2.4.26 first order ode separable

Table 2.1181: first order ode separable [1833]

#

ODE

CAS classification

Solved

Maple

Mma

Sympy

time(sec)

27

\begin{align*} y^{\prime }&=2 x^{2} y^{2} \\ y \left (1\right ) &= -1 \\ \end{align*}

[_separable]

4.572

28

\begin{align*} y^{\prime }&=x \ln \left (y\right ) \\ y \left (1\right ) &= 1 \\ \end{align*}

[_separable]

3.746

33

\begin{align*} y y^{\prime }&=x -1 \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

3.489

34

\begin{align*} y y^{\prime }&=x -1 \\ y \left (1\right ) &= 0 \\ \end{align*}

[_separable]

3.549

41

\begin{align*} y^{\prime }+2 y x&=0 \\ \end{align*}

[_separable]

2.364

42

\begin{align*} y^{\prime }+2 x y^{2}&=0 \\ \end{align*}

[_separable]

3.734

43

\begin{align*} y^{\prime }&=y \sin \left (x \right ) \\ \end{align*}

[_separable]

2.740

44

\begin{align*} \left (x +1\right ) y^{\prime }&=4 y \\ \end{align*}

[_separable]

3.347

45

\begin{align*} 2 \sqrt {x}\, y^{\prime }&=\sqrt {1-y^{2}} \\ \end{align*}

[_separable]

3.089

48

\begin{align*} y^{\prime }&=2 x \sec \left (y\right ) \\ \end{align*}

[_separable]

2.274

49

\begin{align*} \left (-x^{2}+1\right ) y^{\prime }&=2 y \\ \end{align*}

[_separable]

3.142

50

\begin{align*} \left (x +1\right )^{2} y^{\prime }&=\left (y+1\right )^{2} \\ \end{align*}

[_separable]

4.763

51

\begin{align*} y^{\prime }&=x y^{3} \\ \end{align*}

[_separable]

5.185

52

\begin{align*} y y^{\prime }&=x \left (1+y^{2}\right ) \\ \end{align*}

[_separable]

3.264

53

\begin{align*} y^{3} y^{\prime }&=\left (1+y^{4}\right ) \cos \left (x \right ) \\ \end{align*}

[_separable]

5.158

54

\begin{align*} y^{\prime }&=\frac {1+\sqrt {x}}{1+\sqrt {y}} \\ \end{align*}

[_separable]

2.966

55

\begin{align*} y^{\prime }&=\frac {\left (x -1\right ) y^{5}}{x^{2} \left (2 y^{3}-y\right )} \\ \end{align*}

[_separable]

3.290

56

\begin{align*} \left (x^{2}+1\right ) \tan \left (y\right ) y^{\prime }&=x \\ \end{align*}

[_separable]

3.128

57

\begin{align*} y^{\prime }&=1+x +y+y x \\ \end{align*}

[_separable]

2.887

58

\begin{align*} x^{2} y^{\prime }&=1-x^{2}+y^{2}-x^{2} y^{2} \\ \end{align*}

[_separable]

4.664

59

\begin{align*} y^{\prime }&=y \,{\mathrm e}^{x} \\ y \left (0\right ) &= 2 \,{\mathrm e} \\ \end{align*}

[_separable]

4.977

60

\begin{align*} y^{\prime }&=3 x^{2} \left (1+y^{2}\right ) \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

4.512

61

\begin{align*} 2 y y^{\prime }&=\frac {x}{\sqrt {x^{2}-16}} \\ y \left (5\right ) &= 2 \\ \end{align*}

[_separable]

4.045

62

\begin{align*} y^{\prime }&=4 x^{3} y-y \\ y \left (1\right ) &= -3 \\ \end{align*}

[_separable]

4.059

64

\begin{align*} \tan \left (x \right ) y^{\prime }&=y \\ y \left (\frac {\pi }{2}\right ) &= \frac {\pi }{2} \\ \end{align*}

[_separable]

5.896

65

\begin{align*} x y^{\prime }-y&=2 x^{2} y \\ y \left (1\right ) &= 1 \\ \end{align*}

[_separable]

3.611

66

\begin{align*} y^{\prime }&=2 x y^{2}+3 x^{2} y^{2} \\ y \left (1\right ) &= -1 \\ \end{align*}

[_separable]

3.928

67

\begin{align*} y^{\prime }&=6 \,{\mathrm e}^{2 x -y} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

3.409

68

\begin{align*} 2 \sqrt {x}\, y^{\prime }&=\cos \left (y\right )^{2} \\ y \left (4\right ) &= \frac {\pi }{4} \\ \end{align*}

[_separable]

2.923

83

\begin{align*} x y^{\prime }+y&=3 y x \\ y \left (1\right ) &= 0 \\ \end{align*}

[_separable]

3.817

87

\begin{align*} y^{\prime }+2 y x&=x \\ y \left (0\right ) &= -2 \\ \end{align*}

[_separable]

2.177

88

\begin{align*} y^{\prime }&=\left (1-y\right ) \cos \left (x \right ) \\ y \left (\pi \right ) &= 2 \\ \end{align*}

[_separable]

2.785

92

\begin{align*} y^{\prime }&=1+x +y+y x \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

3.244

96

\begin{align*} \left (x^{2}+4\right ) y^{\prime }+3 y x&=x \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

3.434

103

\begin{align*} y^{\prime }+p \left (x \right ) y&=0 \\ \end{align*}

[_separable]

1.721

124

\begin{align*} y^{2} y^{\prime }+2 x y^{3}&=6 x \\ \end{align*}

[_separable]

2.505

146

\begin{align*} \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 \\ \end{align*}

[[_1st_order, _with_linear_symmetries], _exact, _rational]

3.700

180

\begin{align*} x y^{2}+3 y^{2}-x^{2} y^{\prime }&=0 \\ \end{align*}

[_separable]

3.063

183

\begin{align*} 3 y+x^{4} y^{\prime }&=2 y x \\ \end{align*}

[_separable]

3.248

184

\begin{align*} 2 x y^{2}+x^{2} y^{\prime }&=y^{2} \\ \end{align*}

[_separable]

3.076

188

\begin{align*} y^{\prime }&=1+x^{2}+y^{2}+x^{2} y^{2} \\ \end{align*}

[_separable]

3.524

191

\begin{align*} 4 x y^{2}+y^{\prime }&=5 y^{2} x^{4} \\ \end{align*}

[_separable]

3.195

197

\begin{align*} 3 x^{5} y^{2}+x^{3} y^{\prime }&=2 y^{2} \\ \end{align*}

[_separable]

2.779

202

\begin{align*} 9 x^{2} y^{2}+x^{{3}/{2}} y^{\prime }&=y^{2} \\ \end{align*}

[_separable]

3.352

209

\begin{align*} y^{\prime }&=3 \left (y+7\right ) x^{2} \\ \end{align*}

[_separable]

2.554

210

\begin{align*} y^{\prime }&=x y^{3}-y x \\ \end{align*}

[_separable]

5.265

213

\begin{align*} y^{\prime }&=\frac {2 y x +2 x}{x^{2}+1} \\ \end{align*}

[_separable]

2.600

214

\begin{align*} y^{\prime }&=\frac {\sqrt {y}-y}{\tan \left (x \right )} \\ \end{align*}

[_separable]

5.911

669

\begin{align*} y^{\prime }&=2 x^{2} y^{2} \\ y \left (1\right ) &= -1 \\ \end{align*}

[_separable]

4.023

670

\begin{align*} y^{\prime }&=x \ln \left (y\right ) \\ \end{align*}

[_separable]

1.747

673

\begin{align*} y y^{\prime }&=x -1 \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

3.602

674

\begin{align*} y y^{\prime }&=x -1 \\ y \left (1\right ) &= 0 \\ \end{align*}

[_separable]

3.486

677

\begin{align*} y^{\prime }+2 y x&=0 \\ \end{align*}

[_separable]

2.368

678

\begin{align*} y^{\prime }+2 x y^{2}&=0 \\ \end{align*}

[_separable]

3.664

679

\begin{align*} y^{\prime }&=y \sin \left (x \right ) \\ \end{align*}

[_separable]

2.677

680

\begin{align*} \left (x +1\right ) y^{\prime }&=4 y \\ \end{align*}

[_separable]

2.625

681

\begin{align*} 2 \sqrt {x}\, y^{\prime }&=\sqrt {1-y^{2}} \\ \end{align*}

[_separable]

2.698

684

\begin{align*} y^{\prime }&=2 x \sec \left (y\right ) \\ \end{align*}

[_separable]

1.891

685

\begin{align*} \left (-x^{2}+1\right ) y^{\prime }&=2 y \\ \end{align*}

[_separable]

2.558

686

\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=\left (y+1\right )^{2} \\ \end{align*}

[_separable]

3.369

687

\begin{align*} y^{\prime }&=x y^{3} \\ \end{align*}

[_separable]

4.323

688

\begin{align*} y y^{\prime }&=x \left (1+y^{2}\right ) \\ \end{align*}

[_separable]

2.723

689

\begin{align*} y^{\prime }&=\frac {1+\sqrt {x}}{1+\sqrt {y}} \\ \end{align*}

[_separable]

2.460

690

\begin{align*} y^{\prime }&=\frac {\left (x -1\right ) y^{5}}{x^{2} \left (2 y^{3}-y\right )} \\ \end{align*}

[_separable]

2.871

691

\begin{align*} \left (x^{2}+1\right ) \tan \left (y\right ) y^{\prime }&=x \\ \end{align*}

[_separable]

2.756

692

\begin{align*} y^{\prime }&=1+x +y+y x \\ \end{align*}

[_separable]

2.412

693

\begin{align*} x^{2} y^{\prime }&=1-x^{2}+y^{2}-x^{2} y^{2} \\ \end{align*}

[_separable]

3.792

694

\begin{align*} y^{\prime }&=y \,{\mathrm e}^{x} \\ y \left (0\right ) &= 2 \,{\mathrm e} \\ \end{align*}

[_separable]

3.437

695

\begin{align*} y^{\prime }&=3 x^{2} \left (1+y^{2}\right ) \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

3.726

696

\begin{align*} 2 y y^{\prime }&=\frac {x}{\sqrt {x^{2}-16}} \\ y \left (5\right ) &= 2 \\ \end{align*}

[_separable]

3.423

697

\begin{align*} y^{\prime }&=4 x^{3} y-y \\ y \left (1\right ) &= -3 \\ \end{align*}

[_separable]

3.181

699

\begin{align*} \tan \left (x \right ) y^{\prime }&=y \\ y \left (\frac {\pi }{2}\right ) &= \frac {\pi }{2} \\ \end{align*}

[_separable]

4.671

700

\begin{align*} x y^{\prime }-y&=2 x^{2} y \\ y \left (1\right ) &= 1 \\ \end{align*}

[_separable]

2.625

701

\begin{align*} y^{\prime }&=2 x y^{2}+3 x^{2} y^{2} \\ y \left (1\right ) &= -1 \\ \end{align*}

[_separable]

2.903

702

\begin{align*} y^{\prime }&=6 \,{\mathrm e}^{2 x -y} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

2.586

703

\begin{align*} 2 \sqrt {x}\, y^{\prime }&=\cos \left (y\right )^{2} \\ y \left (4\right ) &= \frac {\pi }{4} \\ \end{align*}

[_separable]

2.621

714

\begin{align*} x y^{\prime }+y&=3 y x \\ y \left (1\right ) &= 0 \\ \end{align*}

[_separable]

3.776

718

\begin{align*} y^{\prime }+2 y x&=x \\ y \left (0\right ) &= -2 \\ \end{align*}

[_separable]

2.718

719

\begin{align*} y^{\prime }&=\left (1-y\right ) \cos \left (x \right ) \\ y \left (\pi \right ) &= 2 \\ \end{align*}

[_separable]

3.290

723

\begin{align*} y^{\prime }&=1+x +y+y x \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

2.533

727

\begin{align*} \left (x^{2}+4\right ) y^{\prime }+3 y x&=x \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

2.778

748

\begin{align*} y^{2} y^{\prime }+2 x y^{3}&=6 x \\ \end{align*}

[_separable]

2.618

770

\begin{align*} \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 \\ \end{align*}

[[_1st_order, _with_linear_symmetries], _exact, _rational]

4.339

772

\begin{align*} x y^{2}+3 y^{2}-x^{2} y^{\prime }&=0 \\ \end{align*}

[_separable]

2.918

775

\begin{align*} 3 y+x^{4} y^{\prime }&=2 y x \\ \end{align*}

[_separable]

3.756

776

\begin{align*} 2 x y^{2}+x^{2} y^{\prime }&=y^{2} \\ \end{align*}

[_separable]

3.556

780

\begin{align*} y^{\prime }&=1+x^{2}+y^{2}+x^{2} y^{2} \\ \end{align*}

[_separable]

4.093

789

\begin{align*} 3 x^{5} y^{2}+x^{3} y^{\prime }&=2 y^{2} \\ \end{align*}

[_separable]

2.959

794

\begin{align*} 9 x^{2} y^{2}+x^{{3}/{2}} y^{\prime }&=y^{2} \\ \end{align*}

[_separable]

3.445

800

\begin{align*} y^{\prime }&=3 \left (y+7\right ) x^{2} \\ \end{align*}

[_separable]

2.487

801

\begin{align*} y^{\prime }&=3 \left (y+7\right ) x^{2} \\ \end{align*}

[_separable]

2.433

802

\begin{align*} y^{\prime }&=x y^{3}-y x \\ \end{align*}

[_separable]

6.336

805

\begin{align*} y^{\prime }&=\frac {2 y x +2 x}{x^{2}+1} \\ \end{align*}

[_separable]

2.556

806

\begin{align*} y^{\prime }&=\cot \left (x \right ) \left (\sqrt {y}-y\right ) \\ \end{align*}

[_separable]

6.222

1129

\begin{align*} y^{\prime }&=\frac {x^{2}}{y} \\ \end{align*}

[_separable]

5.070

1130

\begin{align*} y^{\prime }&=\frac {x^{2}}{\left (x^{3}+1\right ) y} \\ \end{align*}

[_separable]

2.087

1131

\begin{align*} \sin \left (x \right ) y^{2}+y^{\prime }&=0 \\ \end{align*}

[_separable]

3.473

1132

\begin{align*} y^{\prime }&=\frac {3 x^{2}-1}{3+2 y} \\ \end{align*}

[_separable]

3.143

1133

\begin{align*} y^{\prime }&=\cos \left (x \right )^{2} \cos \left (2 y\right )^{2} \\ \end{align*}

[_separable]

3.292

1134

\begin{align*} x y^{\prime }&=\sqrt {1-y^{2}} \\ \end{align*}

[_separable]

4.921

1136

\begin{align*} y^{\prime }&=\frac {x^{2}}{1+y^{2}} \\ \end{align*}

[_separable]

1.589

1137

\begin{align*} y^{\prime }&=\left (1-2 x \right ) y^{2} \\ y \left (0\right ) &= -{\frac {1}{6}} \\ \end{align*}

[_separable]

3.685

1138

\begin{align*} y^{\prime }&=\frac {1-2 x}{y} \\ y \left (1\right ) &= -2 \\ \end{align*}

[_separable]

3.247

1139

\begin{align*} x +y y^{\prime } {\mathrm e}^{-x}&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

2.321

1140

\begin{align*} r^{\prime }&=\frac {r^{2}}{x} \\ r \left (1\right ) &= 2 \\ \end{align*}

[_separable]

2.837

1141

\begin{align*} y^{\prime }&=\frac {2 x}{y+x^{2} y} \\ y \left (0\right ) &= -2 \\ \end{align*}

[_separable]

2.165

1142

\begin{align*} y^{\prime }&=\frac {x y^{2}}{\sqrt {x^{2}+1}} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

4.348

1143

\begin{align*} y^{\prime }&=\frac {2 x}{1+2 y} \\ y \left (2\right ) &= 0 \\ \end{align*}

[_separable]

4.519

1144

\begin{align*} y^{\prime }&=\frac {x \left (x^{2}+1\right )}{4 y^{3}} \\ y \left (0\right ) &= -\frac {\sqrt {2}}{2} \\ \end{align*}

[_separable]

2.083

1145

\begin{align*} y^{\prime }&=\frac {-{\mathrm e}^{x}+3 x^{2}}{-5+2 y} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

4.264

1146

\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{-x}-{\mathrm e}^{x}}{3+4 y} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

4.487

1147

\begin{align*} \sin \left (2 x \right )+\cos \left (3 y\right ) y^{\prime }&=0 \\ y \left (\frac {\pi }{2}\right ) &= 0 \\ \end{align*}

[_separable]

27.246

1148

\begin{align*} \sqrt {-x^{2}+1}\, y^{2} y^{\prime }&=\arcsin \left (x \right ) \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

5.916

1149

\begin{align*} y^{\prime }&=\frac {3 x^{2}+1}{-6 y+3 y^{2}} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

2.242

1150

\begin{align*} y^{\prime }&=\frac {3 x^{2}}{-4+3 y^{2}} \\ y \left (1\right ) &= 0 \\ \end{align*}

[_separable]

1.982

1151

\begin{align*} y^{\prime }&=2 y^{2}+x y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

3.817

1152

\begin{align*} y^{\prime }&=\frac {2-{\mathrm e}^{x}}{3+2 y} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

3.404

1153

\begin{align*} y^{\prime }&=\frac {2 \cos \left (2 x \right )}{3+2 y} \\ y \left (0\right ) &= -1 \\ \end{align*}

[_separable]

4.581

1154

\begin{align*} y^{\prime }&=2 \left (x +1\right ) \left (1+y^{2}\right ) \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

3.848

1155

\begin{align*} y^{\prime }&=\frac {t \left (4-y\right ) y}{3} \\ \end{align*}

[_separable]

4.300

1156

\begin{align*} y^{\prime }&=\frac {t y \left (4-y\right )}{t +1} \\ \end{align*}

[_separable]

5.194

1167

\begin{align*} y+\left (-4+t \right ) t y^{\prime }&=0 \\ y \left (2\right ) &= 1 \\ \end{align*}

[_separable]

2.766

1172

\begin{align*} y^{\prime }&=\frac {t^{2}+1}{3 y-y^{2}} \\ \end{align*}

[_separable]

1.957

1173

\begin{align*} y^{\prime }&=\frac {\cot \left (t \right ) y}{1+y} \\ \end{align*}

[_separable]

3.503

1174

\begin{align*} y^{\prime }&=-\frac {4 t}{y} \\ \end{align*}

[_separable]

6.415

1175

\begin{align*} y^{\prime }&=2 t y^{2} \\ \end{align*}

[_separable]

5.247

1177

\begin{align*} y^{\prime }&=\frac {t^{2}}{\left (t^{3}+1\right ) y} \\ \end{align*}

[_separable]

2.154

1178

\begin{align*} y^{\prime }&=t \left (3-y\right ) y \\ \end{align*}

[_separable]

3.540

1193

\begin{align*} 3+2 x +\left (-2+2 y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

5.824

1204

\begin{align*} \frac {x}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}&=0 \\ \end{align*}

[_separable]

6.673

1207

\begin{align*} x^{2} y^{3}+x \left (1+y^{2}\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

2.387

1209

\begin{align*} \left (x +2\right ) \sin \left (y\right )+x \cos \left (y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

2.912

1219

\begin{align*} y^{\prime }&=\frac {1+\cos \left (x \right )}{2-\sin \left (y\right )} \\ \end{align*}

[_separable]

3.331

1221

\begin{align*} y^{\prime }&=3-6 x +y-2 y x \\ \end{align*}

[_separable]

2.667

1224

\begin{align*} y^{\prime }&=\frac {4 x^{3}+1}{y \left (2+3 y\right )} \\ \end{align*}

[_separable]

2.166

1227

\begin{align*} \frac {-x^{2}+x +1}{x^{2}}+\frac {y y^{\prime }}{-2+y}&=0 \\ \end{align*}

[_separable]

3.701

1230

\begin{align*} y^{\prime }&=1+2 x +y^{2}+2 x y^{2} \\ \end{align*}

[_separable]

3.701

1232

\begin{align*} \left (1+{\mathrm e}^{x}\right ) y^{\prime }&=y-y \,{\mathrm e}^{x} \\ \end{align*}

[_separable]

4.056

1237

\begin{align*} y^{\prime }&={\mathrm e}^{x +y} \\ \end{align*}

[_separable]

2.029

1239

\begin{align*} y^{\prime }&=\frac {x^{2}-1}{1+y^{2}} \\ y \left (-1\right ) &= 1 \\ \end{align*}

[_separable]

1.036

1241

\begin{align*} 2 \cos \left (x \right ) \sin \left (x \right ) \sin \left (y\right )+\cos \left (y\right ) \sin \left (x \right )^{2} y^{\prime }&=0 \\ \end{align*}

[_separable]

3.429

1521

\begin{align*} y^{\prime }+2 y x&=x \\ \end{align*}

[_separable]

2.424

1522

\begin{align*} 2 y^{\prime }+x \left (y^{2}-1\right )&=0 \\ \end{align*}

[_separable]

3.840

1523

\begin{align*} y^{\prime }&=x^{2} \left (1+y^{2}\right ) \\ \end{align*}

[_separable]

3.237

1532

\begin{align*} y^{\prime }&=x \left (1+y^{2}\right ) \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

3.647

1533

\begin{align*} y^{\prime }&=-\frac {y \left (y+1\right )}{x} \\ y \left (1\right ) &= -2 \\ \end{align*}

[_separable]

5.891

1538

\begin{align*} y^{\prime }+3 x^{2} y&=0 \\ \end{align*}

[_separable]

2.783

1539

\begin{align*} x y^{\prime }+y \ln \left (x \right )&=0 \\ \end{align*}

[_separable]

3.453

1540

\begin{align*} x y^{\prime }+3 y&=0 \\ \end{align*}

[_separable]

3.420

1541

\begin{align*} x^{2} y^{\prime }+y&=0 \\ \end{align*}

[_separable]

2.839

1542

\begin{align*} y^{\prime }+\frac {\left (x +1\right ) y}{x}&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}

[_separable]

2.440

1543

\begin{align*} x y^{\prime }+\left (1+\frac {1}{\ln \left (x \right )}\right ) y&=0 \\ y \left ({\mathrm e}\right ) &= 1 \\ \end{align*}

[_separable]

3.700

1544

\begin{align*} x y^{\prime }+\left (1+x \cot \left (x \right )\right ) y&=0 \\ y \left (\frac {\pi }{2}\right ) &= 2 \\ \end{align*}

[_separable]

4.272

1545

\begin{align*} y^{\prime }-\frac {2 x y}{x^{2}+1}&=0 \\ y \left (0\right ) &= 2 \\ \end{align*}

[_separable]

2.694

1546

\begin{align*} y^{\prime }+\frac {k y}{x}&=0 \\ y \left (1\right ) &= 3 \\ \end{align*}

[_separable]

3.047

1547

\begin{align*} y^{\prime }+\tan \left (k x \right ) y&=0 \\ y \left (0\right ) &= 2 \\ \end{align*}

[_separable]

3.428

1569

\begin{align*} y^{\prime }+2 y x&=x \\ y \left (0\right ) &= 3 \\ \end{align*}

[_separable]

2.583

1573

\begin{align*} x y^{\prime }-2 y&=-1 \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}

[_separable]

4.168

1578

\begin{align*} y^{\prime }&=\frac {3 x^{2}+2 x +1}{-2+y} \\ \end{align*}

[_separable]

3.747

1579

\begin{align*} \sin \left (x \right ) \sin \left (y\right )+\cos \left (y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

4.409

1580

\begin{align*} x y^{\prime }+y^{2}+y&=0 \\ \end{align*}

[_separable]

4.396

1581

\begin{align*} \left (3 y^{3}+3 y \cos \left (y\right )+1\right ) y^{\prime }+\frac {\left (2 x +1\right ) y}{x^{2}+1}&=0 \\ \end{align*}

[_separable]

3.944

1582

\begin{align*} x^{2} y y^{\prime }&=\left (y^{2}-1\right )^{{3}/{2}} \\ \end{align*}

[_separable]

12.206

1583

\begin{align*} y^{\prime }&=x^{2} \left (1+y^{2}\right ) \\ \end{align*}

[_separable]

3.198

1584

\begin{align*} \left (x^{2}+1\right ) y^{\prime }+y x&=0 \\ \end{align*}

[_separable]

2.542

1585

\begin{align*} y^{\prime }&=\left (x -1\right ) \left (-1+y\right ) \left (-2+y\right ) \\ \end{align*}

[_separable]

5.507

1586

\begin{align*} \left (-1+y\right )^{2} y^{\prime }&=2 x +3 \\ \end{align*}

[_separable]

2.944

1587

\begin{align*} y^{\prime }&=\frac {x^{2}+3 x +2}{-2+y} \\ y \left (1\right ) &= 4 \\ \end{align*}

[_separable]

4.615

1588

\begin{align*} y^{\prime }+x \left (y^{2}+y\right )&=0 \\ y \left (2\right ) &= 1 \\ \end{align*}

[_separable]

4.167

1589

\begin{align*} \left (3 y^{2}+4 y\right ) y^{\prime }+2 x +\cos \left (x \right )&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

3.628

1590

\begin{align*} y^{\prime }+\frac {\left (y+1\right ) \left (-1+y\right ) \left (-2+y\right )}{x +1}&=0 \\ y \left (1\right ) &= 0 \\ \end{align*}

[_separable]

3.658

1591

\begin{align*} y^{\prime }+2 x \left (y+1\right )&=0 \\ y \left (0\right ) &= 2 \\ \end{align*}

[_separable]

2.598

1592

\begin{align*} y^{\prime }&=2 x y \left (1+y^{2}\right ) \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

7.596

1593

\begin{align*} y^{\prime } \left (x^{2}+2\right )&=4 x \left (y^{2}+2 y+1\right ) \\ \end{align*}

