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

[_separable]

7809

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

[_separable]

7814

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

[_separable]

7818

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

[_separable]

7825

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

[_separable]

7826

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

[_separable]

7827

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

[_linear]

7828

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

[[_linear, ‘class A‘]]

7829

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

[_linear]

7830

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

[_separable]

7831

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

[_linear]

7832

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

[_linear]

7833

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

[_linear]

7834

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

[_linear]

7835

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

[_separable]

7836

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

[_linear]

7838

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

[_linear]

7839

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

[[_linear, ‘class A‘]]

7840

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

[_separable]

7848

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

[_separable]

7849

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

[_linear]

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]

7877

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

[_linear]

7885

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

[_linear]

7917

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

[_linear]

7918

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

[_linear]

7919

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

[_separable]

7923

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

[_separable]

7925

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

[_linear]

7926

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

[_linear]

7932

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

[_separable]

8069

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

[[_linear, ‘class A‘]]

8073

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

[_separable]

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‘]]

8436

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

[_quadrature]

8438

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

[_separable]

8439

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

[_quadrature]

8440

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

[_quadrature]

8442

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

[_separable]

8445

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

[_separable]

8452

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

[_quadrature]

8534

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

[_quadrature]

8553

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

[_quadrature]

8697

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

[_separable]

8699

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

[_linear]

8700

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

[_linear]

8723

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

[_linear]

8724

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

[_separable]

8725

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

[_separable]

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]

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‘]]

8999

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

[[_linear, ‘class A‘]]

9000

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

[[_linear, ‘class A‘]]

9010

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

[[_linear, ‘class A‘]]

9012

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

[_linear]

9036

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

[_separable]

9162

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

[_linear]

10016

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

[[_linear, ‘class A‘]]

10017

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

[[_linear, ‘class A‘]]

10018

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

[_linear]

10019

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

[_linear]

10020

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

[_linear]

10021

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

[_linear]

10022

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

[_linear]

10023

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

[_separable]

10024

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

[_linear]

10025

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

[_linear]

10102

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

[_linear]

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]

10141

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

[_linear]

10144

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

[_linear]

10145

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

[_linear]

10146

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

[_separable]

10159

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

[_linear]

10160

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

[_linear]

10161

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

[_linear]

10164

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

[_linear]

10165

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

[_linear]

10172

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

[_linear]

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]

10194

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

[_separable]

10203

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

[_linear]

10204

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

[_linear]

10207

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

[_linear]

10209

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

[_linear]

10211

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

[_linear]

10398

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

[_separable]

10399

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

[_separable]

10442

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

[_separable]

10445

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

[_linear]

10451

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

[_separable]

10526

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

[_separable]

10527

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

[_quadrature]

10566

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

[_separable]

11925

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

[_linear]

12086

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

[_linear]

12722

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

[_linear]

12740

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

[_linear]

12741

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

[_linear]

12742

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

[_linear]

12743

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

[_linear]

12744

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

[_linear]

12751

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

[_separable]

12762

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

[_separable]

12764

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

[_linear]

12770

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

[_linear]

12779

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

[_linear]

12782

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

[_linear]

12784

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

[_linear]

12800

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

[_linear]

12802

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

[_quadrature]

12828

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

[_separable]

12830

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

[_separable]

12946

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

[_separable]

12951

\[ {}x^{\prime }+2 x = t^{2}+4 t +7 \]

[[_linear, ‘class A‘]]

12952

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

[_separable]

12973

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

[_separable]

12992

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

[[_linear, ‘class A‘]]

12996

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

[_linear]

12999

\[ {}7 t^{2} x^{\prime } = 3 x-2 t \]

[_linear]

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]

13010

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

[_linear]

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]

13014

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

[[_linear, ‘class A‘]]

13015

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

[_separable]

13016

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

[_linear]

13020

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

[_separable]

13027

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

[_separable]

13167

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

[[_linear, ‘class A‘]]

13173

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

[[_linear, ‘class A‘]]

13174

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

[_separable]

13179

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

[[_linear, ‘class A‘]]

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‘]]

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]

13218

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

[_linear]

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

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

[_separable]

13241

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

[_linear]

13242

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

[_linear]

13243

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

[_linear]

13245

\[ {}r^{\prime }+r \tan \left (t \right ) = \cos \left (t \right ) \]

[_linear]

13246

\[ {}\cos \left (t \right ) r^{\prime }+r \sin \left (t \right )-\cos \left (t \right )^{4} = 0 \]

[_linear]

13247

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

[_linear]

13248

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

[_linear]

13253

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

[_linear]

13254

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

[_separable]

13255

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

[_linear]

13256

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

[_separable]

13257

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

[_linear]

13258

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

[[_linear, ‘class A‘]]

13261

\[ {}y^{\prime }+y = \left \{\begin {array}{cc} 2 & 0\le x <1 \\ 0 & 1\le x \end {array}\right . \]
i.c.

[[_linear, ‘class A‘]]

13262

\[ {}y^{\prime }+y = \left \{\begin {array}{cc} 5 & 0\le x <10 \\ 1 & 10\le x \end {array}\right . \]
i.c.

[[_linear, ‘class A‘]]

13263

\[ {}y^{\prime }+y = \left \{\begin {array}{cc} {\mathrm e}^{-x} & 0\le x <2 \\ {\mathrm e}^{-2} & 2\le x \end {array}\right . \]
i.c.

[[_linear, ‘class A‘]]

13264

\[ {}\left (x +2\right ) y^{\prime }+y = \left \{\begin {array}{cc} 2 x & 0\le x <2 \\ 4 & 2\le x \end {array}\right . \]
i.c.

[_linear]

13265

\[ {}a y^{\prime }+b y = k \,{\mathrm e}^{-\lambda x} \]

[[_linear, ‘class A‘]]

13266

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

[[_linear, ‘class A‘]]

13272

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

[_separable]

13274

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

[_separable]

13275

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

[_linear]

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]

13281

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

[_linear]

13284

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

[_separable]

13292

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

[_separable]

13293

\[ {}y^{\prime }+y = \left \{\begin {array}{cc} 1 & 0\le x <2 \\ 0 & 0<x \end {array}\right . \]
i.c.