[_separable]

4.357

1594

\begin{align*} y^{\prime }&=-2 x \left (y^{3}-3 y+2\right ) \\ y \left (0\right ) &= 3 \\ \end{align*}

[_separable]

7.504

1595

\begin{align*} y^{\prime }&=\frac {2 x}{1+2 y} \\ y \left (2\right ) &= 0 \\ \end{align*}

[_separable]

5.404

1597

\begin{align*} y y^{\prime }+x&=0 \\ y \left (3\right ) &= -4 \\ \end{align*}

[_separable]

7.565

1598

\begin{align*} y^{\prime }+x^{2} \left (y+1\right ) \left (-2+y\right )^{2}&=0 \\ \end{align*}

[_separable]

6.773

1599

\begin{align*} \left (x +1\right ) \left (x -2\right ) y^{\prime }+y&=0 \\ y \left (1\right ) &= -3 \\ \end{align*}

[_separable]

3.161

1600

\begin{align*} y^{\prime }&=\frac {1+y^{2}}{x^{2}+1} \\ \end{align*}

[_separable]

3.433

1601

\begin{align*} y^{\prime } \sqrt {-x^{2}+1}+\sqrt {1-y^{2}}&=0 \\ \end{align*}

[_separable]

22.372

1602

\begin{align*} y^{\prime }&=\frac {\cos \left (x \right )}{\sin \left (y\right )} \\ y \left (\pi \right ) &= \frac {\pi }{2} \\ \end{align*}

[_separable]

3.421

1613

\begin{align*} y^{\prime }&=2 y x \\ \end{align*}

[_separable]

2.836

1617

\begin{align*} y^{\prime }&=x \left (y^{2}-1\right )^{{2}/{3}} \\ \end{align*}

[_separable]

3.023

1620

\begin{align*} y^{\prime }&=\frac {\tan \left (y\right )}{x -1} \\ \end{align*}

[_separable]

4.016

1622

\begin{align*} y^{\prime }&=3 x \left (-1+y\right )^{{1}/{3}} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

46.484

1623

\begin{align*} y^{\prime }&=3 x \left (-1+y\right )^{{1}/{3}} \\ y \left (0\right ) &= 9 \\ \end{align*}

[_separable]

42.148

1624

\begin{align*} y^{\prime }&=3 x \left (-1+y\right )^{{1}/{3}} \\ y \left (3\right ) &= -7 \\ \end{align*}

[_separable]

11.588

1636

\begin{align*} y^{\prime }-y x&=x y^{{3}/{2}} \\ y \left (1\right ) &= 4 \\ \end{align*}

[_separable]

6.500

1690

\begin{align*} \frac {1}{x}+2 x +\left (\frac {1}{y}+2 y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

4.315

1692

\begin{align*} \frac {x}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}&=0 \\ \end{align*}

[_separable]

9.759

1698

\begin{align*} \left (y^{3}-1\right ) {\mathrm e}^{x}+3 y^{2} \left (1+{\mathrm e}^{x}\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

4.284

1700

\begin{align*} \left (2 x -1\right ) \left (-1+y\right )+\left (x +2\right ) \left (x -3\right ) y^{\prime }&=0 \\ y \left (1\right ) &= -1 \\ \end{align*}

[_separable]

3.692

1711

\begin{align*} -y^{2}+x^{2} y^{\prime }&=0 \\ \end{align*}

[_separable]

5.642

1712

\begin{align*} -x y^{\prime }+y&=0 \\ \end{align*}

[_separable]

2.835

1713

\begin{align*} 3 x^{2} y+2 x^{3} y^{\prime }&=0 \\ \end{align*}

[_separable]

4.676

1721

\begin{align*} x^{2} y+4 y x +2 y+\left (x^{2}+x \right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

4.662

1722

\begin{align*} -y+\left (x^{4}-x \right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

3.645

1725

\begin{align*} \sin \left (y\right ) y+x \left (\sin \left (y\right )-y \cos \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

7.526

1726

\begin{align*} a y+b x y+\left (c x +d x y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

5.724

1728

\begin{align*} 2 y+3 \left (x^{2}+x^{2} y^{3}\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

5.440

1731

\begin{align*} y \left (x \cos \left (x \right )+2 \sin \left (x \right )\right )+x \left (y+1\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

5.984

2298

\begin{align*} \cos \left (t \right ) y+y^{\prime }&=0 \\ \end{align*}

[_separable]

3.493

2299

\begin{align*} \sqrt {t}\, \sin \left (t \right ) y+y^{\prime }&=0 \\ \end{align*}

[_separable]

4.841

2303

\begin{align*} t^{2} y+y^{\prime }&=t^{2} \\ \end{align*}

[_separable]

3.231

2305

\begin{align*} \sqrt {t^{2}+1}\, y+y^{\prime }&=0 \\ y \left (0\right ) &= \sqrt {5} \\ \end{align*}

[_separable]

4.667

2306

\begin{align*} \sqrt {t^{2}+1}\, y \,{\mathrm e}^{-t}+y^{\prime }&=0 \\ \end{align*}

[_separable]

4.456

2307

\begin{align*} y^{\prime }-2 y t&=t \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

2.949

2312

\begin{align*} 4 y t +\left (t^{2}+1\right ) y^{\prime }&=t \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

3.067

2317

\begin{align*} \left (t^{2}+1\right ) y^{\prime }&=1+y^{2} \\ \end{align*}

[_separable]

3.992

2318

\begin{align*} y^{\prime }&=\left (t +1\right ) \left (1+y\right ) \\ \end{align*}

[_separable]

3.233

2319

\begin{align*} y^{\prime }&=1-t +y^{2}-t y^{2} \\ \end{align*}

[_separable]

4.468

2320

\begin{align*} y^{\prime }&={\mathrm e}^{3+t +y} \\ \end{align*}

[_separable]

2.540

2321

\begin{align*} \cos \left (y\right ) \sin \left (t \right ) y^{\prime }&=\cos \left (t \right ) \sin \left (y\right ) \\ \end{align*}

[_separable]

3.658

2322

\begin{align*} t^{2} \left (1+y^{2}\right )+2 y y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

3.428

2323

\begin{align*} y^{\prime }&=\frac {2 t}{y+t^{2} y} \\ y \left (2\right ) &= 3 \\ \end{align*}

[_separable]

3.079

2324

\begin{align*} \sqrt {t^{2}+1}\, y^{\prime }&=\frac {t y^{3}}{\sqrt {t^{2}+1}} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

5.074

2325

\begin{align*} y^{\prime }&=\frac {3 t^{2}+4 t +2}{-2+2 y} \\ y \left (0\right ) &= -1 \\ \end{align*}

[_separable]

4.573

2326

\begin{align*} \cos \left (y\right ) y^{\prime }&=-\frac {t \sin \left (y\right )}{t^{2}+1} \\ y \left (1\right ) &= \frac {\pi }{2} \\ \end{align*}

[_separable]

3.371

2328

\begin{align*} 3 t y^{\prime }&=\cos \left (t \right ) y \\ y \left (1\right ) &= 0 \\ \end{align*}

[_separable]

9.849

2359

\begin{align*} y^{\prime }&=t \left (1+y\right ) \\ y \left (0\right ) &= -1 \\ \end{align*}

[_separable]

3.654

2360

\begin{align*} y^{\prime }&=t \sqrt {1-y^{2}} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

51.204

2471

\begin{align*} \cos \left (t \right ) y+y^{\prime }&=0 \\ \end{align*}

[_separable]

3.652

2472

\begin{align*} \sqrt {t}\, \sin \left (t \right ) y+y^{\prime }&=0 \\ \end{align*}

[_separable]

4.914

2476

\begin{align*} t^{2} y+y^{\prime }&=t^{2} \\ \end{align*}

[_separable]

3.316

2478

\begin{align*} \sqrt {t^{2}+1}\, y+y^{\prime }&=0 \\ y \left (0\right ) &= \sqrt {5} \\ \end{align*}

[_separable]

6.567

2479

\begin{align*} \sqrt {t^{2}+1}\, y \,{\mathrm e}^{-t}+y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

10.796

2480

\begin{align*} \sqrt {t^{2}+1}\, y \,{\mathrm e}^{-t}+y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

5.847

2481

\begin{align*} y^{\prime }-2 y t&=t \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

3.128

2486

\begin{align*} 4 y t +\left (t^{2}+1\right ) y^{\prime }&=t \\ y \left (1\right ) &= {\frac {1}{4}} \\ \end{align*}

[_separable]

5.133

2488

\begin{align*} \left (t^{2}+1\right ) y^{\prime }&=1+y^{2} \\ \end{align*}

[_separable]

4.345

2489

\begin{align*} y^{\prime }&=\left (t +1\right ) \left (1+y\right ) \\ \end{align*}

[_separable]

3.459

2490

\begin{align*} y^{\prime }&=1-t +y^{2}-t y^{2} \\ \end{align*}

[_separable]

4.622

2491

\begin{align*} y^{\prime }&={\mathrm e}^{3+t +y} \\ \end{align*}

[_separable]

2.835

2492

\begin{align*} \cos \left (y\right ) \sin \left (t \right ) y^{\prime }&=\cos \left (t \right ) \sin \left (y\right ) \\ \end{align*}

[_separable]

3.932

2493

\begin{align*} t^{2} \left (1+y^{2}\right )+2 y y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

4.688

2494

\begin{align*} y^{\prime }&=\frac {2 t}{y+t^{2} y} \\ y \left (2\right ) &= 3 \\ \end{align*}

[_separable]

3.178

2495

\begin{align*} \sqrt {1+y^{2}}\, y^{\prime }&=\frac {t y^{3}}{\sqrt {t^{2}+1}} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

6.322

2496

\begin{align*} y^{\prime }&=\frac {3 t^{2}+4 t +2}{-2+2 y} \\ y \left (0\right ) &= -1 \\ \end{align*}

[_separable]

4.644

2497

\begin{align*} \cos \left (y\right ) y^{\prime }&=-\frac {t \sin \left (y\right )}{t^{2}+1} \\ y \left (1\right ) &= \frac {\pi }{2} \\ \end{align*}

[_separable]

3.395

2499

\begin{align*} 3 t y^{\prime }&=\cos \left (t \right ) y \\ y \left (1\right ) &= 0 \\ \end{align*}

[_separable]

10.371

2518

\begin{align*} y^{\prime }&=2 t \left (1+y\right ) \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

3.199

2534

\begin{align*} y^{\prime }&=t \left (1+y\right ) \\ y \left (0\right ) &= -1 \\ \end{align*}

[_separable]

3.949

2535

\begin{align*} y^{\prime }&=t y^{a} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

139.743

2536

\begin{align*} y^{\prime }&=t \sqrt {1-y^{2}} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

53.563

2840

\begin{align*} \left (x^{2}+1\right ) y^{\prime }+y x&=0 \\ \end{align*}

[_separable]

4.102

2841

\begin{align*} x y^{2}+x +\left (y-x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

12.939

2842

\begin{align*} 1+y^{2}+\left (x^{2}+1\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

5.543

2843

\begin{align*} x y^{\prime }+y&=0 \\ \end{align*}

[_separable]

5.181

2844

\begin{align*} y^{\prime }&=2 y x \\ \end{align*}

[_separable]

4.401

2845

\begin{align*} x y^{2}+x +\left (x^{2} y-y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

5.331

2846

\begin{align*} \sqrt {-x^{2}+1}+\sqrt {1-y^{2}}\, y^{\prime }&=0 \\ \end{align*}

[_separable]

8.668

2847

\begin{align*} \left (x +1\right ) y^{\prime }-1+y&=0 \\ \end{align*}

[_separable]

4.547

2848

\begin{align*} \tan \left (x \right ) y^{\prime }-y&=1 \\ \end{align*}

[_separable]

4.717

2849

\begin{align*} y+3+\cot \left (x \right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

5.315

2850

\begin{align*} y^{\prime }&=\frac {x}{y} \\ \end{align*}

[_separable]

14.834

2852

\begin{align*} x y^{\prime }+y&=y^{2} \\ \end{align*}

[_separable]

10.598

2853

\begin{align*} \sin \left (x \right ) \cos \left (y\right )^{2}+\cos \left (x \right )^{2} y^{\prime }&=0 \\ \end{align*}

[_separable]

5.207

2854

\begin{align*} \sec \left (x \right ) \cos \left (y\right )^{2}&=\cos \left (x \right ) \sin \left (y\right ) y^{\prime } \\ \end{align*}

[_separable]

10.553

2855

\begin{align*} x y^{\prime }+y&=x y \left (y^{\prime }-1\right ) \\ \end{align*}

[_separable]

5.814

2856

\begin{align*} y x +\sqrt {x^{2}+1}\, y^{\prime }&=0 \\ \end{align*}

[_separable]

5.833

2857

\begin{align*} y&=y x +x^{2} y^{\prime } \\ \end{align*}

[_separable]

5.650

2858

\begin{align*} \tan \left (x \right ) \sin \left (x \right )^{2}+\cos \left (x \right )^{2} \cot \left (y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

15.701

2859

\begin{align*} y^{2}+y y^{\prime }+x^{2} y y^{\prime }-1&=0 \\ \end{align*}

[_separable]

17.615

2860

\begin{align*} y^{\prime }&=\frac {y}{x} \\ y \left (1\right ) &= 3 \\ \end{align*}

[_separable]

3.947

2861

\begin{align*} x y^{\prime }+2 y&=0 \\ y \left (2\right ) &= 1 \\ \end{align*}

[_separable]

6.245

2862

\begin{align*} \sin \left (x \right ) \cos \left (y\right )+\cos \left (x \right ) \sin \left (y\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

5.248

2863

\begin{align*} x^{2} y^{\prime }+y^{2}&=0 \\ y \left (3\right ) &= 1 \\ \end{align*}

[_separable]

13.194

2866

\begin{align*} 1+y^{2}&=\frac {y^{\prime }}{x^{3} \left (x -1\right )} \\ y \left (2\right ) &= 0 \\ \end{align*}

[_separable]

9.173

2867

\begin{align*} \left (x^{2}+3 x \right ) y^{\prime }&=y^{3}+2 y \\ y \left (1\right ) &= 1 \\ \end{align*}

[_separable]

17.432

2868

\begin{align*} \left (x^{2}+x +1\right ) y^{\prime }&=y^{2}+2 y+5 \\ y \left (1\right ) &= 1 \\ \end{align*}

[_separable]

12.212

2869

\begin{align*} \left (x^{2}-2 x -8\right ) y^{\prime }&=y^{2}+y-2 \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

11.210

2924

\begin{align*} \frac {2}{y}-\frac {y}{x^{2}}+\left (\frac {1}{x}-\frac {2 x}{y^{2}}\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

7.102

2938

\begin{align*} \left (-2 y x +x \right ) y^{\prime }+2 y&=0 \\ \end{align*}

[_separable]

14.432

2952

\begin{align*} \left (x^{2}-1\right ) y+x \left (x^{2}+1\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 2 \\ \end{align*}

[_separable]

5.387

2990

\begin{align*} y^{\prime }-y x&=\frac {x}{y} \\ \end{align*}

[_separable]

5.454

2992

\begin{align*} r^{\prime }+\left (r-\frac {1}{r}\right ) \theta &=0 \\ \end{align*}

[_separable]

7.775

2995

\begin{align*} \cos \left (y\right ) y^{\prime }+\left (\sin \left (y\right )-1\right ) \cos \left (x \right )&=0 \\ \end{align*}

[_separable]

29.940

3003

\begin{align*} \left (1-x \right ) y^{\prime }-y-1&=0 \\ \end{align*}

[_separable]

2.150

3010

\begin{align*} 2 y+6&=x y y^{\prime } \\ \end{align*}

[_separable]

4.075

3014

\begin{align*} -x y^{\prime }+y&=2 y^{\prime }+2 y^{2} \\ \end{align*}

[_separable]

3.019

3015

\begin{align*} \tan \left (y\right )&=\left (3 x +4\right ) y^{\prime } \\ \end{align*}

[_separable]

3.208

3019

\begin{align*} r^{\prime }&=r \cot \left (\theta \right ) \\ \end{align*}

[_separable]

2.770

3023

\begin{align*} y^{\prime }&=\cos \left (y\right ) \cos \left (x \right )^{2} \\ \end{align*}

[_separable]

2.836

3027

\begin{align*} 3 x -6&=x y y^{\prime } \\ \end{align*}

[_separable]

2.345

3030

\begin{align*} x y^{\prime }+y \left (1+y^{2}\right )&=0 \\ \end{align*}

[_separable]

6.205

3032

\begin{align*} 3 \,{\mathrm e}^{x} \tan \left (y\right )&=\left (1-{\mathrm e}^{x}\right ) \sec \left (y\right )^{2} y^{\prime } \\ \end{align*}

[_separable]

4.076

3039

\begin{align*} x \sqrt {1-y}-y^{\prime } \sqrt {-x^{2}+1}&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

4.143

3041

\begin{align*} x \,{\mathrm e}^{-y^{2}}+y y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

2.634

3051

\begin{align*} 4 x y^{2}+\left (x^{2}+1\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

3.709

3056

\begin{align*} 2 \left (x^{2}+1\right ) y^{\prime }&=\left (2 y^{2}-1\right ) x y \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

7.747

3295

\begin{align*} y&=x +3 \ln \left (y^{\prime }\right ) \\ \end{align*}

[_separable]

3.897

3408

\begin{align*} y^{\prime }&=y x \\ \end{align*}

[_separable]

2.871

3409

\begin{align*} y^{\prime }&=x^{2} y^{2} \\ \end{align*}

[_separable]

7.214

3410

\begin{align*} y^{\prime }&=-x \,{\mathrm e}^{y} \\ \end{align*}

[_separable]

2.993

3411

\begin{align*} y^{\prime } \sin \left (y\right )&=x^{2} \\ \end{align*}

[_separable]

2.542

3412

\begin{align*} x y^{\prime }&=\sqrt {1-y^{2}} \\ \end{align*}

[_separable]

6.028

3426

\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{t}}{y} \\ y \left (\ln \left (2\right )\right ) &= -8 \\ \end{align*}

[_separable]

2.726

3430

\begin{align*} y^{\prime }&=\frac {y}{t} \\ \end{align*}

[_separable]

2.665

3431

\begin{align*} y^{\prime }&=-\frac {t}{y} \\ \end{align*}

[_separable]

6.750

3437

\begin{align*} y^{\prime }&=\left (t^{2}+1\right ) y \\ \end{align*}

[_separable]

3.330

3450

\begin{align*} y^{\prime }&=\frac {2 y}{t +1} \\ y \left (0\right ) &= 6 \\ \end{align*}

[_separable]

3.477

3452

\begin{align*} y^{\prime }+4 \tan \left (2 t \right ) y&=\tan \left (2 t \right ) \\ y \left (\frac {\pi }{8}\right ) &= 2 \\ \end{align*}

[_separable]

4.671

3456

\begin{align*} y^{\prime }-x y^{3}&=0 \\ \end{align*}

[_separable]

6.801

3457

\begin{align*} \frac {y^{\prime }}{\tan \left (x \right )}-\frac {y}{x^{2}+1}&=0 \\ \end{align*}

[_separable]

4.672

3458

\begin{align*} x^{2} y^{\prime }+x y^{2}&=4 y^{2} \\ \end{align*}

[_separable]

3.201

3469

\begin{align*} y^{\prime }&=\tan \left (x \right ) \cos \left (y\right ) \left (\cos \left (y\right )+\sin \left (y\right )\right ) \\ \end{align*}

[_separable]

4.948

3472

\begin{align*} y^{\prime }&=\frac {4 y^{2}}{x^{2}}-y^{2} \\ \end{align*}

[_separable]

3.259

3514

\begin{align*} y^{\prime }&=2 y x \\ \end{align*}

[_separable]

3.013

3515

\begin{align*} y^{\prime }&=\frac {y^{2}}{x^{2}+1} \\ \end{align*}

[_separable]

2.860

3516

\begin{align*} {\mathrm e}^{x +y} y^{\prime }-1&=0 \\ \end{align*}

[_separable]

3.357

3517

\begin{align*} y^{\prime }&=\frac {y}{x \ln \left (x \right )} \\ \end{align*}

[_separable]

2.940

3518

\begin{align*} y-\left (x -2\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

2.931

3519

\begin{align*} y^{\prime }&=\frac {2 x \left (-1+y\right )}{x^{2}+3} \\ \end{align*}

[_separable]

2.958

3520

\begin{align*} -x y^{\prime }+y&=3-2 x^{2} y^{\prime } \\ \end{align*}

[_separable]

2.977

3521

\begin{align*} y^{\prime }&=\frac {\cos \left (x -y\right )}{\sin \left (x \right ) \sin \left (y\right )}-1 \\ \end{align*}

[_separable]

3.485

3522

\begin{align*} y^{\prime }&=\frac {x \left (y^{2}-1\right )}{2 \left (x -2\right ) \left (x -1\right )} \\ \end{align*}

[_separable]

5.362

3524

\begin{align*} \left (x -a \right ) \left (x -b \right ) y^{\prime }-y+c&=0 \\ \end{align*}

[_separable]

4.407

3525

\begin{align*} \left (x^{2}+1\right ) y^{\prime }+y^{2}&=-1 \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

4.089

3526

\begin{align*} \left (-x^{2}+1\right ) y^{\prime }+y x&=a x \\ y \left (0\right ) &= 2 a \\ \end{align*}

[_separable]

2.665

3527

\begin{align*} y^{\prime }&=1-\frac {\sin \left (x +y\right )}{\cos \left (x \right ) \sin \left (y\right )} \\ y \left (\frac {\pi }{4}\right ) &= \frac {\pi }{4} \\ \end{align*}

[_separable]

5.106

3528

\begin{align*} y^{\prime }&=y^{3} \sin \left (x \right ) \\ \end{align*}

[_separable]

5.170

3561

\begin{align*} y^{\prime }&=\frac {y}{2 x} \\ \end{align*}

[_separable]

3.737

3592

\begin{align*} y^{\prime }&=2 y x \\ \end{align*}

[_separable]

3.108

3593

\begin{align*} y^{\prime }&=\frac {y^{2}}{x^{2}+1} \\ \end{align*}

[_separable]

3.056

3594

\begin{align*} {\mathrm e}^{x +y} y^{\prime }-1&=0 \\ \end{align*}

[_separable]

3.372

3595

\begin{align*} y^{\prime }&=\frac {y}{x \ln \left (x \right )} \\ \end{align*}

[_separable]

2.974

3596

\begin{align*} y-\left (x -1\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

3.202

3597

\begin{align*} y^{\prime }&=\frac {2 x \left (-1+y\right )}{x^{2}+3} \\ \end{align*}

[_separable]

3.204

3598

\begin{align*} -x y^{\prime }+y&=3-2 x^{2} y^{\prime } \\ \end{align*}

[_separable]

3.250

3599

\begin{align*} y^{\prime }&=\frac {\cos \left (x -y\right )}{\sin \left (x \right ) \sin \left (y\right )}-1 \\ \end{align*}

[_separable]

3.687

3600

\begin{align*} y^{\prime }&=\frac {x \left (y^{2}-1\right )}{2 \left (x -2\right ) \left (x -1\right )} \\ \end{align*}

[_separable]

5.800

3601

\begin{align*} y^{\prime }&=\frac {x^{2} y-32}{-x^{2}+16}+2 \\ \end{align*}

[_separable]

4.026

3602

\begin{align*} \left (x -a \right ) \left (x -b \right ) y^{\prime }-y+c&=0 \\ \end{align*}

[_separable]

4.858

3603

\begin{align*} \left (x^{2}+1\right ) y^{\prime }+y^{2}&=-1 \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

4.407

3604

\begin{align*} \left (-x^{2}+1\right ) y^{\prime }+y x&=a x \\ y \left (0\right ) &= 2 a \\ \end{align*}

[_separable]

2.882

3605

\begin{align*} y^{\prime }&=1-\frac {\sin \left (x +y\right )}{\cos \left (x \right ) \sin \left (y\right )} \\ y \left (\frac {\pi }{4}\right ) &= \frac {\pi }{4} \\ \end{align*}

[_separable]

5.316

3606

\begin{align*} y^{\prime }&=y^{3} \sin \left (x \right ) \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

5.473

3668

\begin{align*} \left (1-\sqrt {3}\right ) y^{\prime }+y \sec \left (x \right )&=y^{\sqrt {3}} \sec \left (x \right ) \\ \end{align*}

[_separable]

10.967

3682

\begin{align*} \sec \left (y\right )^{2} y^{\prime }+\frac {\tan \left (y\right )}{2 \sqrt {x +1}}&=\frac {1}{2 \sqrt {x +1}} \\ \end{align*}

[_separable]

35.721

4093

\begin{align*} x^{2}+x -1+\left (2 y x +y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

3.465

4094

\begin{align*} {\mathrm e}^{2 y}+\left (x +1\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

2.960

4095

\begin{align*} \left (x +1\right ) y^{\prime }-x^{2} y^{2}&=0 \\ \end{align*}

[_separable]

3.362

4101

\begin{align*} y^{\prime }&={\mathrm e}^{x -2 y} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

4.306

4104

\begin{align*} {\mathrm e}^{-y}+\left (x^{2}+1\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

3.531

4109

\begin{align*} 2 \sin \left (3 x \right ) \sin \left (2 y\right ) y^{\prime }-3 \cos \left (3 x \right ) \cos \left (2 y\right )&=0 \\ y \left (\frac {\pi }{12}\right ) &= \frac {\pi }{8} \\ \end{align*}

[_separable]

7.473

4110

\begin{align*} x y y^{\prime }&=\left (x +1\right ) \left (y+1\right ) \\ y \left (1\right ) &= 1 \\ \end{align*}

[_separable]

4.901

4189

\begin{align*} y y^{\prime }&=x \\ \end{align*}

[_separable]