[[_linear, ‘class A‘]]

13294

\[ {}\left (x +2\right ) y^{\prime }+y = \left \{\begin {array}{cc} 2 x & 0\le x \le 2 \\ 4 & 2<x \end {array}\right . \]
i.c.

[_linear]

13634

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

[[_linear, ‘class A‘]]

13640

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

[_separable]

13642

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

[_separable]

13646

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

[_separable]

13647

\[ {}i^{\prime } = p \left (t \right ) i \]

[_separable]

13652

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

[_linear]

13653

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

[_separable]

13654

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

[_linear]

13655

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

[_linear]

13656

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

[_linear]

13657

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

[_linear]

13658

\[ {}x^{\prime }+5 x = t \]

[[_linear, ‘class A‘]]

13659

\[ {}x^{\prime }+\left (a +\frac {1}{t}\right ) x = b \]
i.c.

[_linear]

13660

\[ {}T^{\prime } = -k \left (T-\mu -a \cos \left (\omega \left (t -\phi \right )\right )\right ) \]

[[_linear, ‘class A‘]]

13662

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

[_linear]

13772

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

[_linear]

13774

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

[[_linear, ‘class A‘]]

13775

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

[_linear]

13777

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

[[_linear, ‘class A‘]]

13799

\[ {}x^{\prime }+5 x = 10 t +2 \]
i.c.

[[_linear, ‘class A‘]]

13804

\[ {}x^{\prime }-x \cot \left (t \right ) = 4 \sin \left (t \right ) \]

[_linear]

13813

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

[_linear]

13820

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

[_separable]

13885

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

[_linear]

13889

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

[_separable]

14075

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

[_linear]

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]

14091

\[ {}r^{\prime }+r \tan \left (t \right ) = 0 \]

[_separable]

14097

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

[_linear]

14102

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

[_linear]

14107

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

[_linear]

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]

14114

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

[_linear]

14115

\[ {}s^{\prime } \cos \left (t \right )+s \sin \left (t \right ) = 1 \]

[_linear]

14116

\[ {}s^{\prime }+s \cos \left (t \right ) = \frac {\sin \left (2 t \right )}{2} \]

[_linear]

14117

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

[_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]

14142

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

[_separable]

14145

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

[_linear]

14200

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

[_linear]

14210

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

[_linear]

14232

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

[_separable]

14237

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

[_linear]

14239

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

[_separable]

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‘]]

14260

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

[_separable]

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]

14285

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

[_separable]

14294

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

[_linear]

14310

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

[_linear]

14311

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

[_linear]

14312

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

[_linear]

14313

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

[_linear]

14314

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

[_linear]

14315

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

[_linear]

14332

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

[_separable]

14335

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

[_separable]

14337

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

[_separable]

14340

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

[_linear]

14344

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

[_linear]

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]

14349

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

[_linear]

14351

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

[_separable]

14352

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

[_linear]

14355

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

[_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]

14360

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

[_linear]

14361

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

[_linear]

14362

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

[_linear]

14522

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

[_separable]

14524

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

[_separable]

14534

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

[_separable]

14537

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

[_separable]

14541

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

[_separable]

14543

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

[_separable]

14544

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

[_separable]

14562

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

[[_linear, ‘class A‘]]

14564

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

[[_linear, ‘class A‘]]

14566

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

[_separable]

14577

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

[_separable]

14578

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

[_separable]

14585

\[ {}v^{\prime } = 2 V \left (t \right )-2 v \]

[[_linear, ‘class A‘]]

14647

\[ {}y^{\prime } = -4 y+9 \,{\mathrm e}^{-t} \]

[[_linear, ‘class A‘]]

14648

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

[[_linear, ‘class A‘]]

14649

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

[[_linear, ‘class A‘]]

14650

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

[[_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‘]]

14655

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

[[_linear, ‘class A‘]]

14656

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

14660

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

[[_linear, ‘class A‘]]

14661

\[ {}y^{\prime }-3 y = 2 t -{\mathrm e}^{4 t} \]

[[_linear, ‘class A‘]]

14662

\[ {}y^{\prime }+y = \cos \left (2 t \right )+3 \sin \left (2 t \right )+{\mathrm e}^{-t} \]

[[_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]

14675

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

[_linear]

14676

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

[_linear]

14677

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

[_linear]

14678

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

[[_linear, ‘class A‘]]

14679

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

[_linear]

14680

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

[_linear]

14681

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

[_linear]

14682

\[ {}y^{\prime } = t^{r} y+4 \]

[_linear]

14683

\[ {}v^{\prime }+\frac {2 v}{5} = 3 \cos \left (2 t \right ) \]

[[_linear, ‘class A‘]]

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‘]]

14692

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

[[_linear, ‘class A‘]]

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]

14697

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

[[_linear, ‘class A‘]]

14698

\[ {}y^{\prime } = t +\frac {2 y}{t +1} \]

[_linear]

14701

\[ {}y^{\prime } = -3 y+{\mathrm e}^{-2 t}+t^{2} \]

[[_linear, ‘class A‘]]

14702

\[ {}x^{\prime } = -t x \]
i.c.

[_separable]

14703

\[ {}y^{\prime } = 2 y+\cos \left (4 t \right ) \]
i.c.

[[_linear, ‘class A‘]]

14704

\[ {}y^{\prime } = 3 y+2 \,{\mathrm e}^{3 t} \]
i.c.

[[_linear, ‘class A‘]]

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]

14715

\[ {}y^{\prime } = t^{2} y+1+y+t^{2} \]

[_separable]

14716

\[ {}y^{\prime } = \frac {2 y+1}{t} \]

[_separable]

14902

\[ {}y^{\prime }+4 y = {\mathrm e}^{2 x} \]

[[_linear, ‘class A‘]]

14945

\[ {}y^{\prime }+3 x y = 6 x \]

[_separable]

14951

\[ {}\left (-2+x \right ) y^{\prime } = 3+y \]

[_separable]

14957

\[ {}y^{\prime } = 3 x -y \sin \left (x \right ) \]

[_linear]

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]

14973

\[ {}y^{\prime } = 2 x -1+2 x y-y \]
i.c.