12.827

4212

\begin{align*} 3 y^{2} y^{\prime }&=2 x -1 \\ \end{align*}

[_separable]

4.202

4213

\begin{align*} y^{\prime }&=6 x y^{2} \\ \end{align*}

[_separable]

8.284

4214

\begin{align*} y^{\prime }&={\mathrm e}^{y} \sin \left (x \right ) \\ \end{align*}

[_separable]

2.965

4215

\begin{align*} y^{\prime }&={\mathrm e}^{x -y} \\ \end{align*}

[_separable]

3.295

4216

\begin{align*} y^{\prime }&=x \sec \left (y\right ) \\ \end{align*}

[_separable]

2.704

4218

\begin{align*} x y^{\prime }&=y \\ \end{align*}

[_separable]

3.412

4219

\begin{align*} \left (1-x \right ) y^{\prime }&=y \\ \end{align*}

[_separable]

3.702

4220

\begin{align*} y^{\prime }&=\frac {4 x y}{x^{2}+1} \\ \end{align*}

[_separable]

3.892

4221

\begin{align*} y^{\prime }&=\frac {2 y}{x^{2}-1} \\ \end{align*}

[_separable]

3.978

4222

\begin{align*} -y^{2}+x^{2} y^{\prime }&=0 \\ y \left (1\right ) &= -1 \\ \end{align*}

[_separable]

8.166

4223

\begin{align*} y^{\prime }+2 y x&=0 \\ y \left (0\right ) &= 5 \\ \end{align*}

[_separable]

4.372

4224

\begin{align*} \cot \left (x \right ) y^{\prime }&=y \\ y \left (0\right ) &= 2 \\ \end{align*}

[_separable]

6.964

4225

\begin{align*} y^{\prime }&=x \,{\mathrm e}^{-2 y} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

5.264

4226

\begin{align*} y^{\prime }-2 y x&=2 x \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

3.963

4227

\begin{align*} x y^{\prime }&=y x +y \\ y \left (1\right ) &= 1 \\ \end{align*}

[_separable]

3.204

4229

\begin{align*} x \cos \left (y\right ) y^{\prime }&=1+\sin \left (y\right ) \\ y \left (1\right ) &= 0 \\ \end{align*}

[_separable]

8.933

4230

\begin{align*} x y^{\prime }&=2 y \left (-1+y\right ) \\ y \left (\frac {1}{2}\right ) &= 2 \\ \end{align*}

[_separable]

12.881

4231

\begin{align*} 2 x y^{\prime }&=1-y^{2} \\ y \left (1\right ) &= 0 \\ \end{align*}

[_separable]

6.644

4232

\begin{align*} \left (1-x \right ) y^{\prime }&=y x \\ \end{align*}

[_separable]

4.869

4233

\begin{align*} \left (x^{2}-1\right ) y^{\prime }&=\left (x^{2}+1\right ) y \\ \end{align*}

[_separable]

5.344

4234

\begin{align*} y^{\prime }&={\mathrm e}^{x} \left (1+y^{2}\right ) \\ \end{align*}

[_separable]

5.006

4235

\begin{align*} {\mathrm e}^{y} y^{\prime }+2 x&=2 x \,{\mathrm e}^{y} \\ \end{align*}

[_separable]

3.694

4236

\begin{align*} y \,{\mathrm e}^{2 x} y^{\prime }+2 x&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

3.954

4237

\begin{align*} x y y^{\prime }&=\sqrt {y^{2}-9} \\ y \left ({\mathrm e}^{4}\right ) &= 5 \\ \end{align*}

[_separable]

14.737

4256

\begin{align*} -\frac {\sin \left (\frac {x}{y}\right )}{y}+\frac {x \sin \left (\frac {x}{y}\right ) y^{\prime }}{y^{2}}&=0 \\ \end{align*}

[_separable]

4.712

4257

\begin{align*} 1+y+\left (1-x \right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

4.270

4264

\begin{align*} y-\left (x +x y^{3}\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

8.488

4294

\begin{align*} x^{2} y^{\prime }+2 y x&=0 \\ \end{align*}

[_separable]

5.612

4300

\begin{align*} x^{2} \left (1+y^{2}\right ) y^{\prime }+y^{2} \left (x^{2}+1\right )&=0 \\ \end{align*}

[_separable]

4.175

4301

\begin{align*} x \left (x -1\right ) y^{\prime }&=\cot \left (y\right ) \\ \end{align*}

[_separable]

5.661

4302

\begin{align*} r y^{\prime }&=\frac {\left (a^{2}-r^{2}\right ) \tan \left (y\right )}{a^{2}+r^{2}} \\ \end{align*}

[_separable]

4.464

4303

\begin{align*} \sqrt {x^{2}+1}\, y^{\prime }+\sqrt {1+y^{2}}&=0 \\ \end{align*}

[_separable]

7.901

4304

\begin{align*} y^{\prime }&=\frac {x \left (1+y^{2}\right )}{y \left (x^{2}+1\right )} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

17.273

4306

\begin{align*} \cos \left (y\right )^{2}+\left (1+{\mathrm e}^{-x}\right ) \sin \left (y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

5.117

4307

\begin{align*} y^{\prime }&=\frac {x^{3} {\mathrm e}^{x^{2}}}{\ln \left (y\right ) y} \\ \end{align*}

[_separable]

5.249

4308

\begin{align*} x \cos \left (y\right )^{2}+{\mathrm e}^{x} \tan \left (y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

12.247

4309

\begin{align*} x \left (1+y^{2}\right )+\left (1+2 y\right ) {\mathrm e}^{-x} y^{\prime }&=0 \\ \end{align*}

[_separable]

5.253

4310

\begin{align*} x y^{3}+{\mathrm e}^{x^{2}} y^{\prime }&=0 \\ \end{align*}

[_separable]

7.395

4311

\begin{align*} x \cos \left (y\right )^{2}+\tan \left (y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

43.392

4312

\begin{align*} x y^{3}+\left (y+1\right ) {\mathrm e}^{-x} y^{\prime }&=0 \\ \end{align*}

[_separable]

12.429

4360

\begin{align*} 1-\left (y-2 y x \right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

4.692

4397

\begin{align*} y^{\prime }&=\frac {y+2}{x +1} \\ \end{align*}

[_separable]

3.976

4411

\begin{align*} y x +2 x^{3} y+x^{2} y^{\prime }&=0 \\ \end{align*}

[_separable]

4.615

4428

\begin{align*} y \ln \left (x \right ) \ln \left (y\right )+y^{\prime }&=0 \\ \end{align*}

[_separable]

5.092

4618

\begin{align*} y^{\prime }&=a \,x^{n} y \\ \end{align*}

[_separable]

5.161

4625

\begin{align*} y^{\prime }&=y \cot \left (x \right ) \\ \end{align*}

[_separable]

4.397

4628

\begin{align*} y^{\prime }&=\left (2 \csc \left (2 x \right )+\cot \left (x \right )\right ) y \\ \end{align*}

[_separable]

9.616

4636

\begin{align*} y^{\prime }&=y \sec \left (x \right ) \\ \end{align*}

[_separable]

4.879

4638

\begin{align*} y^{\prime }&=y \tan \left (x \right ) \\ \end{align*}

[_separable]

4.408

4647

\begin{align*} y^{\prime }&=\left (a +\cos \left (\ln \left (x \right )\right )+\sin \left (\ln \left (x \right )\right )\right ) y \\ \end{align*}

[_separable]

5.093

4676

\begin{align*} y^{\prime }&=x y \left (y+3\right ) \\ \end{align*}

[_separable]

6.349

4680

\begin{align*} y^{\prime }&=a x y^{2} \\ \end{align*}

[_separable]

9.109

4681

\begin{align*} y^{\prime }&=x^{n} \left (a +b y^{2}\right ) \\ \end{align*}

[_separable]

7.178

4687

\begin{align*} y^{\prime }+\tan \left (x \right ) \left (1-y^{2}\right )&=0 \\ \end{align*}

[_separable]

8.872

4689

\begin{align*} y^{\prime }&=\left (a +b y+c y^{2}\right ) f \left (x \right ) \\ \end{align*}

[_separable]

9.682

4695

\begin{align*} y^{\prime }&=x y^{3} \\ \end{align*}

[_separable]

14.282

4701

\begin{align*} y^{\prime }+y^{3} \sec \left (x \right ) \tan \left (x \right )&=0 \\ \end{align*}

[_separable]

9.174

4714

\begin{align*} y^{\prime }&=\cos \left (y\right ) \cos \left (x \right )^{2} \\ \end{align*}

[_separable]

4.028

4715

\begin{align*} y^{\prime }&=\sec \left (x \right )^{2} \cot \left (y\right ) \cos \left (y\right ) \\ \end{align*}

[_separable]

4.379

4719

\begin{align*} y^{\prime }+\tan \left (x \right ) \sec \left (x \right ) \cos \left (y\right )^{2}&=0 \\ \end{align*}

[_separable]

3.676

4720

\begin{align*} y^{\prime }&=\cot \left (x \right ) \cot \left (y\right ) \\ \end{align*}

[_separable]

4.414

4721

\begin{align*} y^{\prime }+\cot \left (x \right ) \cot \left (y\right )&=0 \\ \end{align*}

[_separable]

5.168

4722

\begin{align*} y^{\prime }&=\sin \left (x \right ) \left (\csc \left (y\right )-\cot \left (y\right )\right ) \\ \end{align*}

[_separable]

5.980

4723

\begin{align*} y^{\prime }&=\tan \left (x \right ) \cot \left (y\right ) \\ \end{align*}

[_separable]

4.773

4724

\begin{align*} y^{\prime }+\tan \left (x \right ) \cot \left (y\right )&=0 \\ \end{align*}

[_separable]

4.243

4725

\begin{align*} y^{\prime }+\sin \left (2 x \right ) \csc \left (2 y\right )&=0 \\ \end{align*}

[_separable]

5.595

4727

\begin{align*} y^{\prime }&=\cos \left (x \right ) \sec \left (y\right )^{2} \\ \end{align*}

[_separable]

3.215

4728

\begin{align*} y^{\prime }&=\sec \left (x \right )^{2} \sec \left (y\right )^{3} \\ \end{align*}

[_separable]

3.661

4732

\begin{align*} y^{\prime }+\csc \left (2 x \right ) \sin \left (2 y\right )&=0 \\ \end{align*}

[_separable]

6.901

4735

\begin{align*} y^{\prime }&={\mathrm e}^{x +y} \\ \end{align*}

[_separable]

4.028

4736

\begin{align*} y^{\prime }&={\mathrm e}^{x} \left (a +b \,{\mathrm e}^{-y}\right ) \\ \end{align*}

[_separable]

5.370

4737

\begin{align*} y \ln \left (x \right ) \ln \left (y\right )+y^{\prime }&=0 \\ \end{align*}

[_separable]

5.680

4741

\begin{align*} y^{\prime }&=f \left (x \right ) g \left (y\right ) \\ \end{align*}

[_separable]

2.358

4760

\begin{align*} x y^{\prime }&=a y \\ \end{align*}

[_separable]

6.353

4761

\begin{align*} x y^{\prime }&=-a y \\ \end{align*}

[_separable]

6.484

4768

\begin{align*} x y^{\prime }+\left (b x +a \right ) y&=0 \\ \end{align*}

[_separable]

5.244

4771

\begin{align*} x y^{\prime }+\left (-a \,x^{2}+2\right ) y&=0 \\ \end{align*}

[_separable]

6.134

4775

\begin{align*} x y^{\prime }&=a +b y^{2} \\ \end{align*}

[_separable]

7.079

4796

\begin{align*} x y^{\prime }&=y \left (1+y^{2}\right ) \\ \end{align*}

[_separable]

12.938

4803

\begin{align*} x y^{\prime }&=4 y-4 \sqrt {y} \\ \end{align*}

[_separable]

17.864

4804

\begin{align*} x y^{\prime }+2 y&=\sqrt {1+y^{2}} \\ \end{align*}

[_separable]

12.239

4805

\begin{align*} x y^{\prime }+2 y&=-\sqrt {1+y^{2}} \\ \end{align*}

[_separable]

12.200

4815

\begin{align*} x y^{\prime }&=\left (-2 x^{2}+1\right ) \cot \left (y\right )^{2} \\ \end{align*}

[_separable]

4.424

4822

\begin{align*} x y^{\prime }+\tan \left (y\right )&=0 \\ \end{align*}

[_separable]

6.762

4828

\begin{align*} x y^{\prime }&=\ln \left (y\right ) y \\ \end{align*}

[_separable]

8.101

4845

\begin{align*} \left (x +a \right ) y^{\prime }&=b +c y \\ \end{align*}

[_separable]

5.614

4846

\begin{align*} \left (x +a \right ) y^{\prime }&=-b -c y \\ \end{align*}

[_separable]

5.001

4848

\begin{align*} \left (x +a \right ) y^{\prime }&=y \left (1-a y\right ) \\ \end{align*}

[_separable]

7.314

4852

\begin{align*} 2 x y^{\prime }&=y \left (1+y^{2}\right ) \\ \end{align*}

[_separable]

6.481

4853

\begin{align*} 2 x y^{\prime }+y \left (1+y^{2}\right )&=0 \\ \end{align*}

[_separable]

21.595

4855

\begin{align*} 2 x y^{\prime }+4 y+a +\sqrt {a^{2}-4 b -4 c y}&=0 \\ \end{align*}

[_separable]

10.751

4856

\begin{align*} 2 x y^{\prime }+4 y+a -\sqrt {a^{2}-4 b -4 c y}&=0 \\ \end{align*}

[_separable]

12.902

4858

\begin{align*} \left (2 x +1\right ) y^{\prime }&=4 \,{\mathrm e}^{-y}-2 \\ \end{align*}

[_separable]

6.704

4864

\begin{align*} x^{2} y^{\prime }&=a -y \\ \end{align*}

[_separable]

3.875

4869

\begin{align*} x^{2} y^{\prime }&=\left (b x +a \right ) y \\ \end{align*}

[_separable]

4.441

4874

\begin{align*} x^{2} y^{\prime }&=a +b y^{2} \\ \end{align*}

[_separable]

5.750

4902

\begin{align*} \left (-x^{2}+1\right ) y^{\prime }-x +y x&=0 \\ \end{align*}

[_separable]

8.478

4907

\begin{align*} \left (-x^{2}+1\right ) y^{\prime }+2 y x&=0 \\ \end{align*}

[_separable]

4.324

4913

\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=\left (2 b x +a \right ) y \\ \end{align*}

[_separable]

6.053

4914

\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=1+y^{2} \\ \end{align*}

[_separable]

5.055

4915

\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=-1-y^{2} \\ \end{align*}

[_separable]

4.959

4916

\begin{align*} \left (-x^{2}+1\right ) y^{\prime }&=1-y^{2} \\ \end{align*}

[_separable]

6.471

4917

\begin{align*} \left (-x^{2}+1\right ) y^{\prime }&=y^{2}-1 \\ \end{align*}

[_separable]

6.384

4920

\begin{align*} \left (x^{2}+1\right ) y^{\prime }+x y \left (1-y\right )&=0 \\ \end{align*}

[_separable]

14.349

4921

\begin{align*} \left (-x^{2}+1\right ) y^{\prime }&=x y \left (1+a y\right ) \\ \end{align*}

[_separable]

10.882

4927

\begin{align*} \left (a^{2}+x^{2}\right ) y^{\prime }&=\left (b +y\right ) \left (x +\sqrt {a^{2}+x^{2}}\right ) \\ \end{align*}

[_separable]

10.839

4931

\begin{align*} \left (a^{2}+x^{2}\right ) y^{\prime }+y x +b x y^{2}&=0 \\ \end{align*}

[_separable]

14.516

4932

\begin{align*} \left (-a^{2}+x^{2}\right ) y^{\prime }+y x +b x y^{2}&=0 \\ \end{align*}

[_separable]

12.717

4936

\begin{align*} x \left (x +1\right ) y^{\prime }&=\left (1-2 x \right ) y \\ \end{align*}

[_separable]

4.385

4942

\begin{align*} x \left (x +a \right ) y^{\prime }&=\left (b +c y\right ) y \\ \end{align*}

[_separable]

14.095

4943

\begin{align*} \left (x +a \right )^{2} y^{\prime }&=2 \left (x +a \right ) \left (b +y\right ) \\ \end{align*}

[_separable]

6.116

4945

\begin{align*} \left (x -a \right ) \left (x -b \right ) y^{\prime }+k y&=0 \\ \end{align*}

[_separable]

14.625

4947

\begin{align*} \left (x -a \right ) \left (x -b \right ) y^{\prime }&=c y^{2} \\ \end{align*}

[_separable]

8.520

4948

\begin{align*} \left (x -a \right ) \left (x -b \right ) y^{\prime }+k \left (y-a \right ) \left (y-b \right )&=0 \\ \end{align*}

[_separable]

15.760

4950

\begin{align*} 2 x^{2} y^{\prime }&=y \\ \end{align*}

[_separable]

4.941

4962

\begin{align*} \left (b \,x^{2}+a \right ) y^{\prime }&=A +B y^{2} \\ \end{align*}

[_separable]

7.896

4963

\begin{align*} \left (b \,x^{2}+a \right ) y^{\prime }&=-A -B y^{2} \\ \end{align*}

[_separable]

7.116

4964

\begin{align*} \left (b \,x^{2}+a \right ) y^{\prime }&=c x y \ln \left (y\right ) \\ \end{align*}

[_separable]

6.520

4965

\begin{align*} x \left (a x +1\right ) y^{\prime }+a -y&=0 \\ \end{align*}

[_separable]

4.544

4972

\begin{align*} x^{3} y^{\prime }&=\left (x +1\right ) y^{2} \\ \end{align*}

[_separable]

4.291

4980

\begin{align*} x \left (x^{2}+1\right ) y^{\prime }&=\left (-x^{2}+1\right ) y \\ \end{align*}

[_separable]

4.028

4981

\begin{align*} x \left (-x^{2}+1\right ) y^{\prime }&=\left (x^{2}-x +1\right ) y \\ \end{align*}

[_separable]

4.504

4995

\begin{align*} \left (-x^{4}+1\right ) y^{\prime }&=2 x \left (1-y^{2}\right ) \\ \end{align*}

[_separable]

7.629

4999

\begin{align*} x \left (-2 x^{3}+1\right ) y^{\prime }&=2 \left (-x^{3}+1\right ) y \\ \end{align*}

[_separable]

5.292

5011

\begin{align*} y^{\prime } \sqrt {-x^{2}+1}&=1+y^{2} \\ \end{align*}

[_separable]

8.539

5012

\begin{align*} \left (x -\sqrt {x^{2}+1}\right ) y^{\prime }&=y+\sqrt {1+y^{2}} \\ \end{align*}

[_separable]

8.513

5014

\begin{align*} y^{\prime } \sqrt {b^{2}+x^{2}}&=\sqrt {y^{2}+a^{2}} \\ \end{align*}

[_separable]

53.987

5015

\begin{align*} y^{\prime } \sqrt {b^{2}-x^{2}}&=\sqrt {a^{2}-y^{2}} \\ \end{align*}

[_separable]

53.338

5016

\begin{align*} x y^{\prime } \sqrt {a^{2}+x^{2}}&=y \sqrt {b^{2}+y^{2}} \\ \end{align*}

[_separable]

18.372

5017

\begin{align*} x y^{\prime } \sqrt {-a^{2}+x^{2}}&=y \sqrt {y^{2}-b^{2}} \\ \end{align*}

[_separable]

29.101

5019

\begin{align*} y^{\prime } \sqrt {x^{3}+1}&=\sqrt {y^{3}+1} \\ \end{align*}

[_separable]

8.019

5020

\begin{align*} y^{\prime } \sqrt {x \left (1-x \right ) \left (-a x +1\right )}&=\sqrt {y \left (1-y\right ) \left (1-a y\right )} \\ \end{align*}

[_separable]

10.766

5021

\begin{align*} y^{\prime } \sqrt {-x^{4}+1}&=\sqrt {1-y^{4}} \\ \end{align*}

[_separable]

7.624

5022

\begin{align*} y^{\prime } \sqrt {x^{4}+x^{2}+1}&=\sqrt {1+y^{2}+y^{4}} \\ \end{align*}

[_separable]

8.870

5024

\begin{align*} y^{\prime } \sqrt {b \,x^{4}+a \,x^{2}+1}+\sqrt {1+a y^{2}+b y^{4}}&=0 \\ \end{align*}

[_separable]

8.532

5025

\begin{align*} y^{\prime } \sqrt {a_{4} x^{4}+a_{3} x^{3}+a_{2} x^{2}+a_{1} x +a_{0}}&=\sqrt {b_{0} +b_{1} y+b_{2} y^{2}} \\ \end{align*}

[_separable]

12.587

5026

\begin{align*} y^{\prime } \left (x^{3}+1\right )^{{2}/{3}}+\left (y^{3}+1\right )^{{2}/{3}}&=0 \\ \end{align*}

[_separable]

6.280

5027

\begin{align*} y^{\prime } \left (4 x^{3}+a_{1} x +a_{0} \right )^{{2}/{3}}+\left (a_{0} +a_{1} y+4 y^{3}\right )^{{2}/{3}}&=0 \\ \end{align*}

[_separable]

7.166

5029

\begin{align*} \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 \\ \end{align*}

[_separable]

17.209

5030

\begin{align*} \left (1-\sin \left (x \right )\right ) y^{\prime }+\cos \left (x \right ) y&=0 \\ \end{align*}

[_separable]

8.343

5031

\begin{align*} \left (\cos \left (x \right )-\sin \left (x \right )\right ) y^{\prime }+y \left (\cos \left (x \right )+\sin \left (x \right )\right )&=0 \\ \end{align*}

[_separable]

8.751

5035

\begin{align*} y y^{\prime }+x&=0 \\ \end{align*}

[_separable]

11.704

5036

\begin{align*} y y^{\prime }+x \,{\mathrm e}^{x^{2}}&=0 \\ \end{align*}

[_separable]

3.283

5039

\begin{align*} y y^{\prime }+x \,{\mathrm e}^{-x} \left (y+1\right )&=0 \\ \end{align*}

[_separable]

11.342

5045

\begin{align*} y y^{\prime }&=a x +b x y^{2} \\ \end{align*}

[_separable]

8.683

5051

\begin{align*} \left (y+1\right ) y^{\prime }&=x^{2} \left (1-y\right ) \\ \end{align*}

[_separable]

6.118

5094

\begin{align*} 3 y y^{\prime }+5 \cot \left (x \right ) \cot \left (y\right ) \cos \left (y\right )^{2}&=0 \\ \end{align*}

[_separable]

13.265

5095

\begin{align*} 3 \left (2-y\right ) y^{\prime }+y x&=0 \\ \end{align*}

[_separable]

6.296

5123

\begin{align*} x y y^{\prime }+1+y^{2}&=0 \\ \end{align*}

[_separable]

11.709

5130

\begin{align*} x y y^{\prime }&=a +b y^{2} \\ \end{align*}

[_separable]

12.694

5132

\begin{align*} x y y^{\prime }&=\left (x^{2}+1\right ) \left (1-y^{2}\right ) \\ \end{align*}

[_separable]

7.428

5136

\begin{align*} x \left (y+1\right ) y^{\prime }-\left (1-x \right ) y&=0 \\ \end{align*}

[_separable]

6.747

5137

\begin{align*} x \left (1-y\right ) y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}

[_separable]

7.232

5138

\begin{align*} x \left (1-y\right ) y^{\prime }+\left (1-x \right ) y&=0 \\ \end{align*}

[_separable]

6.785

5143

\begin{align*} x \left (y+a \right ) y^{\prime }&=y \left (B x +A \right ) \\ \end{align*}

[_separable]

7.142

5155

\begin{align*} y \left (1-x \right ) y^{\prime }+\left (1-y\right ) x&=0 \\ \end{align*}

[_separable]

7.386

5156

\begin{align*} \left (x +a \right ) \left (x +b \right ) y^{\prime }&=y x \\ \end{align*}

[_separable]

10.252

5158

\begin{align*} 2 x y y^{\prime }+a +y^{2}&=0 \\ \end{align*}

[_separable]

8.499

5178

\begin{align*} x \left (a +b y\right ) y^{\prime }&=c y \\ \end{align*}

[_separable]

15.437

5186

\begin{align*} x^{2} \left (1-y\right ) y^{\prime }+\left (1-x \right ) y&=0 \\ \end{align*}

[_separable]

11.648

5187

\begin{align*} x^{2} \left (1-y\right ) y^{\prime }+\left (x +1\right ) y^{2}&=0 \\ \end{align*}

[_separable]

10.626

5188

\begin{align*} \left (x^{2}+1\right ) y y^{\prime }+x \left (1-y^{2}\right )&=0 \\ \end{align*}

[_separable]

11.641

5195

\begin{align*} 2 \left (x +1\right ) x y y^{\prime }&=1+y^{2} \\ \end{align*}

[_separable]

11.227

5203

\begin{align*} x y \left (b \,x^{2}+a \right ) y^{\prime }&=A +B y^{2} \\ \end{align*}

[_separable]

22.490

5206

\begin{align*} y y^{\prime } \sqrt {x^{2}+1}+x \sqrt {1+y^{2}}&=0 \\ \end{align*}

[_separable]

7.938

5207

\begin{align*} \left (y+1\right ) y^{\prime } \sqrt {x^{2}+1}&=y^{3} \\ \end{align*}

[_separable]

15.631

5208

\begin{align*} y^{2} y^{\prime }+x \left (2-y\right )&=0 \\ \end{align*}

[_separable]

4.247

5209

\begin{align*} y^{2} y^{\prime }&=x \left (1+y^{2}\right ) \\ \end{align*}

[_separable]

4.056

5223

\begin{align*} y \left (y+1\right ) y^{\prime }&=x \left (x +1\right ) \\ \end{align*}