[_separable]

14976

\[ {}y^{\prime } = x y-4 x \]

[_separable]

14982

\[ {}y^{\prime } = x y-4 x \]

[_separable]

14983

\[ {}y^{\prime } = x y-3 x -2 y+6 \]

[_separable]

14986

\[ {}y^{\prime } = \frac {y}{x} \]

[_separable]

14999

\[ {}y^{\prime } = 2 x -1+2 x y-y \]
i.c.

[_separable]

15004

\[ {}x^{2} y^{\prime }+3 x^{2} y = \sin \left (x \right ) \]

[[_linear, ‘class A‘]]

15008

\[ {}y^{\prime } = 1+x y+3 y \]

[_linear]

15011

\[ {}y^{\prime } = y \sin \left (x \right ) \]

[_separable]

15013

\[ {}x y^{\prime }+\cos \left (x^{2}\right ) = 827 y \]

[_linear]

15015

\[ {}2 y+y^{\prime } = 20 \,{\mathrm e}^{3 x} \]

[[_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]

15019

\[ {}2 x y+x^{2} y^{\prime } = \sin \left (x \right ) \]

[_linear]

15020

\[ {}x y^{\prime } = \sqrt {x}+3 y \]

[_linear]

15021

\[ {}\cos \left (x \right ) y^{\prime }+y \sin \left (x \right ) = \cos \left (x \right )^{2} \]

[_linear]

15022

\[ {}x y^{\prime }+\left (5 x +2\right ) y = \frac {20}{x} \]

[_linear]

15023

\[ {}2 \sqrt {x}\, y^{\prime }+y = 2 x \,{\mathrm e}^{-\sqrt {x}} \]

[_linear]

15026

\[ {}y^{\prime }+5 y = {\mathrm e}^{-3 x} \]
i.c.

[[_linear, ‘class A‘]]

15027

\[ {}x y^{\prime }+3 y = 20 x^{2} \]
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]

15030

\[ {}y^{\prime }+6 x y = \sin \left (x \right ) \]
i.c.

[_linear]

15031

\[ {}x^{2} y^{\prime }+x y = \sqrt {x}\, \sin \left (x \right ) \]
i.c.

[_linear]

15032

\[ {}-y+x y^{\prime } = x^{2} {\mathrm e}^{-x^{2}} \]
i.c.

[_linear]

15076

\[ {}2 x \left (y+1\right )-y^{\prime } = 0 \]

[_separable]

15080

\[ {}x y^{\prime } = 2 y-6 x^{3} \]

[_linear]

15087

\[ {}4 x y-6+x^{2} y^{\prime } = 0 \]

[_linear]

15090

\[ {}3 y-x^{3}+x y^{\prime } = 0 \]

[_linear]

15093

\[ {}2+2 x^{2}-2 x y+\left (x^{2}+1\right ) y^{\prime } = 0 \]

[_linear]

15109

\[ {}y^{\prime }-3 y = 12 \,{\mathrm e}^{2 x} \]

[[_linear, ‘class A‘]]

15114

\[ {}2 y-6 x +\left (x +1\right ) y^{\prime } = 0 \]

[_linear]

15120

\[ {}2 y+y^{\prime } = \sin \left (x \right ) \]

[[_linear, ‘class A‘]]

15127

\[ {}y^{\prime } = x \left (6 y+{\mathrm e}^{x^{2}}\right ) \]

[_linear]

15129

\[ {}x^{2} y^{\prime }+3 x y = 6 \,{\mathrm e}^{-x^{2}} \]

[_linear]

15187

\[ {}x y^{\prime }+3 y = {\mathrm e}^{2 x} \]

[_linear]

15712

\[ {}y^{\prime }+x y = 0 \]

[_separable]

15713

\[ {}y^{\prime }+y = \sin \left (x \right ) \]

[[_linear, ‘class A‘]]

15725

\[ {}y^{\prime } = -\frac {2 y}{x}-3 \]

[_linear]

15742

\[ {}y^{\prime }+y = \sin \left (t \right ) \]
i.c.

[[_linear, ‘class A‘]]

15755

\[ {}x y^{\prime }+y = \cos \left (x \right ) \]

[_linear]

15763

\[ {}y^{\prime }+y \cos \left (x \right ) = 0 \]

[_separable]

15764

\[ {}y^{\prime }-y = \sin \left (x \right ) \]

[[_linear, ‘class A‘]]

15777

\[ {}2 y+y^{\prime } = x^{2} \]
i.c.

[[_linear, ‘class A‘]]

15784

\[ {}y^{\prime } = y+\frac {1}{-t +1} \]

[_linear]

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]

15801

\[ {}t y^{\prime }+y = t^{3} \]
i.c.

[_linear]

15802

\[ {}t^{3} y^{\prime }+t^{4} y = 2 t^{3} \]
i.c.

[_linear]

15803

\[ {}2 y^{\prime }+t y = \ln \left (t \right ) \]
i.c.

[_linear]

15804

\[ {}y^{\prime }+y \sec \left (t \right ) = t \]
i.c.

[_linear]

15805

\[ {}y^{\prime }+\frac {y}{t -3} = \frac {1}{t -1} \]
i.c.

[_linear]

15806

\[ {}\left (t -2\right ) y^{\prime }+\left (t^{2}-4\right ) y = \frac {1}{t +2} \]
i.c.

[_linear]

15807

\[ {}y^{\prime }+\frac {y}{\sqrt {-t^{2}+4}} = t \]
i.c.

[_linear]

15808

\[ {}y^{\prime }+\frac {y}{\sqrt {-t^{2}+4}} = t \]
i.c.

[_linear]

15809

\[ {}t y^{\prime }+y = t \sin \left (t \right ) \]
i.c.

[_linear]

15810

\[ {}y^{\prime }+y \tan \left (t \right ) = \sin \left (t \right ) \]
i.c.

[_linear]

15822

\[ {}y^{\prime } = \frac {y+1}{t +1} \]

[_separable]

15823

\[ {}y^{\prime } = \frac {2+y}{2 t +1} \]

[_separable]

15867

\[ {}y^{\prime } = \frac {3+y}{3 x +1} \]
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]

15874

\[ {}y^{\prime }+y f \left (t \right ) = 0 \]
i.c.

[_separable]

15875

\[ {}y^{\prime } = -\frac {y-2}{-2+x} \]
i.c.

[_separable]

15885

\[ {}y^{\prime } = y f \left (t \right ) \]
i.c.

[_separable]

15887

\[ {}y^{\prime }-y = 2 \,{\mathrm e}^{-t} \]

[[_linear, ‘class A‘]]

15888

\[ {}y^{\prime }-y = 2 \cos \left (t \right ) \]

[[_linear, ‘class A‘]]

15889

\[ {}y^{\prime }-y = t^{2}-2 t \]

[[_linear, ‘class A‘]]

15890

\[ {}y^{\prime }-y = 4 t \,{\mathrm e}^{-t} \]

[[_linear, ‘class A‘]]

15891

\[ {}t y^{\prime }+y = t^{2} \]

[_linear]

15892

\[ {}t y^{\prime }+y = t \]

[_linear]

15893

\[ {}x y^{\prime }+y = x \,{\mathrm e}^{x} \]

[_linear]

15894

\[ {}x y^{\prime }+y = {\mathrm e}^{-x} \]

[_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]

15898

\[ {}y^{\prime }+y \cot \left (t \right ) = \cos \left (t \right ) \]

[_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]

15902

\[ {}y^{\prime }+2 y \cot \left (x \right ) = \cos \left (x \right ) \]

[_linear]

15903

\[ {}y^{\prime }+x y = x^{3} \]

[_linear]

15904

\[ {}y^{\prime }-x y = x \]

[_separable]

15906

\[ {}y^{\prime }-x = y \]

[[_linear, ‘class A‘]]

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]

15915

\[ {}t y^{\prime }+y = \cos \left (t \right ) \]
i.c.

[_linear]

15916

\[ {}t y^{\prime }+y = 2 t \,{\mathrm e}^{t} \]
i.c.

[_linear]

15917

\[ {}\left (1+{\mathrm e}^{t}\right ) y^{\prime }+{\mathrm e}^{t} y = t \]
i.c.

[_linear]

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]

15923

\[ {}y^{\prime }+y = \left \{\begin {array}{cc} 4 & 0\le t <2 \\ 0 & 2\le t \end {array}\right . \]
i.c.

[[_linear, ‘class A‘]]

15924

\[ {}y^{\prime }+y = \left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \]
i.c.

[[_linear, ‘class A‘]]

15925

\[ {}y^{\prime }-y = \sin \left (2 t \right ) \]

[[_linear, ‘class A‘]]

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‘]]

15931

\[ {}y^{\prime }-\frac {y}{2} = 5 \cos \left (t \right )+2 \,{\mathrm e}^{t} \]

[[_linear, ‘class A‘]]

15932

\[ {}y^{\prime }+4 y = 8 \cos \left (4 t \right ) \]

[[_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‘]]

15937

\[ {}y^{\prime }+y = 2 \cos \left (t \right )+t \]

[[_linear, ‘class A‘]]

15938

\[ {}y^{\prime }+\frac {y}{2} = \sin \left (t \right ) \]
i.c.

[[_linear, ‘class A‘]]

15939

\[ {}y^{\prime }-\frac {y}{2} = \sin \left (t \right ) \]
i.c.

[[_linear, ‘class A‘]]

15940

\[ {}t y^{\prime }+y = t \cos \left (t \right ) \]

[_linear]

15941

\[ {}y^{\prime }+y = t \]
i.c.

[[_linear, ‘class A‘]]

15942

\[ {}y^{\prime }+y = \sin \left (t \right ) \]
i.c.

[[_linear, ‘class A‘]]

15943

\[ {}y^{\prime }+y = \cos \left (t \right ) \]
i.c.

[[_linear, ‘class A‘]]

15944

\[ {}y^{\prime }+y = {\mathrm e}^{t} \]
i.c.

[[_linear, ‘class A‘]]

15947

\[ {}y \cos \left (t y\right )+t \cos \left (t y\right ) y^{\prime } = 0 \]

[_separable]

15948

\[ {}y \sec \left (t \right )^{2}+2 t +\tan \left (t \right ) y^{\prime } = 0 \]

[_linear]

15953

\[ {}{\mathrm e}^{t y}+\frac {t \,{\mathrm e}^{t y} y^{\prime }}{y} = 0 \]

[_separable]

15956

\[ {}y^{2}+2 t y y^{\prime } = 0 \]

[_separable]

15957

\[ {}\frac {3 t^{2}}{y}-\frac {t^{3} y^{\prime }}{y^{2}} = 0 \]

[_separable]

15966

\[ {}-2 t y^{2} \sin \left (t^{2}\right )+2 y \cos \left (t^{2}\right ) y^{\prime } = 0 \]

[_separable]

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]

15976

\[ {}2 t y+3 t^{2}+\left (t^{2}-1\right ) y^{\prime } = 0 \]
i.c.

[_linear]

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]

16016

\[ {}2 y-3 t +t y^{\prime } = 0 \]

[_linear]

16021

\[ {}t -y+t y^{\prime } = 0 \]

[_linear]

16034

\[ {}t +y-t y^{\prime } = 0 \]
i.c.

[_linear]

16044

\[ {}y^{\prime }-\frac {2 y}{x} = -x^{2} y \]

[_separable]

16053

\[ {}y = t \left (y^{\prime }+1\right )+2 y^{\prime }+1 \]

[_linear]

16065

\[ {}y^{\prime } = \frac {\left (4-7 x \right ) \left (2 y-3\right )}{\left (-1+x \right ) \left (2 x -5\right )} \]

[_separable]

16066

\[ {}y^{\prime }+3 y = -10 \sin \left (t \right ) \]

[[_linear, ‘class A‘]]

16069

\[ {}y-x +y^{\prime } = 0 \]

[[_linear, ‘class A‘]]

16078

\[ {}y^{\prime }+t y = t \]

[_separable]

16079

\[ {}x^{\prime }+\frac {x}{y} = y^{2} \]

[_linear]

16080

\[ {}t r^{\prime }+r = t \cos \left (t \right ) \]

[_linear]

16097

\[ {}y^{\prime } = -\frac {y}{t -2} \]
i.c.