[_separable]

4.334

5251

\begin{align*} x \left (1-y^{2}\right ) y^{\prime }&=\left (x^{2}+1\right ) y \\ \end{align*}

[_separable]

8.415

5258

\begin{align*} x \left (y+a \right )^{2} y^{\prime }&=b y^{2} \\ \end{align*}

[_separable]

9.602

5275

\begin{align*} x^{2} y^{2} y^{\prime }+1-x +x^{3}&=0 \\ \end{align*}

[_separable]

5.012

5280

\begin{align*} x^{2} \left (y+a \right )^{2} y^{\prime }&=\left (x^{2}+1\right ) \left (y^{2}+a^{2}\right ) \\ \end{align*}

[_separable]

5.252

5281

\begin{align*} \left (x^{2}+1\right ) \left (1+y^{2}\right ) y^{\prime }+2 x y \left (1-y^{2}\right )&=0 \\ \end{align*}

[_separable]

15.275

5282

\begin{align*} \left (x^{2}+1\right ) \left (1+y^{2}\right ) y^{\prime }+2 x y \left (1-y\right )^{2}&=0 \\ \end{align*}

[_separable]

6.086

5285

\begin{align*} x^{3} \left (1+y^{2}\right ) y^{\prime }+3 x^{2} y&=0 \\ \end{align*}

[_separable]

12.274

5297

\begin{align*} y \left (2 y^{2}+1\right ) y^{\prime }&=x \left (2 x^{2}+1\right ) \\ \end{align*}

[_separable]

5.084

5303

\begin{align*} x y^{3} y^{\prime }&=\left (-x^{2}+1\right ) \left (1+y^{2}\right ) \\ \end{align*}

[_separable]

8.263

5333

\begin{align*} y^{\prime } \sqrt {b^{2}+y^{2}}&=\sqrt {a^{2}+x^{2}} \\ \end{align*}

[_separable]

10.361

5334

\begin{align*} y^{\prime } \sqrt {b^{2}-y^{2}}&=\sqrt {a^{2}-x^{2}} \\ \end{align*}

[_separable]

11.789

5338

\begin{align*} \left (y+\sqrt {1+y^{2}}\right ) \left (x^{2}+1\right )^{{3}/{2}} y^{\prime }&=1+y^{2} \\ \end{align*}

[_separable]

10.000

5339

\begin{align*} \left (y+\sqrt {1+y^{2}}\right ) \left (x^{2}+1\right )^{{3}/{2}} y^{\prime }&=1+y^{2} \\ \end{align*}

[_separable]

8.833

5353

\begin{align*} y^{\prime } \left (1+\sinh \left (x \right )\right ) \sinh \left (y\right )+\cosh \left (x \right ) \left (\cosh \left (y\right )-1\right )&=0 \\ \end{align*}

[_separable]

13.325

5684

\begin{align*} 2 \left (y+1\right )^{{3}/{2}}+3 x y^{\prime }-3 y&=0 \\ \end{align*}

[_separable]

61.622

5706

\begin{align*} y \ln \left (y^{\prime }\right )+y^{\prime }-\ln \left (y\right ) y-y x&=0 \\ \end{align*}

[_separable]

34.051

6824

\begin{align*} x \left (1-y\right ) y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}

[_separable]

14.122

6825

\begin{align*} y^{2}+x y^{2}+\left (x^{2}-x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

20.681

6826

\begin{align*} x y \left (x^{2}+1\right ) y^{\prime }-1-y^{2}&=0 \\ \end{align*}

[_separable]

34.625

6827

\begin{align*} 1+y^{2}-\left (y+\sqrt {1+y^{2}}\right ) \left (x^{2}+1\right )^{{3}/{2}} y^{\prime }&=0 \\ \end{align*}

[_separable]

15.675

6828

\begin{align*} \sin \left (x \right ) \cos \left (y\right )-\cos \left (x \right ) \sin \left (y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

9.326

6829

\begin{align*} \sec \left (x \right )^{2} \tan \left (y\right )+\sec \left (y\right )^{2} \tan \left (x \right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

31.083

6842

\begin{align*} \left (-x^{2}+1\right ) z^{\prime }-x z&=a x z^{2} \\ \end{align*}

[_separable]

38.214

6873

\begin{align*} \frac {\sqrt {f \,x^{4}+x^{3} c +c \,x^{2}+b x +a}\, y^{\prime }}{\sqrt {a +b y+c y^{2}+c y^{3}+f y^{4}}}&=-1 \\ \end{align*}

[_separable]

22.500

6894

\begin{align*} \frac {-x y^{\prime }+y}{y^{\prime }+y^{2}}&=\frac {-x y^{\prime }+y}{1+x^{2} y^{\prime }} \\ \end{align*}

[_separable]

5.202

6915

\begin{align*} 7 y-3+\left (2 x +1\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

14.941

6983

\begin{align*} y^{\prime }+\frac {y}{x}&=\frac {y^{2}}{x} \\ y \left (-1\right ) &= 1 \\ \end{align*}

[_separable]

112.611

6994

\begin{align*} y^{\prime } \sin \left (y\right )+\sin \left (x \right ) \cos \left (y\right )&=\sin \left (x \right ) \\ \end{align*}

[_separable]

27.723

7004

\begin{align*} 2 y-x y \ln \left (x \right )-2 x \ln \left (x \right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

2.756

7010

\begin{align*} x y^{\prime }-y^{2}+1&=0 \\ \end{align*}

[_separable]

3.609

7023

\begin{align*} \left (x^{2}-1\right ) y^{\prime }+y x -3 x y^{2}&=0 \\ \end{align*}

[_separable]

5.357

7024

\begin{align*} \left (x^{2}-1\right ) y^{\prime }-2 x y \ln \left (y\right )&=0 \\ \end{align*}

[_separable]

4.370

7038

\begin{align*} \left (2 y^{3}+y\right ) y^{\prime }-2 x^{3}-x&=0 \\ \end{align*}

[_separable]

2.108

7039

\begin{align*} y^{\prime }-{\mathrm e}^{x -y}+{\mathrm e}^{x}&=0 \\ \end{align*}

[_separable]

2.307

7149

\begin{align*} y^{\prime }+y \tan \left (x \right )&=0 \\ \end{align*}

[_separable]

2.944

7155

\begin{align*} x \left (1-y\right ) y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}

[_separable]

2.793

7156

\begin{align*} y^{\prime }&=a x y^{2} \\ \end{align*}

[_separable]

3.605

7157

\begin{align*} y^{2}+x y^{2}+\left (x^{2}-x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

4.016

7158

\begin{align*} x y \left (x^{2}+1\right ) y^{\prime }&=1+y^{2} \\ \end{align*}

[_separable]

6.915

7159

\begin{align*} \frac {x}{y+1}&=\frac {y y^{\prime }}{x +1} \\ \end{align*}

[_separable]

2.145

7161

\begin{align*} y^{\prime }&=\frac {1+y^{2}}{x^{2}+1} \\ \end{align*}

[_separable]

3.376

7162

\begin{align*} \sin \left (x \right ) \cos \left (y\right )&=\cos \left (x \right ) \sin \left (y\right ) y^{\prime } \\ \end{align*}

[_separable]

3.717

7163

\begin{align*} a x y^{\prime }+2 y&=x y y^{\prime } \\ \end{align*}

[_separable]

4.767

7217

\begin{align*} x y^{\prime }&=y \\ y \left (2\right ) &= 3 \\ \end{align*}

[_separable]

2.299

7218

\begin{align*} x \sqrt {1-y^{2}}+y \sqrt {-x^{2}+1}\, y^{\prime }&=0 \\ y \left (\frac {1}{2}\right ) &= {\frac {1}{2}} \\ \end{align*}

[_separable]

5.885

7219

\begin{align*} \sin \left (x \right ) y^{\prime }&=\ln \left (y\right ) y \\ y \left (\frac {\pi }{3}\right ) &= {\mathrm e} \\ \end{align*}

[_separable]

3.243

7220

\begin{align*} x y y^{\prime }+1+y^{2}&=0 \\ y \left (5\right ) &= 0 \\ \end{align*}

[_separable]

5.688

7222

\begin{align*} y^{\prime }&=\frac {2 x y^{2}+x}{x^{2} y-y} \\ y \left (\sqrt {2}\right ) &= 0 \\ \end{align*}

[_separable]

3.595

7223

\begin{align*} y y^{\prime }+x y^{2}-8 x&=0 \\ y \left (1\right ) &= 3 \\ \end{align*}

[_separable]

2.658

7224

\begin{align*} y^{\prime }+2 x y^{2}&=0 \\ y \left (2\right ) &= 1 \\ \end{align*}

[_separable]

4.372

7226

\begin{align*} y^{\prime }-y x&=x \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

2.274

7228

\begin{align*} \left (y x +x \right ) y^{\prime }+y&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}

[_separable]

5.238

7245

\begin{align*} 3 x y^{2} y^{\prime }+3 y^{3}&=1 \\ \end{align*}

[_separable]

4.033

7333

\begin{align*} x \ln \left (y\right ) y^{\prime }-y \ln \left (x \right )&=0 \\ \end{align*}

[_separable]

3.001

7341

\begin{align*} u \left (1-v \right )+v^{2} \left (1-u\right ) u^{\prime }&=0 \\ \end{align*}

[_separable]

4.586

7352

\begin{align*} y^{\prime }+y x&=\frac {x}{y} \\ \end{align*}

[_separable]

3.575

7356

\begin{align*} 3 x^{2} y+x^{3} y^{\prime }&=0 \\ y \left (1\right ) &= 2 \\ \end{align*}

[_separable]

4.151

7361

\begin{align*} x y^{\prime }&=y x +y \\ \end{align*}

[_separable]

1.599

7363

\begin{align*} y^{\prime }&=3 x^{2} y \\ \end{align*}

[_separable]

2.523

7365

\begin{align*} x y^{\prime }&=y \\ \end{align*}

[_separable]

2.200

7383

\begin{align*} y^{\prime }&=\frac {y \,{\mathrm e}^{x +y}}{x^{2}+2} \\ \end{align*}

[_separable]

2.892

7384

\begin{align*} \left (x y^{2}+3 y^{2}\right ) y^{\prime }-2 x&=0 \\ \end{align*}

[_separable]

2.183

7386

\begin{align*} x y^{\prime }&=\frac {1}{y^{3}} \\ \end{align*}

[_separable]

3.039

7387

\begin{align*} x^{\prime }&=3 x t^{2} \\ \end{align*}

[_separable]

3.125

7388

\begin{align*} x^{\prime }&=\frac {t \,{\mathrm e}^{-t -2 x}}{x} \\ \end{align*}

[_separable]

2.152

7389

\begin{align*} y^{\prime }&=\frac {x}{y^{2} \sqrt {x +1}} \\ \end{align*}

[_separable]

2.927

7390

\begin{align*} x v^{\prime }&=\frac {1-4 v^{2}}{3 v} \\ \end{align*}

[_separable]

9.695

7391

\begin{align*} y^{\prime }&=\frac {\sec \left (y\right )^{2}}{x^{2}+1} \\ \end{align*}

[_separable]

3.737

7392

\begin{align*} y^{\prime }&=3 x^{2} \left (1+y^{2}\right )^{{3}/{2}} \\ \end{align*}

[_separable]

12.366

7394

\begin{align*} x +x y^{2}+{\mathrm e}^{x^{2}} y y^{\prime }&=0 \\ \end{align*}

[_separable]

4.334

7395

\begin{align*} \frac {y^{\prime }}{y}+y \,{\mathrm e}^{\cos \left (x \right )} \sin \left (x \right )&=0 \\ \end{align*}

[_separable]

4.526

7396

\begin{align*} y^{\prime }&=\left (1+y^{2}\right ) \tan \left (x \right ) \\ y \left (0\right ) &= \sqrt {3} \\ \end{align*}

[_separable]

6.953

7397

\begin{align*} y^{\prime }&=x^{3} \left (1-y\right ) \\ y \left (0\right ) &= 3 \\ \end{align*}

[_separable]

2.994

7398

\begin{align*} \frac {y^{\prime }}{2}&=\sqrt {y+1}\, \cos \left (x \right ) \\ y \left (\pi \right ) &= 0 \\ \end{align*}

[_separable]

3.539

7399

\begin{align*} x^{2} y^{\prime }&=\frac {4 x^{2}-x -2}{\left (x +1\right ) \left (y+1\right )} \\ y \left (1\right ) &= 1 \\ \end{align*}

[_separable]

5.508

7400

\begin{align*} \frac {y^{\prime }}{\theta }&=\frac {y \sin \left (\theta \right )}{y^{2}+1} \\ y \left (\pi \right ) &= 1 \\ \end{align*}

[_separable]

5.118

7401

\begin{align*} x^{2}+2 y y^{\prime }&=0 \\ y \left (0\right ) &= 2 \\ \end{align*}

[_separable]

11.228

7402

\begin{align*} y^{\prime }&=2 t \cos \left (y\right )^{2} \\ y \left (0\right ) &= \frac {\pi }{4} \\ \end{align*}

[_separable]

2.364

7403

\begin{align*} y^{\prime }&=8 x^{3} {\mathrm e}^{-2 y} \\ y \left (1\right ) &= 0 \\ \end{align*}

[_separable]

3.530

7404

\begin{align*} y^{\prime }&=x^{2} \left (y+1\right ) \\ y \left (0\right ) &= 3 \\ \end{align*}

[_separable]

5.095

7405

\begin{align*} \sqrt {y}+\left (x +1\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

4.421

7407

\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{x^{2}}}{y^{2}} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

2.664

7408

\begin{align*} y^{\prime }&=\sqrt {1+\sin \left (x \right )}\, \left (1+y^{2}\right ) \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

25.469

7409

\begin{align*} y^{\prime }&=2 y-2 y t \\ y \left (0\right ) &= 3 \\ \end{align*}

[_separable]

4.829

7412

\begin{align*} y^{\prime }&=\left (x -3\right ) \left (y+1\right )^{{2}/{3}} \\ \end{align*}

[_separable]

6.164

7413

\begin{align*} y^{\prime }&=x y^{3} \\ \end{align*}

[_separable]

7.235

7414

\begin{align*} y^{\prime }&=x y^{3} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

6.434

7415

\begin{align*} y^{\prime }&=x y^{3} \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}

[_separable]

6.641

7416

\begin{align*} y^{\prime }&=x y^{3} \\ y \left (0\right ) &= 2 \\ \end{align*}

[_separable]

5.691

7420

\begin{align*} \left (t^{2}+1\right ) y^{\prime }&=y t -y \\ \end{align*}

[_separable]

3.249

7432

\begin{align*} \left (x^{2}+1\right ) y^{\prime }+y x -x&=0 \\ \end{align*}

[_separable]

2.275

7448

\begin{align*} \sqrt {-2 y-y^{2}}+\left (-x^{2}+2 x +3\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

6.014

7467

\begin{align*} {\mathrm e}^{t} y+t \,{\mathrm e}^{t} y+\left ({\mathrm e}^{t} t +2\right ) y^{\prime }&=0 \\ y \left (0\right ) &= -1 \\ \end{align*}

[_separable]

3.900

7469

\begin{align*} \sin \left (x \right ) y^{2}+\left (\frac {1}{x}-\frac {y}{x}\right ) y^{\prime }&=0 \\ y \left (\pi \right ) &= 1 \\ \end{align*}

[_separable]

7.800

7525

\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{x +y}}{-1+y} \\ \end{align*}

[_separable]

3.391

7529

\begin{align*} 2 x y^{3}-\left (-x^{2}+1\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

4.957

7530

\begin{align*} t^{3} y^{2}+\frac {t^{4} y^{\prime }}{y^{6}}&=0 \\ \end{align*}

[_separable]

3.658

7549

\begin{align*} y^{\prime }+y x&=0 \\ \end{align*}

[_separable]

2.838

7561

\begin{align*} \sqrt {y}+\left (x^{2}+4\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 4 \\ \end{align*}

[_separable]

5.286

7562

\begin{align*} y^{\prime }-\frac {2 y}{x}&=\frac {1}{y x} \\ y \left (1\right ) &= 3 \\ \end{align*}

[_separable]

6.260

7682

\begin{align*} y^{\prime }+y x&=x y^{2} \\ \end{align*}

[_separable]

4.714

7696

\begin{align*} \left (x +1\right )^{2} y^{\prime }&=1+y^{2} \\ \end{align*}

[_separable]

3.731

7700

\begin{align*} x \cos \left (y\right ) y^{\prime }-\sin \left (y\right )&=0 \\ \end{align*}

[_separable]

8.744

7702

\begin{align*} \left (x^{2}-1\right ) y^{\prime }+2 y x&=x \\ \end{align*}

[_separable]

3.067

7707

\begin{align*} x \left (-3+y\right ) y^{\prime }&=4 y \\ \end{align*}

[_separable]

7.925

7708

\begin{align*} \left (x^{3}+1\right ) y^{\prime }&=x^{2} y \\ y \left (1\right ) &= 2 \\ \end{align*}

[_separable]

3.525

7709

\begin{align*} x^{3}+\left (y+1\right )^{2} y^{\prime }&=0 \\ \end{align*}

[_separable]

3.237

7710

\begin{align*} \cos \left (y\right )+\left (1+{\mathrm e}^{-x}\right ) \sin \left (y\right ) y^{\prime }&=0 \\ y \left (0\right ) &= \frac {\pi }{4} \\ \end{align*}

[_separable]

3.799

7711

\begin{align*} x^{2} \left (y+1\right )+y^{2} \left (x -1\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

2.478

7733

\begin{align*} x y y^{\prime }-\left (x +1\right ) \sqrt {-1+y}&=0 \\ \end{align*}

[_separable]

3.017

7735

\begin{align*} y+\left (x^{2}-4 x \right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

2.965

7738

\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=x \left (y+1\right ) \\ \end{align*}

[_separable]

2.526

7741

\begin{align*} y^{\prime }&={\mathrm e}^{3 x -2 y} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

3.526

7748

\begin{align*} y^{\prime }+x +x y^{2}&=0 \\ y \left (1\right ) &= 0 \\ \end{align*}

[_separable]

4.496

7751

\begin{align*} x \left (1+y^{2}\right )-\left (x^{2}+1\right ) y y^{\prime }&=0 \\ \end{align*}

[_separable]

7.634

7752

\begin{align*} \frac {r \tan \left (\theta \right ) r^{\prime }}{a^{2}-r^{2}}&=1 \\ r \left (\frac {\pi }{4}\right ) &= 0 \\ \end{align*}

[_separable]

4.780

7845

\begin{align*} x y^{\prime }&=2 y \\ \end{align*}

[_separable]

4.398

7846

\begin{align*} y y^{\prime }+x&=0 \\ \end{align*}

[_separable]

7.390

7855

\begin{align*} 4 y+x y^{\prime }&=0 \\ \end{align*}

[_separable]

4.162

7856

\begin{align*} 1+2 y+\left (-x^{2}+4\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

6.070

7857

\begin{align*} y^{2}-x^{2} y^{\prime }&=0 \\ \end{align*}

[_separable]

5.429

7858

\begin{align*} 1+y-\left (x +1\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

3.024

7864

\begin{align*} 1+2 y-\left (4-x \right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

3.576

7865

\begin{align*} \left (x^{2}+1\right ) y^{\prime }+y x&=0 \\ \end{align*}

[_separable]

2.711

7869

\begin{align*} x y y^{\prime }&=\left (y+1\right ) \left (1-x \right ) \\ \end{align*}

[_separable]

3.858

7872

\begin{align*} 1+\left (-x^{2}+1\right ) \cot \left (y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

4.862

7875

\begin{align*} x y^{\prime }+2 y&=0 \\ y \left (2\right ) &= 1 \\ \end{align*}

[_separable]

4.356

7877

\begin{align*} \cos \left (y\right )+\left (1+{\mathrm e}^{-x}\right ) \sin \left (y\right ) y^{\prime }&=0 \\ y \left (0\right ) &= \frac {\pi }{4} \\ \end{align*}

[_separable]

3.668

7908

\begin{align*} 1+y^{2}&=\left (x^{2}+x \right ) y^{\prime } \\ \end{align*}

[_separable]

4.259

7918

\begin{align*} y^{\prime }-y&=y x \\ \end{align*}

[_separable]

3.500

7927

\begin{align*} y y^{\prime }-x y^{2}+x&=0 \\ \end{align*}

[_separable]

4.335

8160

\begin{align*} y^{2}-1+x y^{\prime }&=0 \\ \end{align*}

[_separable]

5.703

8167

\begin{align*} y^{\prime }&=2 x y^{2} \\ \end{align*}

[_separable]

6.560

8168

\begin{align*} 2 y^{\prime }&=y^{3} \cos \left (x \right ) \\ \end{align*}

[_separable]

5.395

8179

\begin{align*} x y^{\prime }-2 y&=0 \\ \end{align*}

[_separable]

4.468

8180

\begin{align*} y^{\prime }&=-\frac {x}{y} \\ \end{align*}

[_separable]

7.448

8189

\begin{align*} 3 x y^{\prime }+5 y&=10 \\ \end{align*}

[_separable]

4.934

8210

\begin{align*} y^{\prime }+2 x y^{2}&=0 \\ y \left (2\right ) &= {\frac {1}{3}} \\ \end{align*}

[_separable]

6.339

8211

\begin{align*} y^{\prime }+2 x y^{2}&=0 \\ y \left (-2\right ) &= {\frac {1}{2}} \\ \end{align*}

[_separable]

6.128

8212

\begin{align*} y^{\prime }+2 x y^{2}&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

5.925

8213

\begin{align*} y^{\prime }+2 x y^{2}&=0 \\ y \left (\frac {1}{2}\right ) &= -4 \\ \end{align*}

[_separable]

6.251

8223

\begin{align*} x y^{\prime }&=2 y \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

4.459

8226

\begin{align*} x y^{\prime }&=y \\ \end{align*}

[_separable]

2.971

8228

\begin{align*} \left (4-y^{2}\right ) y^{\prime }&=x^{2} \\ \end{align*}

[_separable]

2.642

8229

\begin{align*} \left (y^{3}+1\right ) y^{\prime }&=x^{2} \\ \end{align*}

[_separable]

2.557

8236

\begin{align*} x y^{\prime }&=y \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

3.210

8243

\begin{align*} y y^{\prime }&=3 x \\ y \left (-2\right ) &= 3 \\ \end{align*}

[_separable]

10.086

8244

\begin{align*} y y^{\prime }&=3 x \\ y \left (2\right ) &= -4 \\ \end{align*}

[_separable]

9.181

8245

\begin{align*} y y^{\prime }&=3 x \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

19.594

8256

\begin{align*} y^{\prime }&=x \sqrt {y} \\ y \left (2\right ) &= 1 \\ \end{align*}

[_separable]

12.375

8260

\begin{align*} x y^{\prime }&=y \\ \end{align*}

[_separable]

3.107

8265

\begin{align*} 3 x y^{\prime }-2 y&=0 \\ \end{align*}

[_separable]

4.749

8266

\begin{align*} \left (-2+2 y\right ) y^{\prime }&=2 x -1 \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

10.430

8279

\begin{align*} x y^{\prime }+y&=\frac {1}{y^{2}} \\ \end{align*}

[_separable]

7.951

8301

\begin{align*} y^{\prime }&=\sin \left (x \right ) \cos \left (y\right ) \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

5.429

8302

\begin{align*} y^{\prime }&=\sin \left (x \right ) \cos \left (y\right ) \\ y \left (1\right ) &= 0 \\ \end{align*}

[_separable]

3.845

8303

\begin{align*} y^{\prime }&=\sin \left (x \right ) \cos \left (y\right ) \\ y \left (3\right ) &= 3 \\ \end{align*}

[_separable]

7.734

8304

\begin{align*} y^{\prime }&=\sin \left (x \right ) \cos \left (y\right ) \\ y \left (0\right ) &= -{\frac {5}{2}} \\ \end{align*}

[_separable]

5.790

8309

\begin{align*} y y^{\prime }&=-x \\ y \left (1\right ) &= 1 \\ \end{align*}

[_separable]

9.392

8310

\begin{align*} y y^{\prime }&=-x \\ y \left (0\right ) &= 4 \\ \end{align*}

[_separable]

29.060

8315

\begin{align*} y^{\prime }&=x \,{\mathrm e}^{y} \\ y \left (0\right ) &= -2 \\ \end{align*}

[_separable]

3.951

8316

\begin{align*} y^{\prime }&=x \,{\mathrm e}^{y} \\ y \left (1\right ) &= {\frac {5}{2}} \\ \end{align*}

[_separable]

4.189

8342

\begin{align*} x y^{\prime }&=4 y \\ \end{align*}

[_separable]

5.218

8343

\begin{align*} y^{\prime }+2 x y^{2}&=0 \\ \end{align*}

[_separable]

7.404

8344

\begin{align*} y^{\prime }&={\mathrm e}^{3 x +2 y} \\ \end{align*}

[_separable]

3.201

8345

\begin{align*} y \,{\mathrm e}^{x} y^{\prime }&={\mathrm e}^{-y}+{\mathrm e}^{-2 x -y} \\ \end{align*}

[_separable]

4.326

8346

\begin{align*} y \ln \left (x \right ) y^{\prime }&=\frac {\left (y+1\right )^{2}}{x^{2}} \\ \end{align*}

[_separable]

5.953

8347

\begin{align*} y^{\prime }&=\frac {\left (3+2 y\right )^{2}}{\left (5+4 x \right )^{2}} \\ \end{align*}

[_separable]

8.510

8348

\begin{align*} \csc \left (y\right )+\sec \left (x \right )^{2} y^{\prime }&=0 \\ \end{align*}

[_separable]

3.463

8349

\begin{align*} \sin \left (3 x \right )+2 y \cos \left (3 x \right )^{3} y^{\prime }&=0 \\ \end{align*}