[_separable]

16221

\[ {}y^{\prime }-4 y = t^{2} \]

[[_linear, ‘class A‘]]

16222

\[ {}y^{\prime }+y = \cos \left (2 t \right ) \]
i.c.

[[_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‘]]

16596

\[ {}x y^{\prime }+y = \cos \left (x \right ) \]

[_linear]

16597

\[ {}2 y+y^{\prime } = {\mathrm e}^{x} \]

[[_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‘]]

16604

\[ {}y^{\prime } = \left (y-1\right ) x \]

[_separable]

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]

16612

\[ {}y^{\prime } = 2 x -y \]

[[_linear, ‘class A‘]]

16613

\[ {}y^{\prime } = x^{2}+y \]

[[_linear, ‘class A‘]]

16614

\[ {}y^{\prime } = -\frac {y}{x} \]

[_separable]

16621

\[ {}y^{\prime } = x +y \]
i.c.

[[_linear, ‘class A‘]]

16622

\[ {}y^{\prime } = 2 y-2 x^{2}-3 \]
i.c.

[[_linear, ‘class A‘]]

16623

\[ {}x y^{\prime } = 2 x -y \]
i.c.

[_linear]

16626

\[ {}\sin \left (x \right ) y^{\prime }-y \cos \left (x \right ) = 0 \]
i.c.

[_separable]

16638

\[ {}y^{\prime } = a x +b y+c \]

[[_linear, ‘class A‘]]

16640

\[ {}x y^{\prime }+y = a \left (1+x y\right ) \]
i.c.

[_linear]

16642

\[ {}y^{\prime } = \frac {y}{x} \]
i.c.

[_separable]

16655

\[ {}\left (x +1\right ) y^{\prime } = y-1 \]

[_separable]

16656

\[ {}y^{\prime } = 2 x \left (\pi +y\right ) \]

[_separable]

16659

\[ {}x -y+x y^{\prime } = 0 \]

[_linear]

16666

\[ {}x +y-2+\left (1-x \right ) y^{\prime } = 0 \]

[_linear]

16678

\[ {}2 y+y^{\prime } = {\mathrm e}^{-x} \]

[[_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]

16682

\[ {}\cos \left (x \right ) y^{\prime }-y \sin \left (x \right ) = 2 x \]
i.c.

[_linear]

16683

\[ {}x y^{\prime }-2 y = x^{3} \cos \left (x \right ) \]

[_linear]

16684

\[ {}y^{\prime }-y \tan \left (x \right ) = \frac {1}{\cos \left (x \right )^{3}} \]
i.c.

[_linear]

16685

\[ {}x \ln \left (x \right ) y^{\prime }-y = 3 x^{3} \ln \left (x \right )^{2} \]

[_linear]

16687

\[ {}y^{\prime }+y \cos \left (x \right ) = \cos \left (x \right ) \]
i.c.

[_separable]

16690

\[ {}y^{\prime }-y \,{\mathrm e}^{x} = 2 x \,{\mathrm e}^{{\mathrm e}^{x}} \]

[_linear]

16691

\[ {}y^{\prime }+x \,{\mathrm e}^{x} y = {\mathrm e}^{\left (1-x \right ) {\mathrm e}^{x}} \]

[_linear]

16692

\[ {}y^{\prime }-y \ln \left (2\right ) = 2^{\sin \left (x \right )} \left (\cos \left (x \right )-1\right ) \ln \left (2\right ) \]

[[_linear, ‘class A‘]]

16693

\[ {}y^{\prime }-y = -2 \,{\mathrm e}^{-x} \]
i.c.

[[_linear, ‘class A‘]]

16694

\[ {}\sin \left (x \right ) y^{\prime }-y \cos \left (x \right ) = -\frac {\sin \left (x \right )^{2}}{x^{2}} \]
i.c.

[_linear]

16695

\[ {}x^{2} y^{\prime } \cos \left (\frac {1}{x}\right )-y \sin \left (\frac {1}{x}\right ) = -1 \]
i.c.

[_linear]

16696

\[ {}2 x y^{\prime }-y = 1-\frac {2}{\sqrt {x}} \]
i.c.

[_linear]

16697

\[ {}x^{2} y^{\prime }+y = \left (x^{2}+1\right ) {\mathrm e}^{x} \]
i.c.

[_linear]

16698

\[ {}x y^{\prime }+y = 2 x \]

[_linear]

16699

\[ {}\sin \left (x \right ) y^{\prime }+y \cos \left (x \right ) = 1 \]

[_linear]

16700

\[ {}\cos \left (x \right ) y^{\prime }-y \sin \left (x \right ) = -\sin \left (2 x \right ) \]
i.c.

[_linear]

16704

\[ {}y^{\prime }+3 x y = y \,{\mathrm e}^{x^{2}} \]

[_separable]

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]

16729

\[ {}x^{2}+y-x y^{\prime } = 0 \]

[_linear]

16731

\[ {}2 x^{2} y+2 y+5+\left (2 x^{3}+2 x \right ) y^{\prime } = 0 \]

[_linear]

16739

\[ {}{y^{\prime }}^{2}-2 y y^{\prime } = y^{2} \left ({\mathrm e}^{2 x}-1\right ) \]

[_separable]

16742

\[ {}{y^{\prime }}^{2}-\left (2 x +y\right ) y^{\prime }+x^{2}+x y = 0 \]

[_quadrature]

16789

\[ {}x \sin \left (x \right ) y^{\prime }+\left (\sin \left (x \right )-x \cos \left (x \right )\right ) y = \sin \left (x \right ) \cos \left (x \right )-x \]

[_linear]

16795

\[ {}2 x y \,{\mathrm e}^{x^{2}}-x \sin \left (x \right )+{\mathrm e}^{x^{2}} y^{\prime } = 0 \]

[_linear]

16800

\[ {}\left (2 x -1\right ) y^{\prime }-2 y = \frac {1-4 x}{x^{2}} \]

[_linear]

16803

\[ {}y^{\prime } \left (3 x^{2}-2 x \right )-y \left (6 x -2\right ) = 0 \]

[_separable]

17244

\[ {}x^{2} y^{\prime } = y-x y \]
i.c.