[_separable]

7.542

8350

\begin{align*} \left (1+{\mathrm e}^{y}\right )^{2} {\mathrm e}^{-y}+\left (1+{\mathrm e}^{x}\right )^{3} {\mathrm e}^{-x} y^{\prime }&=0 \\ \end{align*}

[_separable]

5.007

8351

\begin{align*} x \sqrt {1+y^{2}}&=y y^{\prime } \sqrt {x^{2}+1} \\ \end{align*}

[_separable]

6.302

8355

\begin{align*} n^{\prime }+n&=n t \,{\mathrm e}^{t +2} \\ \end{align*}

[_separable]

4.948

8356

\begin{align*} y^{\prime }&=\frac {y x +3 x -y-3}{y x -2 x +4 y-8} \\ \end{align*}

[_separable]

8.165

8357

\begin{align*} y^{\prime }&=\frac {y x +2 y-x -2}{y x -3 y+x -3} \\ \end{align*}

[_separable]

4.973

8358

\begin{align*} y^{\prime }&=x \sqrt {1-y^{2}} \\ \end{align*}

[_separable]

0.458

8359

\begin{align*} \left ({\mathrm e}^{x}+{\mathrm e}^{-x}\right ) y^{\prime }&=y^{2} \\ \end{align*}

[_separable]

4.831

8361

\begin{align*} y^{\prime }&=\frac {y^{2}-1}{x^{2}-1} \\ y \left (2\right ) &= 2 \\ \end{align*}

[_separable]

5.589

8362

\begin{align*} x^{2} y^{\prime }&=y-y x \\ y \left (-1\right ) &= -1 \\ \end{align*}

[_separable]

4.886

8364

\begin{align*} \sqrt {1-y^{2}}-y^{\prime } \sqrt {-x^{2}+1}&=0 \\ y \left (0\right ) &= \frac {\sqrt {3}}{2} \\ \end{align*}

[_separable]

14.072

8365

\begin{align*} \left (x^{4}+1\right ) y^{\prime }+x \left (1+4 y^{2}\right )&=0 \\ y \left (1\right ) &= 0 \\ \end{align*}

[_separable]

5.365

8367

\begin{align*} x \sinh \left (y\right ) y^{\prime }&=\cosh \left (y\right ) \\ y \left (1\right ) &= 0 \\ \end{align*}

[_separable]

8.928

8368

\begin{align*} y^{\prime }&=y \,{\mathrm e}^{-x^{2}} \\ y \left (4\right ) &= 1 \\ \end{align*}

[_separable]

4.408

8369

\begin{align*} y^{\prime }&=y^{2} \sin \left (x^{2}\right ) \\ y \left (-2\right ) &= {\frac {1}{3}} \\ \end{align*}

[_separable]

6.533

8370

\begin{align*} y^{\prime }&=\left (1+y^{2}\right ) \sqrt {1+\cos \left (x^{3}\right )} \\ y \left (1\right ) &= 1 \\ \end{align*}

[_separable]

16.156

8371

\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{-2 y} \sin \left (x \right )}{x^{2}+1} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

4.175

8372

\begin{align*} y^{\prime }&=\frac {1+3 x}{2 y} \\ y \left (-2\right ) &= -1 \\ \end{align*}

[_separable]

7.496

8373

\begin{align*} \left (-2+2 y\right ) y^{\prime }&=3 x^{2}+4 x +2 \\ y \left (1\right ) &= -2 \\ \end{align*}

[_separable]

5.096

8374

\begin{align*} {\mathrm e}^{y}-{\mathrm e}^{-x} y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

3.788

8375

\begin{align*} \sin \left (x \right )+y y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

4.238

8379

\begin{align*} x y^{\prime }&=y^{2}-y \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

7.670

8380

\begin{align*} x y^{\prime }&=y^{2}-y \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

14.598

8381

\begin{align*} x y^{\prime }&=y^{2}-y \\ y \left (\frac {1}{2}\right ) &= {\frac {1}{2}} \\ \end{align*}

[_separable]

8.046

8382

\begin{align*} x y^{\prime }&=y^{2}-y \\ y \left (2\right ) &= {\frac {1}{4}} \\ \end{align*}

[_separable]

7.257

8383

\begin{align*} 2 x \sin \left (y\right )^{2}-\left (x^{2}+10\right ) \cos \left (y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

5.159

8397

\begin{align*} y^{\prime }&=\frac {\sin \left (\sqrt {x}\right )}{\sqrt {y}} \\ \end{align*}

[_separable]

5.541

8398

\begin{align*} \left (\sqrt {x}+x \right ) y^{\prime }&=\sqrt {y}+y \\ \end{align*}

[_separable]

7.549

8400

\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{\sqrt {x}}}{y} \\ y \left (1\right ) &= 4 \\ \end{align*}

[_separable]

6.534

8401

\begin{align*} y^{\prime }&=\frac {x \arctan \left (x \right )}{y} \\ y \left (0\right ) &= 3 \\ \end{align*}

[_separable]

4.026

8402

\begin{align*} y^{\prime }&=-\frac {x}{y} \\ y \left (1\right ) &= 0 \\ \end{align*}

[_separable]

10.043

8403

\begin{align*} y^{\prime }&=x \sqrt {y} \\ \end{align*}

[_separable]

14.575

8406

\begin{align*} y^{\prime }&=y+\frac {y}{x \ln \left (x \right )} \\ y \left ({\mathrm e}\right ) &= 1 \\ \end{align*}

[_separable]

6.635

8413

\begin{align*} y^{\prime }&=-\frac {8 x +5}{3 y^{2}+1} \\ y \left (0\right ) &= -1 \\ \end{align*}

[_separable]

0.766

8414

\begin{align*} y^{\prime }&=-\frac {8 x +5}{3 y^{2}+1} \\ y \left (0\right ) &= 2 \\ \end{align*}

[_separable]

1.753

8415

\begin{align*} y^{\prime }&=-\frac {8 x +5}{3 y^{2}+1} \\ y \left (-1\right ) &= 4 \\ \end{align*}

[_separable]

1.365

8416

\begin{align*} y^{\prime }&=-\frac {8 x +5}{3 y^{2}+1} \\ y \left (-1\right ) &= -3 \\ \end{align*}

[_separable]

0.812

8417

\begin{align*} \left (2 y+2\right ) y^{\prime }-4 x^{3}-6 x&=0 \\ y \left (0\right ) &= -3 \\ \end{align*}

[_separable]

5.300

8418

\begin{align*} y^{\prime }&=\frac {x \left (1-x \right )}{y \left (-2+y\right )} \\ y \left (0\right ) &= {\frac {3}{2}} \\ \end{align*}

[_separable]

5.708

8419

\begin{align*} y^{\prime }&=\frac {x \left (1-x \right )}{y \left (-2+y\right )} \\ y \left (0\right ) &= -2 \\ \end{align*}

[_separable]

3.583

8424

\begin{align*} y^{\prime }+3 x^{2} y&=x^{2} \\ \end{align*}

[_separable]

4.049

8429

\begin{align*} x y^{\prime }+2 y&=3 \\ \end{align*}

[_separable]

5.794

8441

\begin{align*} p^{\prime }+2 t p&=p+4 t -2 \\ \end{align*}

[_separable]

4.207

8454

\begin{align*} y^{\prime }-y \sin \left (x \right )&=2 \sin \left (x \right ) \\ y \left (\frac {\pi }{2}\right ) &= 1 \\ \end{align*}

[_separable]

4.596

8461

\begin{align*} y^{\prime }+\left (\left \{\begin {array}{cc} 1 & 0\le x \le 2 \\ 5 & 2<x \end {array}\right .\right ) y&=0 \\ y \left (0\right ) &= 4 \\ \end{align*}

[_separable]

5.112

8467

\begin{align*} y^{\prime }-\sin \left (x^{2}\right ) y&=0 \\ y \left (0\right ) &= 5 \\ \end{align*}

[_separable]

9.741

8475

\begin{align*} 2 x -1+\left (3 y+7\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

12.232

8657

\begin{align*} y^{\prime }&=\frac {x^{2}}{y} \\ \end{align*}

[_separable]

8.756

8658

\begin{align*} y^{\prime }&=\frac {x^{2}}{\left (x^{3}+1\right ) y} \\ \end{align*}

[_separable]

3.638

8659

\begin{align*} y^{\prime }&=y \sin \left (x \right ) \\ \end{align*}

[_separable]

4.266

8660

\begin{align*} x y^{\prime }&=\sqrt {1-y^{2}} \\ \end{align*}

[_separable]

8.917

8661

\begin{align*} y^{\prime }&=\frac {x^{2}}{1+y^{2}} \\ \end{align*}

[_separable]

3.028

8662

\begin{align*} x y y^{\prime }&=\sqrt {1+y^{2}} \\ \end{align*}

[_separable]

12.274

8663

\begin{align*} \left (x^{2}-1\right ) y^{\prime }+2 x y^{2}&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

5.004

8665

\begin{align*} x y^{\prime }+y&=y^{2} \\ y \left (1\right ) &= {\frac {1}{2}} \\ \end{align*}

[_separable]

7.943

8666

\begin{align*} 2 x^{2} y y^{\prime }+y^{2}&=2 \\ \end{align*}

[_separable]

7.037

8667

\begin{align*} y^{\prime }-x y^{2}&=2 y x \\ \end{align*}

[_separable]

6.256

8669

\begin{align*} y^{\prime }&=\frac {3 x^{2}+4 x +2}{-2+2 y} \\ y \left (0\right ) &= -1 \\ \end{align*}

[_separable]

5.652

8670

\begin{align*} {\mathrm e}^{x}-\left (1+{\mathrm e}^{x}\right ) y y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

6.725

8671

\begin{align*} \frac {y}{x -1}+\frac {x y^{\prime }}{y+1}&=0 \\ \end{align*}

[_separable]

9.253

8672

\begin{align*} x +2 x^{3}+\left (2 y^{3}+y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

3.621

8673

\begin{align*} \frac {1}{\sqrt {x}}+\frac {y^{\prime }}{\sqrt {y}}&=0 \\ \end{align*}

[_separable]

29.169

8674

\begin{align*} \frac {1}{\sqrt {-x^{2}+1}}+\frac {y^{\prime }}{\sqrt {1-y^{2}}}&=0 \\ \end{align*}

[_separable]

31.009

8675

\begin{align*} 2 x \sqrt {1-y^{2}}+y y^{\prime }&=0 \\ \end{align*}

[_separable]

5.548

8676

\begin{align*} y^{\prime }&=\left (-1+y\right ) \left (x +1\right ) \\ \end{align*}

[_separable]

4.543

8677

\begin{align*} y^{\prime }&={\mathrm e}^{x -y} \\ \end{align*}

[_separable]

3.388

8678

\begin{align*} y^{\prime }&=\frac {\sqrt {y}}{\sqrt {x}} \\ \end{align*}

[_separable]

25.947

8679

\begin{align*} y^{\prime }&=\frac {\sqrt {y}}{x} \\ \end{align*}

[_separable]

8.479

8680

\begin{align*} z^{\prime }&=10^{x +z} \\ \end{align*}

[_separable]

4.438

8690

\begin{align*} y^{2}+x y^{2}+\left (x^{2}-x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

7.779

8691

\begin{align*} \left (1+y^{2}\right ) \left ({\mathrm e}^{2 x}-{\mathrm e}^{y} y^{\prime }\right )-\left (y+1\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

5.412

8693

\begin{align*} y-2 y x +x^{2} y^{\prime }&=0 \\ \end{align*}

[_separable]

5.259

8751

\begin{align*} 3+2 x +\left (-2+2 y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

13.214

8777

\begin{align*} y^{\prime }&=x^{2} \left (1+y^{2}\right ) \\ \end{align*}

[_separable]

5.161

8778

\begin{align*} y^{\prime }&=\frac {x^{2}}{1-y^{2}} \\ \end{align*}

[_separable]

3.411

8779

\begin{align*} y^{\prime }&=\frac {3 x^{2}+4 x +2}{-2+2 y} \\ y \left (0\right ) &= -1 \\ \end{align*}

[_separable]

6.419

8787

\begin{align*} y^{\prime }&=-\frac {2}{t}+\frac {y}{t}+\frac {y^{2}}{t} \\ \end{align*}

[_separable]

14.332

8858

\begin{align*} y^{\prime }+\cos \left (x \right ) y&=0 \\ \end{align*}

[_separable]

5.055

8876

\begin{align*} y^{\prime }+2 y x&=x \\ \end{align*}

[_separable]

4.456

8878

\begin{align*} y^{\prime }+y \,{\mathrm e}^{x}&=3 \,{\mathrm e}^{x} \\ \end{align*}

[_separable]

4.644

9006

\begin{align*} y^{\prime }&=x^{2} y \\ \end{align*}

[_separable]

5.063

9007

\begin{align*} y y^{\prime }&=x \\ \end{align*}

[_separable]

13.756

9008

\begin{align*} y^{\prime }&=\frac {x^{2}+x}{y-y^{2}} \\ \end{align*}

[_separable]

3.704

9009

\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{x -y}}{1+{\mathrm e}^{x}} \\ \end{align*}

[_separable]

2.989

9010

\begin{align*} y^{\prime }&=x^{2} y^{2}-4 x^{2} \\ \end{align*}

[_separable]

8.346

9049

\begin{align*} x y^{\prime }&=2 y \\ \end{align*}

[_separable]

7.090

9050

\begin{align*} y y^{\prime }&={\mathrm e}^{2 x} \\ \end{align*}

[_separable]

4.972

9082

\begin{align*} x^{5} y^{\prime }+y^{5}&=0 \\ \end{align*}

[_separable]

14.411

9083

\begin{align*} y^{\prime }&=4 y x \\ \end{align*}

[_separable]

5.006

9084

\begin{align*} y^{\prime }+y \tan \left (x \right )&=0 \\ \end{align*}

[_separable]

4.736

9085

\begin{align*} 1+y^{2}+\left (x^{2}+1\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

5.616

9086

\begin{align*} \ln \left (y\right ) y-x y^{\prime }&=0 \\ \end{align*}

[_separable]

8.771

9087

\begin{align*} x y^{\prime }&=\left (-4 x^{2}+1\right ) \tan \left (y\right ) \\ \end{align*}

[_separable]

3.961

9088

\begin{align*} y^{\prime } \sin \left (y\right )&=x^{2} \\ \end{align*}

[_separable]

3.373

9089

\begin{align*} y^{\prime }-y \tan \left (x \right )&=0 \\ \end{align*}

[_separable]

4.868

9090

\begin{align*} x y y^{\prime }&=-1+y \\ \end{align*}

[_separable]

9.548

9091

\begin{align*} x y^{2}-x^{2} y^{\prime }&=0 \\ \end{align*}

[_separable]

4.806

9092

\begin{align*} y y^{\prime }&=x +1 \\ y \left (1\right ) &= 3 \\ \end{align*}

[_separable]

6.135

9093

\begin{align*} x^{2} y^{\prime }&=y \\ y \left (1\right ) &= 0 \\ \end{align*}

[_separable]

13.283

9094

\begin{align*} \frac {y^{\prime }}{x^{2}+1}&=\frac {x}{y} \\ y \left (1\right ) &= 3 \\ \end{align*}

[_separable]

3.820

9095

\begin{align*} y^{2} y^{\prime }&=x +2 \\ y \left (0\right ) &= 4 \\ \end{align*}

[_separable]

7.277

9096

\begin{align*} y^{\prime }&=x^{2} y^{2} \\ y \left (-1\right ) &= 2 \\ \end{align*}

[_separable]

12.135

9097

\begin{align*} \left (y+1\right ) y^{\prime }&=-x^{2}+1 \\ y \left (-1\right ) &= -2 \\ \end{align*}

[_separable]

6.381

9119

\begin{align*} y^{\prime }+y x&=x y^{4} \\ \end{align*}

[_separable]

6.129

9123

\begin{align*} x y^{\prime }&=2 x^{2} y+y \ln \left (x \right ) \\ \end{align*}

[_separable]

7.890

9133

\begin{align*} 1+y+\left (1-x \right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

4.420

9139

\begin{align*} x \ln \left (y\right )+y x +\left (y \ln \left (x \right )+y x \right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

6.898

9194

\begin{align*} x^{2} y^{\prime }&=y \\ \end{align*}

[_separable]

5.766

9195

\begin{align*} \sec \left (x \right ) y^{\prime }&=\sec \left (y\right ) \\ \end{align*}

[_separable]

3.674

9198

\begin{align*} x^{2} y^{\prime }+2 y x&=0 \\ \end{align*}

[_separable]

6.743

9199

\begin{align*} -\sin \left (x \right ) \sin \left (y\right )+\cos \left (x \right ) \cos \left (y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

4.648

9202

\begin{align*} y^{2} y^{\prime }&=x \\ y \left (-1\right ) &= 3 \\ \end{align*}

[_separable]

8.951

9203

\begin{align*} \csc \left (x \right ) y^{\prime }&=\csc \left (y\right ) \\ y \left (\frac {\pi }{2}\right ) &= 1 \\ \end{align*}

[_separable]

5.165

9206

\begin{align*} 2 x \cos \left (y\right )-x^{2} \sin \left (y\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}

[_separable]

22.325

9207

\begin{align*} \frac {1}{y}-\frac {x y^{\prime }}{y^{2}}&=0 \\ \end{align*}

[_separable]

4.963

9348

\begin{align*} y^{\prime }&=2 y x \\ \end{align*}

[_separable]

5.616

9360

\begin{align*} x y^{\prime }&=y \\ \end{align*}

[_separable]

4.616

9362

\begin{align*} x^{2} y^{\prime }&=y \\ \end{align*}

[_separable]

5.513

9971

\begin{align*} y^{\prime }&=\frac {y}{x \ln \left (x \right )} \\ \end{align*}

[_separable]

5.665

9972

\begin{align*} \left (x^{2}+1\right ) y^{\prime }+y^{2}&=-1 \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

6.827

9987

\begin{align*} y^{\prime }&=\frac {\cos \left (y\right ) \sec \left (x \right )}{x} \\ \end{align*}

[_separable]

8.570

9988

\begin{align*} y^{\prime }&=x \left (\cos \left (y\right )+y\right ) \\ \end{align*}

[_separable]

3.469

9989

\begin{align*} y^{\prime }&=\frac {\sec \left (x \right ) \left (\sin \left (y\right )+y\right )}{x} \\ \end{align*}

[_separable]

5.766

9990

\begin{align*} y^{\prime }&=\left (5+\frac {\sec \left (x \right )}{x}\right ) \left (\sin \left (y\right )+y\right ) \\ \end{align*}

[_separable]

17.450

9998

\begin{align*} y^{\prime }&=\frac {2 y}{x} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

8.431

9999

\begin{align*} y^{\prime }&=\frac {2 y}{x} \\ \end{align*}

[_separable]

6.559

10000

\begin{align*} y^{\prime }&=\frac {\ln \left (1+y^{2}\right )}{\ln \left (x^{2}+1\right )} \\ \end{align*}

[_separable]

5.849

10066

\begin{align*} 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 )}} \\ \end{align*}

[_separable]

122.758

10256

\begin{align*} x^{2} y^{\prime }+{\mathrm e}^{-y}&=0 \\ \end{align*}

[_separable]

3.288

10264

\begin{align*} y^{\prime }&=a x y \\ \end{align*}

[_separable]

2.480

10324

\begin{align*} y^{\prime }&={\mathrm e}^{x +y} \\ \end{align*}

[_separable]

2.362

11311

\begin{align*} y^{\prime }-\left (a +\cos \left (\ln \left (x \right )\right )+\sin \left (\ln \left (x \right )\right )\right ) y&=0 \\ \end{align*}

[_separable]

2.695

11331

\begin{align*} y^{\prime }-x y^{2}-3 y x&=0 \\ \end{align*}

[_separable]

3.406

11333

\begin{align*} y^{\prime }-a \,x^{n} \left (1+y^{2}\right )&=0 \\ \end{align*}

[_separable]

3.225

11337

\begin{align*} y^{\prime }+f \left (x \right ) \left (y^{2}+2 a y+b \right )&=0 \\ \end{align*}

[_separable]

4.733

11361

\begin{align*} y^{\prime }-\frac {\sqrt {y^{2}-1}}{\sqrt {x^{2}-1}}&=0 \\ \end{align*}

[_separable]

21.086

11362

\begin{align*} y^{\prime }-\frac {\sqrt {x^{2}-1}}{\sqrt {y^{2}-1}}&=0 \\ \end{align*}

[_separable]

4.601

11364

\begin{align*} y^{\prime }-\frac {1+y^{2}}{{| y+\sqrt {y+1}|} \left (x +1\right )^{{3}/{2}}}&=0 \\ \end{align*}

[_separable]

13.746

11367

\begin{align*} y^{\prime }-\frac {\sqrt {{| y \left (-1+y\right ) \left (a y-1\right )|}}}{\sqrt {{| x \left (x -1\right ) \left (a x -1\right )|}}}&=0 \\ \end{align*}

[_separable]

26.593

11368

\begin{align*} y^{\prime }-\frac {\sqrt {1-y^{4}}}{\sqrt {-x^{4}+1}}&=0 \\ \end{align*}

[_separable]

5.575

11373

\begin{align*} y^{\prime }-\operatorname {R1} \left (x , \sqrt {a_{4} x^{4}+a_{3} x^{3}+a_{2} x^{2}+a_{1} x +a_{0}}\right ) \operatorname {R2} \left (y, \sqrt {b_{4} y^{4}+b_{3} y^{3}+b_{2} y^{2}+b_{1} y+b_{0}}\right )&=0 \\ \end{align*}

[_separable]

4.359

11376

\begin{align*} y^{\prime }-{\mathrm e}^{x -y}+{\mathrm e}^{x}&=0 \\ \end{align*}

[_separable]

3.374

11396

\begin{align*} x y^{\prime }-y^{2}+1&=0 \\ \end{align*}

[_separable]

4.477

11417

\begin{align*} x y^{\prime }-\ln \left (y\right ) y&=0 \\ \end{align*}

[_separable]

4.042

11430

\begin{align*} \left (2 x +1\right ) y^{\prime }-4 \,{\mathrm e}^{-y}+2&=0 \\ \end{align*}

[_separable]

4.273

11434

\begin{align*} x^{2} y^{\prime }-\left (x -1\right ) y&=0 \\ \end{align*}

[_separable]

3.441

11457

\begin{align*} \left (x^{2}-1\right ) y^{\prime }+a x y^{2}+y x&=0 \\ \end{align*}

[_separable]

6.523

11458

\begin{align*} \left (x^{2}-1\right ) y^{\prime }-2 x y \ln \left (y\right )&=0 \\ \end{align*}

[_separable]

5.537

11473

\begin{align*} x \left (x^{2}+1\right ) y^{\prime }+x^{2} y&=0 \\ \end{align*}

[_separable]

3.256

11482

\begin{align*} \left (2 x^{4}-x \right ) y^{\prime }-2 \left (x^{3}-1\right ) y&=0 \\ \end{align*}

[_separable]

4.330

11489

\begin{align*} \sqrt {x^{2}-1}\, y^{\prime }-\sqrt {y^{2}-1}&=0 \\ \end{align*}

[_separable]

11.553

11490

\begin{align*} y^{\prime } \sqrt {-x^{2}+1}-y \sqrt {y^{2}-1}&=0 \\ \end{align*}

[_separable]

21.487

11498

\begin{align*} y^{\prime } \sin \left (2 x \right )+\sin \left (2 y\right )&=0 \\ \end{align*}

[_separable]

23.190

11508

\begin{align*} y y^{\prime }+x y^{2}-4 x&=0 \\ \end{align*}

[_separable]

4.544

11539

\begin{align*} 2 x y y^{\prime }+2 y^{2}+1&=0 \\ \end{align*}

[_separable]

7.844

11552

\begin{align*} x^{2} \left (-1+y\right ) y^{\prime }+\left (x -1\right ) y&=0 \\ \end{align*}

[_separable]

7.414

11603

\begin{align*} \left (2 y^{3}+y\right ) y^{\prime }-2 x^{3}-x&=0 \\ \end{align*}

[_separable]

3.169

11628

\begin{align*} \sqrt {y^{2}-1}\, y^{\prime }-\sqrt {x^{2}-1}&=0 \\ \end{align*}

[_separable]

5.924

11640

\begin{align*} y^{\prime } \left (1+\sin \left (x \right )\right ) \sin \left (y\right )+\cos \left (x \right ) \left (\cos \left (y\right )-1\right )&=0 \\ \end{align*}

[_separable]

6.976

11646

\begin{align*} x \cos \left (y\right ) y^{\prime }+\sin \left (y\right )&=0 \\ \end{align*}

[_separable]

12.260

11651

\begin{align*} \sin \left (x \right ) \cos \left (y\right )+\cos \left (x \right ) \sin \left (y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

4.083

11652

\begin{align*} 3 \sin \left (x \right ) \sin \left (y\right ) y^{\prime }+5 \cos \left (x \right )^{4} y&=0 \\ \end{align*}

[_separable]

7.821

11837

\begin{align*} {y^{\prime }}^{n}-f \left (x \right )^{n} \left (y-a \right )^{n +1} \left (y-b \right )^{n -1}&=0 \\ \end{align*}

[_separable]

9.915

11851

\begin{align*} y \ln \left (y^{\prime }\right )+y^{\prime }-\ln \left (y\right ) y-y x&=0 \\ \end{align*}

[_separable]

6.617

13203

\begin{align*} y^{\prime }&=f \left (x \right ) g \left (y\right ) \\ \end{align*}

[_separable]

1.767

13971

\begin{align*} \sec \left (x \right ) \cos \left (y\right )^{2}-\cos \left (x \right ) \sin \left (y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

12.557

13972

\begin{align*} \left (x +1\right ) y^{2}-x^{3} y^{\prime }&=0 \\ \end{align*}

[_separable]