[_separable]

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‘]]

17261

\[ {}y^{\prime }+\frac {y}{t} = 5+\cos \left (2 t \right ) \]

[_linear]

17262

\[ {}y^{\prime }-2 y = 3 \,{\mathrm e}^{t} \]

[[_linear, ‘class A‘]]

17263

\[ {}t y^{\prime }+2 y = \sin \left (t \right ) \]

[_linear]

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

\[ {}y+2 y^{\prime } = 3 t \]

[[_linear, ‘class A‘]]

17267

\[ {}t y^{\prime }-y = t^{3} {\mathrm e}^{-t} \]

[_linear]

17268

\[ {}y^{\prime }+y = 5 \sin \left (2 t \right ) \]

[[_linear, ‘class A‘]]

17269

\[ {}y+2 y^{\prime } = 3 t^{2} \]

[[_linear, ‘class A‘]]

17270

\[ {}y^{\prime }-y = 2 t \,{\mathrm e}^{2 t} \]
i.c.

[[_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]

17273

\[ {}y^{\prime }+\frac {2 y}{t} = \frac {\cos \left (t \right )}{t^{2}} \]
i.c.

[_linear]

17274

\[ {}y^{\prime }-2 y = {\mathrm e}^{2 t} \]
i.c.

[[_linear, ‘class A‘]]

17275

\[ {}t y^{\prime }+2 y = \sin \left (t \right ) \]
i.c.

[_linear]

17276

\[ {}t^{3} y^{\prime }+4 t^{2} y = {\mathrm e}^{-t} \]
i.c.

[_linear]

17277

\[ {}t y^{\prime }+\left (t +1\right ) y = t \]
i.c.

[_linear]

17278

\[ {}y^{\prime }-\frac {y}{3} = 3 \cos \left (t \right ) \]
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]

17282

\[ {}t y^{\prime }+2 y = \frac {\sin \left (t \right )}{t} \]
i.c.

[_linear]

17283

\[ {}\sin \left (t \right ) y^{\prime }+y \cos \left (t \right ) = {\mathrm e}^{t} \]
i.c.

[_linear]

17284

\[ {}y^{\prime }+\frac {y}{2} = 2 \cos \left (t \right ) \]
i.c.

[[_linear, ‘class A‘]]

17285

\[ {}y^{\prime }+\frac {4 y}{3} = 1-\frac {t}{4} \]
i.c.

[[_linear, ‘class A‘]]

17286

\[ {}y^{\prime }+\frac {y}{4} = 3+2 \cos \left (2 t \right ) \]
i.c.

[[_linear, ‘class A‘]]

17287

\[ {}y^{\prime }-y = 1+3 \sin \left (t \right ) \]
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‘]]

17290

\[ {}y^{\prime }+\frac {y}{t} = 3 \cos \left (2 t \right ) \]

[_linear]

17291

\[ {}t y^{\prime }+2 y = \sin \left (t \right ) \]

[_linear]

17292

\[ {}y+2 y^{\prime } = 3 t^{2} \]

[[_linear, ‘class A‘]]

17293

\[ {}\left (t -3\right ) y^{\prime }+\ln \left (t \right ) y = 2 t \]
i.c.

[_linear]

17294

\[ {}t \left (-4+t \right ) y^{\prime }+y = 0 \]
i.c.

[_separable]

17295

\[ {}y^{\prime }+y \tan \left (t \right ) = \sin \left (t \right ) \]
i.c.

[_linear]

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]

17298

\[ {}y+\ln \left (t \right ) y^{\prime } = \cot \left (t \right ) \]
i.c.

[_linear]

17314

\[ {}y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & 0\le t \le 1 \\ 0 & 1<t \end {array}\right . \]
i.c.

[[_linear, ‘class A‘]]

17315

\[ {}y^{\prime }+\left (\left \{\begin {array}{cc} 2 & 0\le t \le 1 \\ 1 & 1<t \end {array}\right .\right ) y = 0 \]
i.c.

[_separable]

17319

\[ {}2 x y^{2}+2 y+\left (2 x +2 x^{2} y\right ) y^{\prime } = 0 \]

[_separable]

17325

\[ {}\frac {y}{x}+6 x +\left (\ln \left (x \right )-2\right ) y^{\prime } = 0 \]

[_linear]

17335

\[ {}y^{\prime } = {\mathrm e}^{2 x}+y-1 \]

[[_linear, ‘class A‘]]

17367

\[ {}x y^{\prime }+\left (x +1\right ) y = x \]

[_linear]

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]

17828

\[ {}\cos \left (x \right ) y^{\prime } = y \sin \left (x \right )+\cos \left (x \right )^{2} \]

[_linear]

17829

\[ {}y^{\prime } = 2 x y-x^{3}+x \]

[_linear]

17830

\[ {}y^{\prime }+\frac {x y}{x^{2}+1} = \frac {1}{x \left (x^{2}+1\right )} \]

[_linear]

17844

\[ {}y^{\prime } = k y+f \left (x \right ) \]

[[_linear, ‘class A‘]]

17854

\[ {}y^{\prime } = 2 x y-x^{3}+x \]

[_linear]

17859

\[ {}{y^{\prime }}^{3}-\left (y^{2}+x y+x^{2}\right ) {y^{\prime }}^{2}+\left (x^{3} y+y^{2} x^{2}+x y^{3}\right ) y^{\prime }-x^{3} y^{3} = 0 \]

[_quadrature]

17978

\[ {}x y^{\prime } = 2 y \]

[_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]

18021

\[ {}y^{\prime } = 2 x y+1 \]

[_linear]

18031

\[ {}x y^{\prime } = 2 x +3 y \]

[_linear]

18041

\[ {}2 x +3 y-1-4 \left (x +1\right ) y^{\prime } = 0 \]

[_linear]

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]

18082

\[ {}-y+x y^{\prime } = 2 x^{2}-3 \]

[_linear]

18088

\[ {}y^{\prime }+\frac {y}{x} = \sin \left (x \right ) \]

[_linear]

18090

\[ {}x y^{\prime }-3 y = x^{4} \]

[_linear]

18091

\[ {}y^{\prime }+y = \frac {1}{1+{\mathrm e}^{2 x}} \]

[_linear]

18092

\[ {}\left (x^{2}+1\right ) y^{\prime }+2 x y = \cot \left (x \right ) \]

[_linear]

18093

\[ {}y^{\prime }+y = 2 x \,{\mathrm e}^{-x}+x^{2} \]

[[_linear, ‘class A‘]]

18094

\[ {}y^{\prime }+y \cot \left (x \right ) = 2 x \csc \left (x \right ) \]

[_linear]

18095

\[ {}2 y-x^{3} = x y^{\prime } \]

[_linear]

18096

\[ {}y-x +x y \cot \left (x \right )+x y^{\prime } = 0 \]

[_linear]

18097

\[ {}y^{\prime }-2 x y = 6 x \,{\mathrm e}^{x^{2}} \]

[_linear]

18098

\[ {}x \ln \left (x \right ) y^{\prime }+y = 3 x^{3} \]

[_linear]

18099

\[ {}y-2 x y-x^{2}+x^{2} y^{\prime } = 0 \]

[_linear]

18107

\[ {}y^{\prime } \sin \left (2 x \right ) = 2 y+2 \cos \left (x \right ) \]

[_linear]

18131

\[ {}x^{2}+y = x y^{\prime } \]

[_linear]

18132

\[ {}x y^{\prime }+y = x^{2} \cos \left (x \right ) \]

[_linear]

18138

\[ {}y^{\prime }+2 x y = {\mathrm e}^{-x^{2}} \]

[_linear]

18140

\[ {}\left (x^{2}+1\right ) y^{\prime }+2 x y = 4 x^{3} \]

[_linear]

18146

\[ {}y^{\prime } = 1+3 y \tan \left (x \right ) \]

[_linear]

18152

\[ {}\frac {y-x}{\left (x +y\right )^{3}}-\frac {2 x y^{\prime }}{\left (x +y\right )^{3}} = 0 \]

[_linear]

18156

\[ {}x \left (x^{2}+1\right ) y^{\prime }+2 y = \left (x^{2}+1\right )^{3} \]

[_linear]

18158

\[ {}{\mathrm e}^{x^{2} y} \left (1+2 x^{2} y\right )+x^{3} {\mathrm e}^{x^{2} y} y^{\prime } = 0 \]

[_linear]

18166

\[ {}x y+y-1+x y^{\prime } = 0 \]

[_linear]

18169

\[ {}x^{\prime }+x \cot \left (y \right ) = \sec \left (y \right ) \]

[_linear]

18422

\[ {}1+2 x+\left (-t^{2}+4\right ) x^{\prime } = 0 \]

[_separable]

18425

\[ {}x^{\prime } {\mathrm e}^{3 t}+3 x \,{\mathrm e}^{3 t} = 2 t \]

[[_linear, ‘class A‘]]

18427

\[ {}x^{\prime }+2 x = {\mathrm e}^{t} \]

[[_linear, ‘class A‘]]

18428

\[ {}x^{\prime }+x \tan \left (t \right ) = 0 \]

[_separable]

18429

\[ {}x^{\prime }-x \tan \left (t \right ) = 4 \sin \left (t \right ) \]

[_linear]

18430

\[ {}t^{3} x^{\prime }+\left (-3 t^{2}+2\right ) x = t^{3} \]

[_linear]

18432

\[ {}t x^{\prime }+x \ln \left (t \right ) = t^{2} \]

[_linear]

18433

\[ {}t x^{\prime }+x g \left (t \right ) = h \left (t \right ) \]

[_linear]

18458

\[ {}v^{\prime }+u^{2} v = \sin \left (u \right ) \]

[_linear]

18460

\[ {}v^{\prime }+\frac {2 v}{u} = 3 \]

[_linear]

18463

\[ {}y-x y^{\prime } = b \left (1+x^{2} y^{\prime }\right ) \]

[_separable]

18473

\[ {}y^{\prime }+x y = x \]

[_separable]

18474

\[ {}y^{\prime }+\frac {y}{x} = \sin \left (x \right ) \]

[_linear]

18476

\[ {}p^{\prime } = \frac {p+a \,t^{3}-2 p t^{2}}{t \left (-t^{2}+1\right )} \]

[_linear]

18478

\[ {}y^{\prime }+y \cos \left (x \right ) = \frac {\sin \left (2 x \right )}{2} \]

[_linear]

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]

18497

\[ {}v^{\prime }+2 u v = 2 u \]

[_separable]

18509

\[ {}5 x^{\prime }+x = \sin \left (3 t \right ) \]

[[_linear, ‘class A‘]]

18525

\[ {}y^{\prime }+\frac {x y}{x^{2}+1} = \frac {1}{x \left (x^{2}+1\right )} \]

[_linear]

18540

\[ {}y^{\prime }+\frac {y}{x} = -x^{2}+1 \]

[_linear]

18541

\[ {}y^{\prime }+y \cot \left (x \right ) = \csc \left (x \right )^{2} \]

[_linear]

18542

\[ {}y^{\prime } = x -y \]

[[_linear, ‘class A‘]]

18544

\[ {}y^{\prime }+\frac {x y}{x^{2}+1} = \frac {1}{x \left (x^{2}+1\right )} \]

[_linear]

18545

\[ {}x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}-1\right ) y = x^{3} \]

[_linear]

18546

\[ {}y^{\prime }+y \cos \left (x \right ) = \frac {\sin \left (2 x \right )}{2} \]

[_linear]

18547

\[ {}x \left (-x^{2}+1\right ) y^{\prime }+\left (2 x^{2}-1\right ) y = a \,x^{3} \]

[_linear]

18566

\[ {}\left (x^{2}-2 x y\right ) y^{\prime }+x^{2}-3 x y+2 y^{2} = 0 \]

[_linear]

18648

\[ {}\left (1-x \right ) y^{\prime }-y-1 = 0 \]

[_separable]

18663

\[ {}y-x y^{\prime }+\ln \left (x \right ) = 0 \]

[_linear]

18677

\[ {}x y^{\prime }-a y = x +1 \]