5.024

13973

\begin{align*} \left (x^{2}+1\right ) \left (1+y^{2}\right ) y^{\prime }+2 x y \left (1-y^{2}\right )&=0 \\ \end{align*}

[_separable]

11.835

13974

\begin{align*} \sin \left (x \right ) \cos \left (y\right )^{2}+\cos \left (x \right )^{2} y^{\prime }&=0 \\ \end{align*}

[_separable]

6.050

13979

\begin{align*} y^{3}+x^{3} y^{\prime }&=0 \\ \end{align*}

[_separable]

20.206

13993

\begin{align*} y y^{\prime }+x y^{2}&=x \\ \end{align*}

[_separable]

6.770

13994

\begin{align*} y^{\prime } \sin \left (y\right )+\sin \left (x \right ) \cos \left (y\right )&=\sin \left (x \right ) \\ \end{align*}

[_separable]

28.431

14015

\begin{align*} x \sqrt {1-y^{2}}+y \sqrt {-x^{2}+1}\, y^{\prime }&=0 \\ \end{align*}

[_separable]

9.548

14016

\begin{align*} y^{\prime } \sqrt {-x^{2}+1}+\sqrt {1-y^{2}}&=0 \\ \end{align*}

[_separable]

36.295

14020

\begin{align*} x \left (1-y\right ) y^{\prime }+\left (1-x \right ) y&=0 \\ \end{align*}

[_separable]

7.241

14027

\begin{align*} \left (-x^{2}+1\right ) y^{\prime }-y x&=a x y^{2} \\ \end{align*}

[_separable]

13.158

14033

\begin{align*} \left (1-x \right ) y-x \left (y+1\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

7.247

14034

\begin{align*} 3 x^{2} y+\left (x^{3}+x^{3} y^{2}\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

10.939

14192

\begin{align*} x^{\prime }&=\frac {2 x}{t} \\ \end{align*}

[_separable]

8.268

14193

\begin{align*} x^{\prime }&=-\frac {t}{x} \\ \end{align*}

[_separable]

14.992

14198

\begin{align*} 2 x^{\prime } t&=x \\ \end{align*}

[_separable]

6.815

14219

\begin{align*} x^{\prime }&=\frac {2 x}{t +1} \\ \end{align*}

[_separable]

6.390

14220

\begin{align*} \theta ^{\prime }&=t \sqrt {t^{2}+1}\, \sec \left (\theta \right ) \\ \end{align*}

[_separable]

4.493

14221

\begin{align*} \left (2 u+1\right ) u^{\prime }-t -1&=0 \\ \end{align*}

[_separable]

15.597

14222

\begin{align*} R^{\prime }&=\left (t +1\right ) \left (1+R^{2}\right ) \\ \end{align*}

[_separable]

7.027

14224

\begin{align*} \left (t +1\right ) x^{\prime }+x^{2}&=0 \\ \end{align*}

[_separable]

4.839

14227

\begin{align*} x^{\prime }&=2 t x^{2} \\ x \left (0\right ) &= 1 \\ \end{align*}

[_separable]

13.350

14228

\begin{align*} x^{\prime }&=t^{2} {\mathrm e}^{-x} \\ x \left (0\right ) &= \ln \left (2\right ) \\ \end{align*}

[_separable]

8.334

14230

\begin{align*} x^{\prime }&={\mathrm e}^{t +x} \\ x \left (0\right ) &= 0 \\ \end{align*}

[_separable]

7.116

14231

\begin{align*} T^{\prime }&=2 a t \left (T^{2}-a^{2}\right ) \\ T \left (0\right ) &= 0 \\ \end{align*}

[_separable]

9.295

14232

\begin{align*} y^{\prime }&=t^{2} \tan \left (y\right ) \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

13.732

14233

\begin{align*} x^{\prime }&=\frac {\left (4+2 t \right ) x}{\ln \left (x\right )} \\ x \left (0\right ) &= {\mathrm e} \\ \end{align*}

[_separable]

6.681

14234

\begin{align*} y^{\prime }&=\frac {2 t y^{2}}{t^{2}+1} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

7.769

14235

\begin{align*} x^{\prime }&=\frac {t^{2}}{1-x^{2}} \\ x \left (1\right ) &= 1 \\ \end{align*}

[_separable]

10.259

14236

\begin{align*} x^{\prime }&=6 t \left (x-1\right )^{{2}/{3}} \\ \end{align*}

[_separable]

11.272

14241

\begin{align*} y^{\prime }&=-y^{2} {\mathrm e}^{-t^{2}} \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}

[_separable]

6.388

14243

\begin{align*} \cos \left (t \right ) x^{\prime }-2 x \sin \left (x\right )&=0 \\ \end{align*}

[_separable]

5.976

14253

\begin{align*} \left (t^{2}+1\right ) x^{\prime }&=-3 x t +6 t \\ \end{align*}

[_separable]

6.000

14255

\begin{align*} x^{\prime }&=\left (a +\frac {b}{t}\right ) x \\ x \left (1\right ) &= 1 \\ \end{align*}

[_separable]

5.264

14258

\begin{align*} \cos \left (\theta \right ) v^{\prime }+v&=3 \\ \end{align*}

[_separable]

7.405

14261

\begin{align*} x^{\prime }&=2 x t \\ \end{align*}

[_separable]

5.854

14266

\begin{align*} x^{\prime }+p \left (t \right ) x&=0 \\ \end{align*}

[_separable]

5.874

14269

\begin{align*} x^{\prime }&=-\frac {x}{t}+\frac {1}{t x^{2}} \\ \end{align*}

[_separable]

11.992

14277

\begin{align*} x^{2}-t^{2} x^{\prime }&=0 \\ \end{align*}

[_separable]

11.280

14278

\begin{align*} t \cot \left (x\right ) x^{\prime }&=-2 \\ \end{align*}

[_separable]

10.963

14420

\begin{align*} y^{\prime }+4 y x&=8 x \\ \end{align*}

[_separable]

5.292

14436

\begin{align*} y^{\prime }&=x^{2} \sin \left (y\right ) \\ y \left (1\right ) &= -2 \\ \end{align*}

[_separable]

11.070

14437

\begin{align*} y^{\prime }&=\frac {y^{2}}{x -2} \\ y \left (1\right ) &= 0 \\ \end{align*}

[_separable]

13.105

14446

\begin{align*} \frac {\left (2 s-1\right ) s^{\prime }}{t}+\frac {s-s^{2}}{t^{2}}&=0 \\ \end{align*}

[_separable]

51.015

14457

\begin{align*} \left (x^{2}+1\right ) y^{\prime }+4 y x&=0 \\ \end{align*}

[_separable]

5.103

14458

\begin{align*} y x +2 x +y+2+\left (x^{2}+2 x \right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

5.437

14459

\begin{align*} 2 r \left (s^{2}+1\right )+\left (r^{4}+1\right ) s^{\prime }&=0 \\ \end{align*}

[_separable]

7.433

14460

\begin{align*} \csc \left (y\right )+\sec \left (x \right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

4.488

14461

\begin{align*} \tan \left (\theta \right )+2 r \theta ^{\prime }&=0 \\ \end{align*}

[_separable]

11.650

14462

\begin{align*} \left ({\mathrm e}^{v}+1\right ) \cos \left (u \right )+{\mathrm e}^{v} \left (1+\sin \left (u \right )\right ) v^{\prime }&=0 \\ \end{align*}

[_separable]

4.823

14463

\begin{align*} \left (x +4\right ) \left (1+y^{2}\right )+y \left (x^{2}+3 x +2\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

8.565

14471

\begin{align*} y+2+y \left (x +4\right ) y^{\prime }&=0 \\ y \left (-3\right ) &= -1 \\ \end{align*}

[_separable]

11.194

14472

\begin{align*} 8 \cos \left (y\right )^{2}+\csc \left (x \right )^{2} y^{\prime }&=0 \\ y \left (\frac {\pi }{12}\right ) &= \frac {\pi }{4} \\ \end{align*}

[_separable]

5.914

14473

\begin{align*} \left (3 x +8\right ) \left (4+y^{2}\right )-4 y \left (x^{2}+5 x +6\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 2 \\ \end{align*}

[_separable]

8.581

14484

\begin{align*} y^{\prime }+4 y x&=8 x \\ \end{align*}

[_separable]

5.124

14485

\begin{align*} x^{\prime }+\frac {x}{t^{2}}&=\frac {1}{t^{2}} \\ \end{align*}

[_separable]

5.630

14486

\begin{align*} \left (u^{2}+1\right ) v^{\prime }+4 u v&=3 u \\ \end{align*}

[_separable]

6.472

14495

\begin{align*} y^{\prime }-\frac {y}{x}&=-\frac {y^{2}}{x} \\ \end{align*}

[_separable]

8.415

14497

\begin{align*} y^{\prime }+\left (4 y-\frac {8}{y^{3}}\right ) x&=0 \\ \end{align*}

[_separable]

6.237

14498

\begin{align*} x^{\prime }+\frac {\left (t +1\right ) x}{2 t}&=\frac {t +1}{x t} \\ \end{align*}

[_separable]

8.355

14500

\begin{align*} y^{\prime }+3 x^{2} y&=x^{2} \\ y \left (0\right ) &= 2 \\ \end{align*}

[_separable]

5.638

14502

\begin{align*} 2 x \left (y+1\right )-\left (x^{2}+1\right ) y^{\prime }&=0 \\ y \left (1\right ) &= -5 \\ \end{align*}

[_separable]

5.355

14514

\begin{align*} \left (y+1\right ) y^{\prime }+x \left (y^{2}+2 y\right )&=x \\ \end{align*}

[_separable]

12.825

14518

\begin{align*} 6 x^{2} y-\left (x^{3}+1\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

6.363

14520

\begin{align*} y-1+x \left (x +1\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

5.804

14524

\begin{align*} 8 x^{3} y-12 x^{3}+\left (x^{4}+1\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

6.787

14529

\begin{align*} y x +x^{2} y^{\prime }&=x y^{3} \\ \end{align*}

[_separable]

31.299

14530

\begin{align*} \left (x^{3}+1\right ) y^{\prime }+6 x^{2} y&=6 x^{2} \\ \end{align*}

[_separable]

6.537

14533

\begin{align*} 8+2 y^{2}+\left (-x^{2}+1\right ) y y^{\prime }&=0 \\ y \left (3\right ) &= 0 \\ \end{align*}

[_separable]

10.054

14536

\begin{align*} 4 x y y^{\prime }&=1+y^{2} \\ y \left (2\right ) &= 1 \\ \end{align*}

[_separable]

13.404

14538

\begin{align*} y^{\prime }&=\frac {x y}{x^{2}+1} \\ y \left (\sqrt {15}\right ) &= 2 \\ \end{align*}

[_separable]

5.770

14886

\begin{align*} x^{\prime }&=t^{3} \left (1-x\right ) \\ x \left (0\right ) &= 3 \\ \end{align*}

[_separable]

6.209

14887

\begin{align*} y^{\prime }&=\left (1+y^{2}\right ) \tan \left (x \right ) \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

12.720

14888

\begin{align*} x^{\prime }&=x t^{2} \\ \end{align*}

[_separable]

7.314

14890

\begin{align*} y^{\prime }&=y^{2} {\mathrm e}^{-t^{2}} \\ \end{align*}

[_separable]

7.172

14892

\begin{align*} x y^{\prime }&=k y \\ \end{align*}

[_separable]

8.968

14893

\begin{align*} i^{\prime }&=p \left (t \right ) i \\ \end{align*}

[_separable]

7.189

14899

\begin{align*} x^{\prime }+x t&=4 t \\ x \left (0\right ) &= 2 \\ \end{align*}

[_separable]

6.193

14912

\begin{align*} V^{\prime }\left (x \right )+2 y y^{\prime }&=0 \\ \end{align*}

[_separable]

2.759

14913

\begin{align*} \left (\frac {1}{y}-a \right ) y^{\prime }+\frac {2}{x}-b&=0 \\ \end{align*}

[_separable]

11.964

15015

\begin{align*} \tan \left (y\right )-\cot \left (x \right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

5.151

15022

\begin{align*} y^{\prime }&={\mathrm e}^{x -y} \\ \end{align*}

[_separable]

5.672

15029

\begin{align*} y&=x y^{\prime }+\frac {1}{y} \\ \end{align*}

[_separable]

39.815

15115

\begin{align*} y^{\prime }&=y \,{\mathrm e}^{x +y} \left (x^{2}+1\right ) \\ \end{align*}

[_separable]

4.185

15116

\begin{align*} x^{2} y^{\prime }&=1+y^{2} \\ \end{align*}

[_separable]

6.618

15118

\begin{align*} x \left ({\mathrm e}^{y}+4\right )&={\mathrm e}^{x +y} y^{\prime } \\ \end{align*}

[_separable]

9.404

15122

\begin{align*} y^{\prime }&=x \,{\mathrm e}^{y^{2}-x} \\ \end{align*}

[_separable]

4.387

15124

\begin{align*} x \left (y+1\right )^{2}&=\left (x^{2}+1\right ) y \,{\mathrm e}^{y} y^{\prime } \\ \end{align*}

[_separable]

7.261

15135

\begin{align*} 5 y^{\prime }-y x&=0 \\ \end{align*}

[_separable]

6.583

15335

\begin{align*} -x y^{\prime }+y&=0 \\ \end{align*}

[_separable]

6.102

15336

\begin{align*} \left (1+u \right ) v+\left (1-v\right ) u v^{\prime }&=0 \\ \end{align*}

[_separable]

10.058

15337

\begin{align*} 1+y-\left (1-x \right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

7.510

15338

\begin{align*} \left (t^{2}+x t^{2}\right ) x^{\prime }+x^{2}+t x^{2}&=0 \\ \end{align*}

[_separable]

15.386

15339

\begin{align*} y-a +x^{2} y^{\prime }&=0 \\ \end{align*}

[_separable]

6.507

15340

\begin{align*} z-\left (-a^{2}+t^{2}\right ) z^{\prime }&=0 \\ \end{align*}

[_separable]

9.735

15341

\begin{align*} y^{\prime }&=\frac {1+y^{2}}{x^{2}+1} \\ \end{align*}

[_separable]

7.939

15342

\begin{align*} 1+s^{2}-\sqrt {t}\, s^{\prime }&=0 \\ \end{align*}

[_separable]

9.344

15343

\begin{align*} r^{\prime }+r \tan \left (t \right )&=0 \\ \end{align*}

[_separable]

6.925

15344

\begin{align*} \left (x^{2}+1\right ) y^{\prime }-\sqrt {1-y^{2}}&=0 \\ \end{align*}

[_separable]

11.155

15345

\begin{align*} y^{\prime } \sqrt {-x^{2}+1}-\sqrt {1-y^{2}}&=0 \\ \end{align*}

[_separable]

23.822

15346

\begin{align*} 3 \,{\mathrm e}^{x} \tan \left (y\right )+\left (1-{\mathrm e}^{x}\right ) \sec \left (y\right )^{2} y^{\prime }&=0 \\ \end{align*}

[_separable]

7.607

15347

\begin{align*} x -x y^{2}+\left (y-x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

9.107

15374

\begin{align*} \left (-x^{2}+1\right ) y^{\prime }-y x +a x y^{2}&=0 \\ \end{align*}

[_separable]

20.723

15386

\begin{align*} \frac {x^{2} y^{\prime }}{\left (x -y\right )^{2}}-\frac {y^{2}}{\left (x -y\right )^{2}}&=0 \\ \end{align*}

[_separable]

13.929

15394

\begin{align*} y&=x y^{\prime }+y^{\prime } \\ \end{align*}

[_separable]

6.948

15449

\begin{align*} \frac {x^{2} y^{\prime }}{\left (x -y\right )^{2}}-\frac {y^{2}}{\left (x -y\right )^{2}}&=0 \\ \end{align*}

[_separable]

14.068

15457

\begin{align*} 3 \,{\mathrm e}^{x} \tan \left (y\right )+\left (1-{\mathrm e}^{x}\right ) \sec \left (y\right )^{2} y^{\prime }&=0 \\ \end{align*}

[_separable]

6.950

15484

\begin{align*} x y^{\prime }-y&=0 \\ \end{align*}

[_separable]

5.606

15491

\begin{align*} x^{2} y^{\prime }+2 y x&=0 \\ \end{align*}

[_separable]

10.433

15499

\begin{align*} 2 x y^{\prime }-y&=0 \\ \end{align*}

[_separable]

8.534

15506

\begin{align*} y^{\prime }-2 y x&=0 \\ \end{align*}

[_separable]

7.058

15509

\begin{align*} y^{\prime }&=x \sqrt {y} \\ \end{align*}

[_separable]

28.382

15512

\begin{align*} x \ln \left (x \right ) y^{\prime }-\left (1+\ln \left (x \right )\right ) y&=0 \\ \end{align*}

[_separable]

9.199

15530

\begin{align*} y^{\prime }&=y x \\ \end{align*}

[_separable]

7.401

15531

\begin{align*} y^{\prime }&=-y x \\ \end{align*}

[_separable]

6.827

15535

\begin{align*} y^{\prime }&=y x \\ \end{align*}

[_separable]

7.168

15536

\begin{align*} y^{\prime }&=\frac {x}{y} \\ \end{align*}

[_separable]

21.445

15537

\begin{align*} y^{\prime }&=\frac {y}{x} \\ \end{align*}

[_separable]

5.685

15542

\begin{align*} y^{\prime }&={\mathrm e}^{x -y} \\ \end{align*}

[_separable]

5.851

15548

\begin{align*} y^{\prime }&=\frac {1}{y x} \\ \end{align*}

[_separable]

8.984

15552

\begin{align*} y^{\prime }&=\frac {x}{y^{2}} \\ \end{align*}

[_separable]

9.466

15553

\begin{align*} y^{\prime }&=\frac {\sqrt {y}}{x} \\ \end{align*}

[_separable]

14.672

15554

\begin{align*} y^{\prime }&=\frac {x y}{1-y} \\ \end{align*}

[_separable]

8.243

15568

\begin{align*} y^{\prime }&=-x \sqrt {1-y^{2}} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

37.537

15583

\begin{align*} y^{\prime }&=x \,{\mathrm e}^{y-x^{2}} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

4.401

15584

\begin{align*} y^{\prime }&=\frac {y}{x} \\ y \left (-1\right ) &= 2 \\ \end{align*}

[_separable]

6.307

15585

\begin{align*} y^{\prime }&=\frac {2 x}{y} \\ y \left (0\right ) &= 2 \\ \end{align*}

[_separable]

85.439

15587

\begin{align*} y^{\prime }&=y x +x \\ y \left (1\right ) &= 2 \\ \end{align*}

[_separable]

5.993

15588

\begin{align*} x \,{\mathrm e}^{y}+y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

7.596

15589

\begin{align*} y-x^{2} y^{\prime }&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}

[_separable]

7.286

15591

\begin{align*} 2 x y y^{\prime }+y^{2}&=-1 \\ \end{align*}

[_separable]

10.841

15597

\begin{align*} y^{\prime }&=\frac {y}{x} \\ y \left (-1\right ) &= 2 \\ \end{align*}

[_separable]

6.261

15602

\begin{align*} x -y y^{\prime }&=0 \\ \end{align*}

[_separable]

22.604

15603

\begin{align*} -x y^{\prime }+y&=0 \\ \end{align*}

[_separable]

6.018

15605

\begin{align*} x y \left (1-y\right )-2 y^{\prime }&=0 \\ \end{align*}

[_separable]

14.324

15606

\begin{align*} x \left (1-y^{3}\right )-3 y^{2} y^{\prime }&=0 \\ \end{align*}

[_separable]

6.789

15607

\begin{align*} \left (2 x -1\right ) y+x \left (x +1\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

6.840

15610

\begin{align*} y^{\prime }&=\frac {y}{x} \\ y \left (-1\right ) &= 1 \\ \end{align*}

[_separable]

6.630

15611

\begin{align*} y^{\prime }&=\frac {y}{x} \\ y \left (-1\right ) &= -1 \\ \end{align*}

[_separable]

6.243

15621

\begin{align*} y^{\prime }&=-\frac {3 x^{2}}{2 y} \\ y \left (-1\right ) &= 1 \\ \end{align*}

[_separable]

49.432

15622

\begin{align*} y^{\prime }&=-\frac {3 x^{2}}{2 y} \\ y \left (-1\right ) &= {\frac {1}{2}} \\ \end{align*}

[_separable]

16.570

15623

\begin{align*} y^{\prime }&=-\frac {3 x^{2}}{2 y} \\ y \left (-1\right ) &= 0 \\ \end{align*}

[_separable]

12.170

15624

\begin{align*} y^{\prime }&=-\frac {3 x^{2}}{2 y} \\ y \left (-1\right ) &= -1 \\ \end{align*}

[_separable]

48.282

15625

\begin{align*} y^{\prime }&=\frac {\sqrt {y}}{x} \\ y \left (-1\right ) &= 1 \\ \end{align*}

[_separable]

16.067

15626

\begin{align*} y^{\prime }&=\frac {\sqrt {y}}{x} \\ y \left (-1\right ) &= 0 \\ \end{align*}

[_separable]

13.271

15627

\begin{align*} y^{\prime }&=\frac {\sqrt {y}}{x} \\ y \left (-1\right ) &= -1 \\ \end{align*}

[_separable]

13.366

15628

\begin{align*} y^{\prime }&=\frac {\sqrt {y}}{x} \\ y \left (1\right ) &= 1 \\ \end{align*}

[_separable]

13.710

15629

\begin{align*} y^{\prime }&=3 x y^{{1}/{3}} \\ y \left (-1\right ) &= {\frac {3}{2}} \\ \end{align*}

[_separable]

43.302

15630

\begin{align*} y^{\prime }&=3 x y^{{1}/{3}} \\ y \left (-1\right ) &= 1 \\ \end{align*}

[_separable]

83.362

15631

\begin{align*} y^{\prime }&=3 x y^{{1}/{3}} \\ y \left (-1\right ) &= {\frac {1}{2}} \\ \end{align*}

[_separable]

32.628

15632

\begin{align*} y^{\prime }&=3 x y^{{1}/{3}} \\ y \left (-1\right ) &= 0 \\ \end{align*}

[_separable]

31.229

15633

\begin{align*} y^{\prime }&=3 x y^{{1}/{3}} \\ y \left (-1\right ) &= -1 \\ \end{align*}

[_separable]

89.987

15644

\begin{align*} y^{\prime }&=x \sqrt {1-y^{2}} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

30.438

15645

\begin{align*} y^{\prime }&=x \sqrt {1-y^{2}} \\ y \left (0\right ) &= {\frac {9}{10}} \\ \end{align*}

[_separable]

17.255

15646

\begin{align*} y^{\prime }&=x \sqrt {1-y^{2}} \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}

[_separable]

18.581

15647

\begin{align*} y^{\prime }&=x \sqrt {1-y^{2}} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

4.013

15774

\begin{align*} y^{\prime }&=\frac {1+y}{t +1} \\ \end{align*}

[_separable]

2.535

15775

\begin{align*} y^{\prime }&=y^{2} t^{2} \\ \end{align*}

[_separable]

4.696

15776

\begin{align*} y^{\prime }&=t^{4} y \\ \end{align*}

[_separable]

2.767

15781

\begin{align*} y^{\prime }&=2 t y^{2}+3 y^{2} \\ \end{align*}

[_separable]

3.223

15782

\begin{align*} y^{\prime }&=\frac {t}{y} \\ \end{align*}

[_separable]

6.638

15783

\begin{align*} y^{\prime }&=\frac {t}{y+t^{2} y} \\ \end{align*}

[_separable]

2.174

15784

\begin{align*} y^{\prime }&=t y^{{1}/{3}} \\ \end{align*}

[_separable]

8.281

15786

\begin{align*} y^{\prime }&=\frac {2 y+1}{t} \\ \end{align*}

[_separable]

3.460

15788

\begin{align*} y^{\prime }&=\frac {4 t}{1+3 y^{2}} \\ \end{align*}

[_separable]

1.810

15789

\begin{align*} v^{\prime }&=t^{2} v-2-2 v+t^{2} \\ \end{align*}

[_separable]

2.952

15790

\begin{align*} y^{\prime }&=\frac {1}{y t +t +y+1} \\ \end{align*}

[_separable]

3.822

15791

\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{t} y}{1+y^{2}} \\ \end{align*}

[_separable]

2.442

15793

\begin{align*} w^{\prime }&=\frac {w}{t} \\ \end{align*}

[_separable]

2.368

15795

\begin{align*} x^{\prime }&=-x t \\ x \left (0\right ) &= \frac {1}{\sqrt {\pi }} \\ \end{align*}

[_separable]

2.826

15796

\begin{align*} y^{\prime }&=y t \\ y \left (0\right ) &= 3 \\ \end{align*}

[_separable]

2.709

15798

\begin{align*} y^{\prime }&=t^{2} y^{3} \\ y \left (0\right ) &= -1 \\ \end{align*}

[_separable]

9.678

15800

\begin{align*} y^{\prime }&=\frac {t}{y-t^{2} y} \\ y \left (0\right ) &= 4 \\ \end{align*}

[_separable]

2.639

15802

\begin{align*} y^{\prime }&=t y^{2}+2 y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

3.564

15803

\begin{align*} x^{\prime }&=\frac {t^{2}}{x+t^{3} x} \\ x \left (0\right ) &= -2 \\ \end{align*}

[_separable]

2.797

15805

\begin{align*} y^{\prime }&=\left (1+y^{2}\right ) t \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

3.787

15807

\begin{align*} y^{\prime }&=2 t y^{2}+3 y^{2} t^{2} \\ y \left (1\right ) &= -1 \\ \end{align*}

[_separable]

3.237

15818

\begin{align*} y^{\prime }&=\left (t +1\right ) y \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}

[_separable]

2.912

15828

\begin{align*} y^{\prime }&=y t +t y^{2} \\ \end{align*}

[_separable]

3.806

15829

\begin{align*} y^{\prime }&=t^{2}+t^{2} y \\ \end{align*}

[_separable]

2.676

15830

\begin{align*} y^{\prime }&=t +y t \\ \end{align*}

[_separable]

2.461

15857

\begin{align*} y^{\prime }&=\frac {1}{\left (1+y\right ) \left (t -2\right )} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

5.416

15859

\begin{align*} y^{\prime }&=\frac {t}{-2+y} \\ y \left (-1\right ) &= 0 \\ \end{align*}

[_separable]

4.322

15941

\begin{align*} y^{\prime }&=\frac {\left (t^{2}-4\right ) \left (1+y\right ) {\mathrm e}^{y}}{\left (t -1\right ) \left (3-y\right )} \\ \end{align*}

[_separable]

4.094

15946

\begin{align*} y^{\prime }&=y t \\ \end{align*}

[_separable]

2.923

15948

\begin{align*} y^{\prime }&=\frac {t y}{t^{2}+1} \\ \end{align*}

[_separable]

2.677

15954

\begin{align*} x^{\prime }&=-x t \\ x \left (0\right ) &= {\mathrm e} \\ \end{align*}

[_separable]

2.967

15957

\begin{align*} y^{\prime }&=t^{2} y^{3}+y^{3} \\ y \left (0\right ) &= -{\frac {1}{2}} \\ \end{align*}

[_separable]

3.494

15960

\begin{align*} y^{\prime }&=\frac {\left (t +1\right )^{2}}{\left (1+y\right )^{2}} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

9.852

15961

\begin{align*} y^{\prime }&=2 t y^{2}+3 y^{2} t^{2} \\ y \left (1\right ) &= -1 \\ \end{align*}

[_separable]

3.355

15963

\begin{align*} y^{\prime }&=\frac {t^{2}}{y+t^{3} y} \\ y \left (0\right ) &= -2 \\ \end{align*}

[_separable]

2.862

15967

\begin{align*} y^{\prime }&=t^{2} y+1+y+t^{2} \\ \end{align*}

[_separable]

3.158

15968

\begin{align*} y^{\prime }&=\frac {2 y+1}{t} \\ \end{align*}

[_separable]

4.130

16156

\begin{align*} y y^{\prime }&=2 x \\ \end{align*}

[_separable]

8.122

16197

\begin{align*} y^{\prime }+3 y x&=6 x \\ \end{align*}

[_separable]

2.857

16200

\begin{align*} x^{2} y^{\prime }+x y^{2}&=x \\ \end{align*}

[_separable]

4.740

16203

\begin{align*} \left (x -2\right ) y^{\prime }&=y+3 \\ \end{align*}

[_separable]

3.224

16204

\begin{align*} \left (-2+y\right ) y^{\prime }&=x -3 \\ \end{align*}

[_separable]

9.656

16208

\begin{align*} y^{\prime }&=3 y^{2}-\sin \left (x \right ) y^{2} \\ \end{align*}

[_separable]

3.627

16213

\begin{align*} y^{\prime }+y x&=4 x \\ \end{align*}

[_separable]

2.877

16215

\begin{align*} y^{\prime }&=y x -3 x -2 y+6 \\ \end{align*}

[_separable]

3.221

16217

\begin{align*} y y^{\prime }&={\mathrm e}^{x -3 y^{2}} \\ \end{align*}

[_separable]

2.853

16218

\begin{align*} y^{\prime }&=\frac {x}{y} \\ \end{align*}

[_separable]

8.156

16220

\begin{align*} x y y^{\prime }&=y^{2}+9 \\ \end{align*}

[_separable]

7.000

16221

\begin{align*} y^{\prime }&=\frac {1+y^{2}}{x^{2}+1} \\ \end{align*}

[_separable]

3.756

16222

\begin{align*} \cos \left (y\right ) y^{\prime }&=\sin \left (x \right ) \\ \end{align*}

[_separable]

2.665

16223

\begin{align*} y^{\prime }&={\mathrm e}^{2 x -3 y} \\ \end{align*}

[_separable]

2.578

16224

\begin{align*} y^{\prime }&=\frac {x}{y} \\ y \left (1\right ) &= 3 \\ \end{align*}

[_separable]

9.335

16225

\begin{align*} y^{\prime }&=2 x -1+2 y x -y \\ y \left (0\right ) &= 2 \\ \end{align*}

[_separable]

3.065

16226

\begin{align*} y y^{\prime }&=x y^{2}+x \\ y \left (0\right ) &= -2 \\ \end{align*}

[_separable]

3.137

16228

\begin{align*} y^{\prime }&=y x -4 x \\ \end{align*}

[_separable]

2.877

16230

\begin{align*} y y^{\prime }&=x y^{2}-9 x \\ \end{align*}

[_separable]

3.463

16232

\begin{align*} y^{\prime }&={\mathrm e}^{x +y^{2}} \\ \end{align*}

[_separable]

1.670

16234

\begin{align*} y^{\prime }&=y x -4 x \\ \end{align*}

[_separable]

2.853

16235

\begin{align*} y^{\prime }&=y x -3 x -2 y+6 \\ \end{align*}

[_separable]

3.159

16236

\begin{align*} y^{\prime }&=3 y^{2}-\sin \left (x \right ) y^{2} \\ \end{align*}

[_separable]

3.648

16238

\begin{align*} y^{\prime }&=\frac {y}{x} \\ \end{align*}

[_separable]

2.674

16239

\begin{align*} y^{\prime }&=\frac {6 x^{2}+4}{3 y^{2}-4 y} \\ \end{align*}

[_separable]

2.468

16240

\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=1+y^{2} \\ \end{align*}

[_separable]

3.703

16241

\begin{align*} \left (y^{2}-1\right ) y^{\prime }&=4 x y^{2} \\ \end{align*}

[_separable]

25.142

16244

\begin{align*} y^{\prime }&=3 x y^{3} \\ \end{align*}

[_separable]

7.119

16245

\begin{align*} y^{\prime }&=\frac {2+\sqrt {x}}{2+\sqrt {y}} \\ \end{align*}

[_separable]

3.645

16246

\begin{align*} y^{\prime }-3 x^{2} y^{2}&=-3 x^{2} \\ \end{align*}

[_separable]

4.412

16247

\begin{align*} y^{\prime }-3 x^{2} y^{2}&=3 x^{2} \\ \end{align*}

[_separable]

3.756

16250

\begin{align*} y y^{\prime }&=\sin \left (x \right ) \\ y \left (0\right ) &= -4 \\ \end{align*}

[_separable]

3.109

16251

\begin{align*} y^{\prime }&=2 x -1+2 y x -y \\ y \left (0\right ) &= -1 \\ \end{align*}

[_separable]

3.493

16252

\begin{align*} x y^{\prime }&=y^{2}-y \\ y \left (2\right ) &= 1 \\ \end{align*}

[_separable]

9.799

16253

\begin{align*} x y^{\prime }&=y^{2}-y \\ y \left (1\right ) &= 2 \\ \end{align*}

[_separable]

5.263

16254

\begin{align*} y^{\prime }&=\frac {y^{2}-1}{y x} \\ y \left (1\right ) &= -2 \\ \end{align*}

[_separable]

10.401

16255

\begin{align*} \left (y^{2}-1\right ) y^{\prime }&=4 y x \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

2.810

16263

\begin{align*} y^{\prime }&=y \sin \left (x \right ) \\ \end{align*}

[_separable]

3.194

16269

\begin{align*} y^{\prime }-2 y x&=x \\ \end{align*}

[_separable]

2.818

16317

\begin{align*} 2-2 x +3 y^{2} y^{\prime }&=0 \\ \end{align*}

[_separable]

3.331

16321

\begin{align*} 1+{\mathrm e}^{y}+x \,{\mathrm e}^{y} y^{\prime }&=0 \\ \end{align*}

[_separable]

4.569

16323

\begin{align*} 1+y^{4}+x y^{3} y^{\prime }&=0 \\ \end{align*}

[_separable]

5.201

16327

\begin{align*} 3 y+3 y^{2}+\left (2 x +4 y x \right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

20.189

16328

\begin{align*} 2 x \left (y+1\right )-y^{\prime }&=0 \\ \end{align*}

[_separable]

3.019

16333

\begin{align*} x y^{\prime }&=2 y^{2}-6 y \\ \end{align*}

[_separable]

9.275

16334

\begin{align*} 4 y^{2}-x^{2} y^{2}+y^{\prime }&=0 \\ \end{align*}

[_separable]

3.467

16348

\begin{align*} y^{\prime }&=\frac {1}{y x -3 x} \\ \end{align*}

[_separable]

11.770

16351

\begin{align*} \sin \left (y\right )+\left (x +1\right ) \cos \left (y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

12.413

16357

\begin{align*} y^{\prime }&=x y^{2}+3 y^{2}+x +3 \\ \end{align*}

[_separable]

4.528

16371

\begin{align*} y^{2}-y^{2} \cos \left (x \right )+y^{\prime }&=0 \\ \end{align*}

[_separable]

3.927

16374

\begin{align*} y^{\prime }&=y^{3}-y^{3} \cos \left (x \right ) \\ \end{align*}

[_separable]

5.627

16376

\begin{align*} y^{\prime }&={\mathrm e}^{4 x +3 y} \\ \end{align*}

[_separable]

2.904

16378

\begin{align*} y^{\prime }&={\mathrm e}^{4 x +3 y} \\ \end{align*}

[_separable]

2.385

16964

\begin{align*} y^{\prime }+y x&=0 \\ \end{align*}

[_separable]

3.482

16975

\begin{align*} y^{\prime }&=-\frac {x}{y} \\ \end{align*}

[_separable]

9.132

17005

\begin{align*} y^{\prime }&=\frac {\left (x -4\right ) y^{3}}{x^{3} \left (-2+y\right )} \\ \end{align*}

[_separable]

12.125

17015

\begin{align*} y^{\prime }+\cos \left (x \right ) y&=0 \\ \end{align*}

[_separable]

3.694

17038

\begin{align*} \frac {y^{\prime }}{t}&=\sqrt {y} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

35.115

17040

\begin{align*} y^{\prime }&=y \sqrt {t} \\ y \left (1\right ) &= 1 \\ \end{align*}

[_separable]

4.573

17042

\begin{align*} t y^{\prime }&=y \\ \end{align*}

[_separable]

3.196

17043

\begin{align*} y^{\prime }&=\tan \left (t \right ) y \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

4.652

17064

\begin{align*} y^{\prime }&=t y^{2} \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}

[_separable]

10.471

17065

\begin{align*} y^{\prime }&=-\frac {t}{y} \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}

[_separable]

41.807

17067

\begin{align*} y^{\prime }&=\frac {x}{y^{2}} \\ \end{align*}

[_separable]

6.146

17068

\begin{align*} \frac {1}{2 \sqrt {t}}+y^{2} y^{\prime }&=0 \\ \end{align*}

[_separable]

8.683

17069

\begin{align*} y^{\prime }&=\frac {\sqrt {y}}{x^{2}} \\ \end{align*}

[_separable]

15.724

17071

\begin{align*} 6+4 t^{3}+\left (5+\frac {9}{y^{8}}\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

4.144

17072

\begin{align*} \frac {6}{t^{9}}-\frac {6}{t^{3}}+t^{7}+\left (9+\frac {1}{s^{2}}-4 s^{8}\right ) s^{\prime }&=0 \\ \end{align*}

[_separable]

4.975

17073

\begin{align*} 4 \sinh \left (4 y\right ) y^{\prime }&=6 \cosh \left (3 x \right ) \\ \end{align*}

[_separable]

5.601

17074

\begin{align*} y^{\prime }&=\frac {1+y}{t +1} \\ \end{align*}

[_separable]

3.832

17075

\begin{align*} y^{\prime }&=\frac {y+2}{2 t +1} \\ \end{align*}

[_separable]

10.402

17076

\begin{align*} \frac {3}{t^{2}}&=\left (\frac {1}{\sqrt {y}}+\sqrt {y}\right ) y^{\prime } \\ \end{align*}

[_separable]

6.062

17077

\begin{align*} 3 \sin \left (x \right )-4 \cos \left (y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

3.292

17078

\begin{align*} \cos \left (y\right ) y^{\prime }&=8 \sin \left (8 t \right ) \\ \end{align*}

[_separable]

5.421

17080

\begin{align*} \left (5 x^{5}-4 \cos \left (x\right )\right ) x^{\prime }+2 \cos \left (9 t \right )+2 \sin \left (7 t \right )&=0 \\ \end{align*}

[_separable]

7.301

17081

\begin{align*} \cosh \left (6 t \right )+5 \sinh \left (4 t \right )+20 \sinh \left (y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

8.209

17082

\begin{align*} y^{\prime }&={\mathrm e}^{2 y+10 t} \\ \end{align*}

[_separable]

3.556

17083

\begin{align*} y^{\prime }&={\mathrm e}^{3 y+2 t} \\ \end{align*}

[_separable]

3.493

17084

\begin{align*} \sin \left (t \right )^{2}&=\cos \left (y\right )^{2} y^{\prime } \\ \end{align*}

[_separable]

4.002

17085

\begin{align*} 3 \sin \left (t \right )-\sin \left (3 t \right )&=\left (\cos \left (4 y\right )-4 \cos \left (y\right )\right ) y^{\prime } \\ \end{align*}

[_separable]

27.938

17086

\begin{align*} x^{\prime }&=\frac {\sec \left (t \right )^{2}}{\sec \left (x\right ) \tan \left (x\right )} \\ \end{align*}

[_separable]

26.936

17087

\begin{align*} \left (2-\frac {5}{y^{2}}\right ) y^{\prime }+4 \cos \left (x \right )^{2}&=0 \\ \end{align*}

[_separable]

5.040

17089

\begin{align*} \tan \left (y\right ) \sec \left (y\right )^{2} y^{\prime }+\cos \left (2 x \right )^{3} \sin \left (2 x \right )&=0 \\ \end{align*}

[_separable]

5.998

17090

\begin{align*} y^{\prime }&=\frac {\left (1+2 \,{\mathrm e}^{y}\right ) {\mathrm e}^{-y}}{t \ln \left (t \right )} \\ \end{align*}

[_separable]

7.322

17091

\begin{align*} x \sin \left (x^{2}\right )&=\frac {\cos \left (\sqrt {y}\right ) y^{\prime }}{\sqrt {y}} \\ \end{align*}

[_separable]

14.462

17092

\begin{align*} \frac {x -2}{x^{2}-4 x +3}&=\frac {\left (1-\frac {1}{y}\right )^{2} y^{\prime }}{y^{2}} \\ \end{align*}

[_separable]

5.234

17093

\begin{align*} \frac {\cos \left (y\right ) y^{\prime }}{\left (1-\sin \left (y\right )\right )^{2}}&=\sin \left (x \right )^{3} \cos \left (x \right ) \\ \end{align*}

[_separable]

11.573

17094

\begin{align*} y^{\prime }&=\frac {\left (5-2 \cos \left (x \right )\right )^{3} \sin \left (x \right ) \cos \left (y\right )^{4}}{\sin \left (y\right )} \\ \end{align*}

[_separable]

13.776

17095

\begin{align*} \frac {\sqrt {\ln \left (x \right )}}{x}&=\frac {{\mathrm e}^{\frac {3}{y}} y^{\prime }}{y} \\ \end{align*}

[_separable]

3.701

17096

\begin{align*} y^{\prime }&=\frac {5^{-t}}{y^{2}} \\ \end{align*}

[_separable]

3.757

17097

\begin{align*} y^{\prime }&=y^{2} t^{2}+y^{2}-t^{2}-1 \\ \end{align*}

[_separable]

6.022

17099

\begin{align*} 4 \left (x -1\right )^{2} y^{\prime }-3 \left (y+3\right )^{2}&=0 \\ \end{align*}

[_separable]

9.948

17100

\begin{align*} y^{\prime }&=\sin \left (t -y\right )+\sin \left (t +y\right ) \\ \end{align*}

[_separable]

9.782

17111

\begin{align*} y^{\prime }&=\frac {\sqrt {t}}{y} \\ y \left (0\right ) &= 2 \\ \end{align*}

[_separable]

31.276

17113

\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{t}}{1+y} \\ y \left (0\right ) &= -2 \\ \end{align*}

[_separable]

6.411

17114

\begin{align*} y^{\prime }&={\mathrm e}^{t -y} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

16.835

17118

\begin{align*} y^{\prime }&=\frac {\sin \left (x \right )}{\cos \left (y\right )+1} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

4.257

17119

\begin{align*} y^{\prime }&=\frac {y+3}{1+3 x} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

4.800

17120

\begin{align*} y^{\prime }&={\mathrm e}^{x -y} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

4.913

17121

\begin{align*} y^{\prime }&={\mathrm e}^{2 x -y} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

5.405

17122

\begin{align*} y^{\prime }&=\frac {3 y+1}{x +3} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

5.253

17123

\begin{align*} y^{\prime }&=\cos \left (t \right ) y \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

4.866

17124

\begin{align*} y^{\prime }&=y^{2} \cos \left (t \right ) \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

4.796

17125

\begin{align*} y^{\prime }&=\sqrt {y}\, \cos \left (t \right ) \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

6.536

17126

\begin{align*} y^{\prime }+y f \left (t \right )&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

5.640

17127

\begin{align*} y^{\prime }&=-\frac {-2+y}{x -2} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

4.931

17137

\begin{align*} y^{\prime }&=y f \left (t \right ) \\ y \left (1\right ) &= 1 \\ \end{align*}

[_separable]

4.602

17156

\begin{align*} y^{\prime }-y x&=x \\ \end{align*}

[_separable]

3.799

17160

\begin{align*} x^{\prime }&=\frac {3 x t^{2}}{-t^{3}+1} \\ \end{align*}

[_separable]

3.263

17166

\begin{align*} 2 y t +y^{\prime }&=2 t \\ y \left (0\right ) &= -1 \\ \end{align*}

[_separable]

3.877

17170

\begin{align*} \left (t^{2}+4\right ) y^{\prime }+2 y t&=2 t \\ y \left (0\right ) &= -4 \\ \end{align*}

[_separable]

4.168

17198

\begin{align*} \frac {t}{\sqrt {t^{2}+y^{2}}}+\frac {y y^{\prime }}{\sqrt {t^{2}+y^{2}}}&=0 \\ \end{align*}

[_separable]

13.264

17205

\begin{align*} {\mathrm e}^{y t}+\frac {t \,{\mathrm e}^{y t} y^{\prime }}{y}&=0 \\ \end{align*}

[_separable]

8.341

17209

\begin{align*} \frac {3 t^{2}}{y}-\frac {t^{3} y^{\prime }}{y^{2}}&=0 \\ \end{align*}

[_separable]

8.079

17214

\begin{align*} \sin \left (y\right )^{2}+t \sin \left (2 y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

23.070

17238

\begin{align*} t^{2} y+t^{3} y^{\prime }&=0 \\ \end{align*}

[_separable]

5.017

17239

\begin{align*} y \left (2 \,{\mathrm e}^{t}+4 t \right )+3 \left ({\mathrm e}^{t}+t^{2}\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

5.483

17259

\begin{align*} y^{\prime }-\frac {y}{t}&=\frac {y^{2}}{t} \\ \end{align*}

[_separable]

6.812

17263

\begin{align*} 2 \ln \left (t \right )-\ln \left (4 y^{2}\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

10.539

17265

\begin{align*} \frac {\sin \left (2 t \right )}{\cos \left (2 y\right )}+\frac {\ln \left (y\right ) y^{\prime }}{\ln \left (t \right )}&=0 \\ \end{align*}

[_separable]

18.299

17266

\begin{align*} \sqrt {t^{2}+1}+y y^{\prime }&=0 \\ \end{align*}

[_separable]

4.542

17296

\begin{align*} y^{\prime }-\frac {2 y}{x}&=-x^{2} y \\ \end{align*}

[_separable]

5.453

17310

\begin{align*} y^{\prime }&=\frac {2 t^{5}}{5 y^{2}} \\ \end{align*}

[_separable]

6.786

17311

\begin{align*} \cos \left (4 x \right )-8 y^{\prime } \sin \left (y\right )&=0 \\ \end{align*}

[_separable]

4.498

17312

\begin{align*} y^{\prime }-\frac {y}{t}&=\frac {y^{2}}{t} \\ \end{align*}

[_separable]

5.450

17313

\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{8 y}}{t} \\ \end{align*}

[_separable]

4.041

17314

\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{5 t}}{y^{4}} \\ \end{align*}

[_separable]

5.225

17315

\begin{align*} -\frac {1}{x^{5}}+\frac {1}{x^{3}}&=\left (2 y^{4}-6 y^{9}\right ) y^{\prime } \\ \end{align*}

[_separable]

3.965

17316

\begin{align*} y^{\prime }&=\frac {y \,{\mathrm e}^{-2 t}}{\ln \left (y\right )} \\ \end{align*}

[_separable]

4.594

17317

\begin{align*} y^{\prime }&=\frac {\left (4-7 x \right ) \left (2 y-3\right )}{\left (x -1\right ) \left (2 x -5\right )} \\ \end{align*}

[_separable]

5.687

17330

\begin{align*} y t +y^{\prime }&=t \\ \end{align*}

[_separable]

4.513

17347

\begin{align*} y^{\prime }&=t y^{3} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

26.632

17348

\begin{align*} y^{\prime }&=\frac {t}{y^{3}} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

35.856

17349

\begin{align*} y^{\prime }&=-\frac {y}{t -2} \\ y \left (2\right ) &= 0 \\ \end{align*}

[_separable]

4.898

17838

\begin{align*} y^{\prime }&=\frac {x}{y} \\ \end{align*}

[_separable]

17.878

17850

\begin{align*} \left (-x^{2}+1\right ) y^{\prime }+y x&=2 x \\ \end{align*}

[_separable]

9.140

17856

\begin{align*} y^{\prime }&=\left (-1+y\right ) x \\ \end{align*}

[_separable]

4.329

17861

\begin{align*} y^{\prime }&=\frac {y+1}{x -1} \\ \end{align*}

[_separable]

4.398

17866

\begin{align*} y^{\prime }&=-\frac {y}{x} \\ \end{align*}

[_separable]

5.790

17876

\begin{align*} 1+y^{2}+\left (x^{2}+1\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

5.685

17877

\begin{align*} x y y^{\prime }+1+y^{2}&=0 \\ \end{align*}

[_separable]

10.597

17878

\begin{align*} \sin \left (x \right ) y^{\prime }-\cos \left (x \right ) y&=0 \\ y \left (\frac {\pi }{2}\right ) &= 1 \\ \end{align*}

[_separable]

7.650

17879

\begin{align*} 1+y^{2}&=x y^{\prime } \\ \end{align*}

[_separable]

6.719

17880

\begin{align*} y y^{\prime } \sqrt {x^{2}+1}+x \sqrt {1+y^{2}}&=0 \\ \end{align*}

[_separable]

7.031

17881

\begin{align*} x \sqrt {1-y^{2}}+y \sqrt {-x^{2}+1}\, y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

12.096

17883

\begin{align*} \ln \left (y\right ) y+x y^{\prime }&=1 \\ y \left (1\right ) &= 1 \\ \end{align*}

[_separable]

7.334

17884

\begin{align*} y^{\prime }&=a^{x +y} \\ \end{align*}

[_separable]

5.635

17885

\begin{align*} {\mathrm e}^{y} \left (x^{2}+1\right ) y^{\prime }-2 x \left (1+{\mathrm e}^{y}\right )&=0 \\ \end{align*}

[_separable]

9.227

17886

\begin{align*} 2 x \sqrt {1-y^{2}}&=\left (x^{2}+1\right ) y^{\prime } \\ \end{align*}

[_separable]

9.001

17887

\begin{align*} {\mathrm e}^{x} \sin \left (y\right )^{3}+\left ({\mathrm e}^{2 x}+1\right ) \cos \left (y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

6.980

17888

\begin{align*} \sin \left (x \right ) y^{2}+\cos \left (x \right )^{2} \ln \left (y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

9.414

17893

\begin{align*} a^{2}+y^{2}+2 x \sqrt {a x -x^{2}}\, y^{\prime }&=0 \\ y \left (a \right ) &= 0 \\ \end{align*}

[_separable]

13.954

17894

\begin{align*} y^{\prime }&=\frac {y}{x} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

4.576

17904

\begin{align*} x^{3} y^{\prime }-\sin \left (y\right )&=1 \\ y \left (\infty \right ) &= 5 \pi \\ \end{align*}

[_separable]

7.881

17905

\begin{align*} \left (x^{2}+1\right ) y^{\prime }-\frac {\cos \left (2 y\right )^{2}}{2}&=0 \\ y \left (-\infty \right ) &= \frac {7 \pi }{2} \\ \end{align*}

[_separable]

7.266

17907

\begin{align*} \left (x +1\right ) y^{\prime }&=-1+y \\ \end{align*}

[_separable]

4.640

17908

\begin{align*} y^{\prime }&=2 x \left (\pi +y\right ) \\ \end{align*}

[_separable]

4.585

17939

\begin{align*} y^{\prime }+\cos \left (x \right ) y&=\cos \left (x \right ) \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

6.025

17953

\begin{align*} y^{\prime }+2 y x&=2 x y^{2} \\ \end{align*}

[_separable]

8.554

17956

\begin{align*} y^{\prime }+3 y x&=y \,{\mathrm e}^{x^{2}} \\ \end{align*}

[_separable]

6.844

17961

\begin{align*} y^{\prime }-\cos \left (x \right ) y&=y^{2} \cos \left (x \right ) \\ \end{align*}

[_separable]

9.482

17974

\begin{align*} \frac {x y}{\sqrt {x^{2}+1}}+2 y x -\frac {y}{x}+\left (\sqrt {x^{2}+1}+x^{2}-\ln \left (x \right )\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