[_linear]

18678

\[ {}y^{\prime }+y = {\mathrm e}^{-x} \]

[[_linear, ‘class A‘]]

18679

\[ {}\cos \left (x \right )^{2} y^{\prime }+y = \tan \left (x \right ) \]

[_linear]

18680

\[ {}\left (x +1\right ) y^{\prime }-n y = {\mathrm e}^{x} \left (x +1\right )^{n +1} \]

[_linear]

18681

\[ {}\left (x^{2}+1\right ) y^{\prime }+2 x y = 4 x^{2} \]

[_linear]

18692

\[ {}y^{\prime }+\frac {\left (1-2 x \right ) y}{x^{2}} = 1 \]

[_linear]

18695

\[ {}y^{\prime }+\frac {y}{\sqrt {-x^{2}+1}} = \frac {x +\sqrt {-x^{2}+1}}{\left (-x^{2}+1\right )^{2}} \]

[_linear]

18698

\[ {}y^{\prime }+\frac {4 x y}{x^{2}+1} = \frac {1}{\left (x^{2}+1\right )^{3}} \]

[_linear]

18700

\[ {}x \left (-x^{2}+1\right ) y^{\prime }+\left (2 x^{2}-1\right ) y = a \,x^{3} \]

[_linear]

18711

\[ {}\sqrt {a^{2}+x^{2}}\, y^{\prime }+y = \sqrt {a^{2}+x^{2}}-x \]

[_linear]

18715

\[ {}y-x y^{\prime } = b \left (1+x^{2} y^{\prime }\right ) \]

[_separable]

18720

\[ {}y^{\prime }+\frac {n y}{x} = a \,x^{-n} \]

[_linear]

18757

\[ {}{y^{\prime }}^{2}+2 y y^{\prime } \cot \left (x \right ) = y^{2} \]

[_separable]

18762

\[ {}{y^{\prime }}^{3}-\left (y^{2}+x y+x^{2}\right ) {y^{\prime }}^{2}+\left (x^{3} y+y^{2} x^{2}+x y^{3}\right ) y^{\prime }-x^{3} y^{3} = 0 \]

[_quadrature]

18968

\[ {}y+x +x y^{\prime } = 0 \]

[_linear]

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]

18980

\[ {}x^{2} y^{\prime }+y = 1 \]

[_separable]

18981

\[ {}2 y+\left (x^{2}+1\right ) \arctan \left (x \right ) y^{\prime } = 0 \]

[_separable]

19017

\[ {}y^{\prime }+y \cot \left (x \right ) = 2 \cos \left (x \right ) \]

[_linear]

19018

\[ {}\cos \left (x \right )^{2} y^{\prime }+y = \tan \left (x \right ) \]

[_linear]

19019

\[ {}x \cos \left (x \right ) y^{\prime }+y \left (x \sin \left (x \right )+\cos \left (x \right )\right ) = 1 \]

[_linear]

19020

\[ {}y-x \sin \left (x^{2}\right )+x y^{\prime } = 0 \]

[_linear]

19021

\[ {}x \ln \left (x \right ) y^{\prime }+y = 2 \ln \left (x \right ) \]

[_linear]

19022

\[ {}\sin \left (x \right ) \cos \left (x \right ) y^{\prime } = y+\sin \left (x \right ) \]

[_linear]

19025

\[ {}y^{\prime }+3 x^{2} y = x^{5} {\mathrm e}^{x^{3}} \]

[_linear]

19027

\[ {}y^{\prime }+\frac {\left (1-2 x \right ) y}{x^{2}} = 1 \]

[_linear]

19028

\[ {}y^{\prime }+\frac {2 y}{x} = \sin \left (x \right ) \]

[_linear]

19030

\[ {}1+y+x^{2} y+\left (x^{3}+x \right ) y^{\prime } = 0 \]

[_linear]

19031

\[ {}y^{\prime }+\frac {x y}{x^{2}+1} = \frac {1}{2 x \left (x^{2}+1\right )} \]

[_linear]

19076

\[ {}y^{\prime }+\frac {y}{\left (-x^{2}+1\right )^{{3}/{2}}} = \frac {x +\sqrt {-x^{2}+1}}{\left (-x^{2}+1\right )^{2}} \]

[_linear]

19136

\[ {}{y^{\prime }}^{2}+2 y y^{\prime } \cot \left (x \right ) = y^{2} \]

[_separable]

19138

\[ {}y^{\prime } \left (y^{\prime }-y\right ) = \left (x +y\right ) x \]

[_quadrature]

19141

\[ {}x {y^{\prime }}^{2}+\left (y-x \right ) y^{\prime }-y = 0 \]

[_quadrature]

19144

\[ {}{y^{\prime }}^{3}-y^{\prime } \left (y^{2}+x y+x^{2}\right )+x y \left (x +y\right ) = 0 \]

[_quadrature]

19145

\[ {}\left (y^{\prime }+y+x \right ) \left (y+x +x y^{\prime }\right ) \left (y^{\prime }+2 x \right ) = 0 \]

[_quadrature]

19158

\[ {}y = \sin \left (x \right ) y^{\prime }+\cos \left (x \right ) \]

[_linear]

19231

\[ {}4 {y^{\prime }}^{2} x^{2} \left (-1+x \right )-4 y^{\prime } x y \left (4 x -3\right )+\left (16 x -9\right ) y^{2} = 0 \]

[_separable]

19234

\[ {}y-x y^{\prime } = b \left (1+x^{2} y^{\prime }\right ) \]

[_separable]

19430

\[ {}y-x y^{\prime } = 0 \]

[_separable]

19439

\[ {}\cos \left (x \right ) y^{\prime }+y \sin \left (x \right ) = 1 \]

[_linear]

19440

\[ {}y^{\prime }+2 x y = {\mathrm e}^{-x^{2}} \]

[_linear]

19465

\[ {}{y^{\prime }}^{3}-\left (y^{2}+x y+x^{2}\right ) {y^{\prime }}^{2}+\left (x^{3} y+y^{2} x^{2}+x y^{3}\right ) y^{\prime }-x^{3} y^{3} = 0 \]

[_quadrature]