38.215

18054

\begin{align*} y^{\prime }+\cos \left (\frac {x}{2}+\frac {y}{2}\right )&=\cos \left (\frac {x}{2}-\frac {y}{2}\right ) \\ \end{align*}

[_separable]

23.363

18055

\begin{align*} y^{\prime } \left (3 x^{2}-2 x \right )-y \left (6 x -2\right )&=0 \\ \end{align*}

[_separable]

5.913

18062

\begin{align*} \left (x -1\right ) \left (y^{2}-y+1\right )&=\left (-1+y\right ) \left (x^{2}+x +1\right ) y^{\prime } \\ \end{align*}

[_separable]

11.481

18071

\begin{align*} \sin \left (\ln \left (x \right )\right )-\cos \left (\ln \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

8.773

18098

\begin{align*} y x&=y^{\prime } \ln \left (\frac {y^{\prime }}{x}\right ) \\ \end{align*}

[_separable]

12.331

18473

\begin{align*} y^{\prime }&=\frac {x^{4}}{y} \\ \end{align*}

[_separable]

11.591

18474

\begin{align*} y^{\prime }&=\frac {x^{2} \left (x^{3}+1\right )}{y} \\ \end{align*}

[_separable]

4.454

18475

\begin{align*} y^{\prime }+y^{3} \sin \left (x \right )&=0 \\ \end{align*}

[_separable]

7.986

18476

\begin{align*} y^{\prime }&=\frac {7 x^{2}-1}{7+5 y} \\ \end{align*}

[_separable]

8.467

18477

\begin{align*} y^{\prime }&=\sin \left (2 x \right )^{2} \cos \left (y\right )^{2} \\ \end{align*}

[_separable]

4.007

18478

\begin{align*} x y^{\prime }&=\sqrt {1-y^{2}} \\ \end{align*}

[_separable]

13.249

18479

\begin{align*} y y^{\prime }&=\left (x y^{2}+x \right ) {\mathrm e}^{x^{2}} \\ \end{align*}

[_separable]

7.743

18480

\begin{align*} y^{\prime }&=\frac {x^{2}+{\mathrm e}^{-x}}{y^{2}-{\mathrm e}^{y}} \\ \end{align*}

[_separable]

6.389

18481

\begin{align*} y^{\prime }&=\frac {x^{2}}{1+y^{2}} \\ \end{align*}

[_separable]

3.986

18482

\begin{align*} y^{\prime }&=\frac {\sec \left (x \right )^{2}}{y^{3}+1} \\ \end{align*}

[_separable]

5.218

18484

\begin{align*} y^{\prime }&=x \left (y-y^{2}\right ) \\ \end{align*}

[_separable]

9.852

18485

\begin{align*} y^{\prime }&=\left (1-12 x \right ) y^{2} \\ y \left (0\right ) &= -{\frac {1}{8}} \\ \end{align*}

[_separable]

8.377

18486

\begin{align*} y^{\prime }&=\frac {3-2 x}{y} \\ y \left (1\right ) &= -6 \\ \end{align*}

[_separable]

11.894

18487

\begin{align*} x +y y^{\prime } {\mathrm e}^{-x}&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

5.227

18488

\begin{align*} r^{\prime }&=\frac {r^{2}}{\theta } \\ r \left (1\right ) &= 2 \\ \end{align*}

[_separable]

7.868

18489

\begin{align*} y^{\prime }&=\frac {3 x}{y+x^{2} y} \\ y \left (0\right ) &= -7 \\ \end{align*}

[_separable]

5.995

18490

\begin{align*} y^{\prime }&=\frac {2 x}{1+2 y} \\ y \left (2\right ) &= 0 \\ \end{align*}

[_separable]

12.430

18491

\begin{align*} y^{\prime }&=2 x y^{2}+4 x^{3} y^{2} \\ y \left (1\right ) &= -2 \\ \end{align*}

[_separable]

5.955

18492

\begin{align*} y^{\prime }&=x^{2} {\mathrm e}^{-3 y} \\ y \left (2\right ) &= 0 \\ \end{align*}

[_separable]

8.095

18493

\begin{align*} y^{\prime }&=\left (1+y^{2}\right ) \tan \left (2 x \right ) \\ y \left (0\right ) &= -\sqrt {3} \\ \end{align*}

[_separable]

15.498

18494

\begin{align*} y^{\prime }&=\frac {x \left (x^{2}+1\right ) y^{5}}{6} \\ y \left (0\right ) &= -2^{{1}/{3}} \\ \end{align*}

[_separable]

4.940

18495

\begin{align*} y^{\prime }&=\frac {-{\mathrm e}^{x}+3 x^{2}}{2 y-11} \\ y \left (0\right ) &= 11 \\ \end{align*}

[_separable]

8.722

18496

\begin{align*} x^{2} y^{\prime }&=y-y x \\ y \left (1\right ) &= 2 \\ \end{align*}

[_separable]

7.810

18497

\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{-x}-{\mathrm e}^{x}}{3+4 y} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

8.074

18498

\begin{align*} 2 y y^{\prime }&=\frac {x}{\sqrt {x^{2}-4}} \\ y \left (3\right ) &= -1 \\ \end{align*}

[_separable]

8.989

18499

\begin{align*} \sin \left (2 x \right )+\cos \left (3 y\right ) y^{\prime }&=0 \\ y \left (\frac {\pi }{2}\right ) &= \frac {\pi }{3} \\ \end{align*}

[_separable]

26.310

18500

\begin{align*} \sqrt {-x^{2}+1}\, y^{2} y^{\prime }&=\arcsin \left (x \right ) \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

13.842

18501

\begin{align*} y^{\prime }&=\frac {3 x^{2}+1}{12 y^{2}-12 y} \\ y \left (0\right ) &= 2 \\ \end{align*}

[_separable]

19.260

18502

\begin{align*} y^{\prime }&=\frac {2 x^{2}}{2 y^{2}-6} \\ y \left (1\right ) &= 0 \\ \end{align*}

[_separable]

4.561

18503

\begin{align*} y^{\prime }&=2 y^{2}+x y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

8.276

18504

\begin{align*} y^{\prime }&=\frac {6-{\mathrm e}^{x}}{3+2 y} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

8.498

18505

\begin{align*} y^{\prime }&=\frac {2 \cos \left (2 x \right )}{10+2 y} \\ y \left (0\right ) &= -1 \\ \end{align*}

[_separable]

8.336

18506

\begin{align*} y^{\prime }&=2 \left (x +1\right ) \left (1+y^{2}\right ) \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

7.580

18507

\begin{align*} y^{\prime }&=\frac {t \left (4-y\right ) y}{3} \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}

[_separable]

10.971

18508

\begin{align*} y^{\prime }&=\frac {t y \left (4-y\right )}{t +1} \\ y \left (0\right ) &= 2 \\ \end{align*}

[_separable]

14.471

18546

\begin{align*} y+\left (-4+t \right ) t y^{\prime }&=0 \\ y \left (2\right ) &= 1 \\ \end{align*}

[_separable]

6.140

18555

\begin{align*} y^{\prime }&=\frac {t^{2}+1}{3 y-y^{2}} \\ \end{align*}

[_separable]

4.423

18556

\begin{align*} y^{\prime }&=\frac {\cot \left (t \right ) y}{1+y} \\ \end{align*}

[_separable]

9.205

18559

\begin{align*} y^{\prime }&=-\frac {4 t}{y} \\ y \left (0\right ) &= y_{0} \\ \end{align*}

[_separable]

21.904

18560

\begin{align*} y^{\prime }&=2 t y^{2} \\ y \left (0\right ) &= y_{0} \\ \end{align*}

[_separable]

14.780

18562

\begin{align*} y^{\prime }&=\frac {t^{2}}{\left (t^{3}+1\right ) y} \\ y \left (0\right ) &= y_{0} \\ \end{align*}

[_separable]

5.789

18563

\begin{align*} y^{\prime }&=t \left (3-y\right ) y \\ \end{align*}

[_separable]

10.116

18567

\begin{align*} y^{\prime }+\left (\left \{\begin {array}{cc} 2 & 0\le t \le 1 \\ 1 & 1<t \end {array}\right .\right ) y&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

7.890

18568

\begin{align*} 3+2 x +\left (-2+2 y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

18.656

18578

\begin{align*} x \ln \left (y\right )+y x +\left (y \ln \left (x \right )+y x \right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

8.735

18579

\begin{align*} \frac {x}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}&=0 \\ \end{align*}

[_separable]

20.427

18582

\begin{align*} x^{2} y^{3}+x \left (1+y^{2}\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

5.940

18585

\begin{align*} \left (x +2\right ) \sin \left (y\right )+x \cos \left (y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

5.730

18594

\begin{align*} y y^{\prime }&=x +1 \\ \end{align*}

[_separable]

7.912

18595

\begin{align*} \left (1+y^{4}\right ) y^{\prime }&=x^{4}+1 \\ \end{align*}

[_separable]

4.665

18597

\begin{align*} x \left (x -1\right ) y^{\prime }&=y \left (y+1\right ) \\ \end{align*}

[_separable]

11.375

18610

\begin{align*} 5 \left (t^{2}+1\right ) y^{\prime }&=4 t y \left (y^{3}-1\right ) \\ \end{align*}

[_separable]

21.014

18621

\begin{align*} \frac {\sqrt {x}\, y^{\prime }}{y}&=1 \\ \end{align*}

[_separable]

11.043

19066

\begin{align*} y y^{\prime } \sqrt {x^{2}+1}+x \sqrt {1+y^{2}}&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

4.982

19067

\begin{align*} \sec \left (x \right )^{2} \tan \left (y\right )+\sec \left (y\right )^{2} \tan \left (x \right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

25.997

19068

\begin{align*} y^{\prime } \sqrt {-x^{2}+1}+\sqrt {1-y^{2}}&=0 \\ \end{align*}

[_separable]

18.232

19228

\begin{align*} x y^{\prime }&=2 y \\ \end{align*}

[_separable]

5.875

19229

\begin{align*} y y^{\prime }&={\mathrm e}^{2 x} \\ \end{align*}

[_separable]

3.793

19249

\begin{align*} x y y^{\prime }&=-1+y \\ \end{align*}

[_separable]

4.989

19250

\begin{align*} x^{5} y^{\prime }+y^{5}&=0 \\ \end{align*}

[_separable]

7.980

19251

\begin{align*} x y^{\prime }&=\left (-2 x^{2}+1\right ) \tan \left (y\right ) \\ \end{align*}

[_separable]

2.749

19252

\begin{align*} y^{\prime }&=2 y x \\ \end{align*}

[_separable]

2.894

19253

\begin{align*} y^{\prime } \sin \left (y\right )&=x^{2} \\ \end{align*}

[_separable]

2.297

19255

\begin{align*} y^{\prime }+y \tan \left (x \right )&=0 \\ \end{align*}

[_separable]

2.971

19256

\begin{align*} y^{\prime }-y \tan \left (x \right )&=0 \\ \end{align*}

[_separable]

3.000

19257

\begin{align*} 1+y^{2}+\left (x^{2}+1\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

3.510

19258

\begin{align*} \ln \left (y\right ) y-x y^{\prime }&=0 \\ \end{align*}

[_separable]

4.288

19265

\begin{align*} y^{\prime }&={\mathrm e}^{3 x -2 y} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

3.791

19267

\begin{align*} {\mathrm e}^{-y}+\left (x^{2}+1\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

3.043

19268

\begin{align*} 3 \cos \left (3 x \right ) \cos \left (2 y\right )-2 \sin \left (3 x \right ) \sin \left (2 y\right ) y^{\prime }&=0 \\ y \left (\frac {\pi }{12}\right ) &= \frac {\pi }{8} \\ \end{align*}

[_separable]

6.162

19270

\begin{align*} x y y^{\prime }&=\left (x +1\right ) \left (y+1\right ) \\ y \left (1\right ) &= 0 \\ \end{align*}

[_separable]

4.135

19301

\begin{align*} -\frac {\sin \left (\frac {x}{y}\right )}{y}+\frac {x \sin \left (\frac {x}{y}\right ) y^{\prime }}{y^{2}}&=0 \\ \end{align*}

[_separable]

3.599

19302

\begin{align*} 1+y+\left (1-x \right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

4.332

19308

\begin{align*} x \ln \left (y\right )+y x +\left (y \ln \left (x \right )+y x \right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

3.796

19311

\begin{align*} \frac {x}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}&=0 \\ \end{align*}

[_separable]

12.393

19319

\begin{align*} \left (x +2\right ) \sin \left (y\right )+x \cos \left (y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

3.817

19327

\begin{align*} -x y^{\prime }+y&=x y^{3} y^{\prime } \\ \end{align*}

[_separable]

6.131

19331

\begin{align*} x y^{\prime }-y+y^{2}&=0 \\ \end{align*}

[_separable]

3.886

19377

\begin{align*} x y^{\prime }+y&=x^{2} y^{\prime }+y^{2} \\ \end{align*}

[_separable]

5.831

19400

\begin{align*} 3 x^{2} \ln \left (y\right )+\frac {x^{3} y^{\prime }}{y}&=0 \\ \end{align*}

[_separable]

5.724

19672

\begin{align*} 1+2 x+\left (-t^{2}+4\right ) x^{\prime }&=0 \\ \end{align*}

[_separable]

7.307

19678

\begin{align*} x^{\prime }+x \tan \left (t \right )&=0 \\ \end{align*}

[_separable]

3.606

19681

\begin{align*} x^{\prime }+2 x t +t x^{4}&=0 \\ \end{align*}

[_separable]

3.875

19706

\begin{align*} y^{\prime }&=\frac {\sqrt {1-y^{2}}\, \arcsin \left (y\right )}{x} \\ \end{align*}

[_separable]

10.345

19711

\begin{align*} \sin \left (x \right ) \cos \left (y\right )^{2}+\cos \left (x \right )^{2} y^{\prime }&=0 \\ \end{align*}

[_separable]

4.820

19713

\begin{align*} -x y^{\prime }+y&=b \left (1+x^{2} y^{\prime }\right ) \\ \end{align*}

[_separable]

3.343

19715

\begin{align*} y^{\prime }&=1+\frac {1}{x}-\frac {1}{y^{2}+2}-\frac {1}{x \left (y^{2}+2\right )} \\ \end{align*}

[_separable]

2.717

19719

\begin{align*} \sec \left (x \right )^{2} \tan \left (y\right ) y^{\prime }+\sec \left (y\right )^{2} \tan \left (x \right )&=0 \\ \end{align*}

[_separable]

27.791

19723

\begin{align*} y^{\prime }+y x&=x \\ \end{align*}

[_separable]

3.095

19740

\begin{align*} y^{\prime }&=x \left (a y^{2}+b \right ) \\ \end{align*}

[_separable]

4.588

19741

\begin{align*} n^{\prime }&=\left (n^{2}+1\right ) x \\ \end{align*}

[_separable]

4.010

19742

\begin{align*} v^{\prime }+\frac {2 v}{u}&=3 v \\ \end{align*}

[_separable]

2.850

19743

\begin{align*} \sqrt {-u^{2}+1}\, v^{\prime }&=2 u \sqrt {1-v^{2}} \\ \end{align*}

[_separable]

5.678

19745

\begin{align*} \frac {y^{\prime }}{x}&=y \sin \left (x^{2}-1\right )-\frac {2 y}{\sqrt {x}} \\ \end{align*}

[_separable]

5.787

19747

\begin{align*} v^{\prime }+2 u v&=2 u \\ \end{align*}

[_separable]

3.153

19748

\begin{align*} 1+v^{2}+\left (u^{2}+1\right ) v v^{\prime }&=0 \\ \end{align*}

[_separable]

6.285

19749

\begin{align*} u \ln \left (u \right ) v^{\prime }+\sin \left (v\right )^{2}&=1 \\ \end{align*}

[_separable]

5.167

19797

\begin{align*} y^{\prime }+y \sin \left (x \right )&=\sin \left (x \right ) y^{2} \\ \end{align*}

[_separable]

7.441

19798

\begin{align*} \left (-x^{2}+1\right ) y^{\prime }-y x&=a x y^{2} \\ \end{align*}

[_separable]

8.297

19802

\begin{align*} y \sqrt {x^{2}-1}+x \sqrt {y^{2}-1}\, y^{\prime }&=0 \\ \end{align*}

[_separable]

7.114

19803

\begin{align*} \left (1+{\mathrm e}^{y}\right ) \cos \left (x \right )+{\mathrm e}^{y} \sin \left (x \right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

3.292

19804

\begin{align*} \sqrt {2 a y-y^{2}}\, \csc \left (x \right )+y \tan \left (x \right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

11.336

19805

\begin{align*} y \left (y+3\right ) y^{\prime }&=x \left (3+2 y\right ) \\ \end{align*}

[_separable]

3.711

19808

\begin{align*} \sin \left (x \right ) \cos \left (y\right )+\cos \left (x \right ) \sin \left (y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

3.759

19896

\begin{align*} \left (1-x \right ) y^{\prime }-y-1&=0 \\ \end{align*}

[_separable]

3.862

19898

\begin{align*} -x y^{\prime }+y&=a \left (y^{\prime }+y^{2}\right ) \\ \end{align*}

[_separable]

6.586

19899

\begin{align*} 3 \,{\mathrm e}^{x} \tan \left (y\right )+\left (1-{\mathrm e}^{x}\right ) \sec \left (y\right )^{2} y^{\prime }&=0 \\ \end{align*}

[_separable]

4.550

19913

\begin{align*} a \left (x y^{\prime }+2 y\right )&=x y y^{\prime } \\ \end{align*}

[_separable]

9.839

19938

\begin{align*} \sec \left (x \right )^{2} \tan \left (y\right )+\sec \left (y\right )^{2} \tan \left (x \right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

27.498

19939

\begin{align*} y^{2}+x y^{2}+\left (x^{2}-x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

7.480

19952

\begin{align*} \left (x +1\right ) y^{\prime }+1&=2 \,{\mathrm e}^{y} \\ \end{align*}

[_separable]

5.426

19958

\begin{align*} y y^{\prime }&=a x \\ \end{align*}

[_separable]

8.958

19963

\begin{align*} -x y^{\prime }+y&=b \left (1+x^{2} y^{\prime }\right ) \\ \end{align*}

[_separable]

3.748

19990

\begin{align*} x y \left (-x y^{\prime }+y\right )&=y y^{\prime }+x \\ \end{align*}

[_separable]

5.485

20019

\begin{align*} \sqrt {x}\, y^{\prime }&=\sqrt {y} \\ \end{align*}

[_separable]

10.427

20226

\begin{align*} x \cos \left (y\right )^{2}&=y \cos \left (x \right )^{2} y^{\prime } \\ \end{align*}

[_separable]

6.483

20227

\begin{align*} y^{\prime }&={\mathrm e}^{x -y}+x^{2} {\mathrm e}^{-y} \\ \end{align*}

[_separable]

2.961

20228

\begin{align*} x^{2} y^{\prime }+y&=1 \\ \end{align*}

[_separable]

3.660

20229

\begin{align*} 2 y+\left (x^{2}+1\right ) \arctan \left (x \right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

4.696

20230

\begin{align*} x y^{2}+x +\left (y+x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

4.801

20231

\begin{align*} y^{\prime }&={\mathrm e}^{x +y}+x^{2} {\mathrm e}^{y} \\ \end{align*}

[_separable]

2.997

20232

\begin{align*} \left (3+2 \sin \left (x \right )+\cos \left (x \right )\right ) y^{\prime }&=1+2 \sin \left (y\right )+\cos \left (y\right ) \\ \end{align*}

[_separable]

10.300

20233

\begin{align*} \frac {\cos \left (y\right )^{2} y^{\prime }}{x}+\frac {\cos \left (x \right )^{2}}{y}&=0 \\ \end{align*}

[_separable]

6.821

20234

\begin{align*} \left (1+{\mathrm e}^{x}\right ) y y^{\prime }&=\left (y+1\right ) {\mathrm e}^{x} \\ \end{align*}

[_separable]

5.272

20235

\begin{align*} \csc \left (x \right ) \ln \left (y\right ) y^{\prime }+x^{2} y^{2}&=0 \\ \end{align*}

[_separable]

5.539

20236

\begin{align*} y^{\prime }&=\frac {\sin \left (x \right )+x \cos \left (x \right )}{y \left (2 \ln \left (y\right )+1\right )} \\ \end{align*}

[_separable]

0.526

20237

\begin{align*} \cos \left (y\right ) \ln \left (\sec \left (x \right )+\tan \left (x \right )\right )&=\cos \left (x \right ) \ln \left (\sec \left (y\right )+\tan \left (y\right )\right ) y^{\prime } \\ \end{align*}

[_separable]

35.875

20238

\begin{align*} y^{2}+x y^{2}+\left (x^{2}-x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

6.701

20239

\begin{align*} \left (\sin \left (y\right )+y \cos \left (y\right )\right ) y^{\prime }-\left (2 \ln \left (x \right )+1\right ) x&=0 \\ \end{align*}

[_separable]

5.245

20240

\begin{align*} 3 \,{\mathrm e}^{x} \tan \left (y\right )+\left (1-{\mathrm e}^{x}\right ) \sec \left (y\right )^{2} y^{\prime }&=0 \\ \end{align*}

[_separable]

5.202

20241

\begin{align*} -x y^{\prime }+y&=a \left (y^{\prime }+y^{2}\right ) \\ \end{align*}

[_separable]

4.983

20282

\begin{align*} x +y^{\prime }&=x \,{\mathrm e}^{\left (n -1\right ) y} \\ \end{align*}

[_separable]

5.003

20311

\begin{align*} y^{\prime }&={\mathrm e}^{3 x -2 y}+x^{2} {\mathrm e}^{-2 y} \\ \end{align*}

[_separable]

2.210

20316

\begin{align*} y^{\prime }&=\frac {\left (2 \ln \left (x \right )+1\right ) x}{\sin \left (y\right )+y \cos \left (y\right )} \\ \end{align*}

[_separable]

3.824

20317

\begin{align*} s^{\prime }+x^{2}&=x^{2} {\mathrm e}^{3 s} \\ \end{align*}

[_separable]

3.134

20398

\begin{align*} y&=3 x +a \ln \left (y^{\prime }\right ) \\ \end{align*}

[_separable]

6.319

20410

\begin{align*} x&=y+a \ln \left (y^{\prime }\right ) \\ \end{align*}

[_separable]

5.169

20481

\begin{align*} -x y^{\prime }+y&=a \left (y^{\prime }+y^{2}\right ) \\ \end{align*}

[_separable]

5.903

20482

\begin{align*} -x y^{\prime }+y&=b \left (1+x^{2} y^{\prime }\right ) \\ \end{align*}

[_separable]

2.685

20677

\begin{align*} -x y^{\prime }+y&=0 \\ \end{align*}

[_separable]

2.859

20678

\begin{align*} \cot \left (y\right )-\tan \left (x \right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

3.013

20681

\begin{align*} \sec \left (x \right )^{2} \tan \left (y\right )+\sec \left (y\right )^{2} \tan \left (x \right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

28.813

20682

\begin{align*} 1+y^{2}-x y y^{\prime }&=0 \\ \end{align*}

[_separable]

13.916

20728

\begin{align*} x y \left (-x y^{\prime }+y\right )&=y y^{\prime }+x \\ \end{align*}

[_separable]

6.948

20811

\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{x}}{2 y} \\ \end{align*}

[_separable]

4.166

20812

\begin{align*} y^{\prime }&=y^{2} \left (t^{2}+1\right ) \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

3.740

20813

\begin{align*} y^{\prime }&=\frac {\sqrt {1-y^{2}}}{x} \\ \end{align*}

[_separable]

11.790

20814

\begin{align*} x y^{\prime }&=y \left (-2 y+1\right ) \\ y \left (1\right ) &= 2 \\ \end{align*}

[_separable]

6.117

20815

\begin{align*} y^{\prime }-y \sin \left (x \right )&=\sin \left (x \right ) \\ \end{align*}

[_separable]

3.976

20817

\begin{align*} s^{\prime }+2 s&=s t^{2} \\ s \left (0\right ) &= 1 \\ \end{align*}

[_separable]

4.470

20826

\begin{align*} y^{\prime }&=\frac {x}{y}-\frac {x}{y+1} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

3.242

20829

\begin{align*} y^{\prime }+2 y x&=2 x y^{2} \\ \end{align*}

[_separable]

9.329

20969

\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{-y^{2}}}{y \left (x^{2}+2 x \right )} \\ y \left (2\right ) &= 0 \\ \end{align*}

[_separable]

5.855

20970

\begin{align*} y^{\prime }&=\frac {y \ln \left (y\right )}{\sin \left (x \right )} \\ y \left (\frac {\pi }{2}\right ) &= {\mathrm e}^{{\mathrm e}} \\ \end{align*}

[_separable]

8.427

20971

\begin{align*} y^{\prime }&=\frac {\cos \left (x \right )}{\cos \left (y\right )^{2}} \\ y \left (\pi \right ) &= \frac {\pi }{4} \\ \end{align*}

[_separable]

4.049

20973

\begin{align*} y^{\prime }&=\frac {2 y \left (-1+y\right )}{x \left (2-y\right )} \\ \end{align*}

[_separable]

27.250

20975

\begin{align*} y^{\prime }&=f \left (x \right ) y \ln \left (\frac {1}{y}\right ) \\ \end{align*}

[_separable]

4.644

20983

\begin{align*} y&=x y^{\prime }+a y^{\prime }+b \\ \end{align*}

[_separable]

3.944

21005

\begin{align*} x^{\prime }+\frac {\left (2 t^{3}+\sin \left (t \right )+5\right ) x}{t^{12}+5}&=0 \\ x \left (0\right ) &= 0 \\ \end{align*}

[_separable]

32.652

21008

\begin{align*} x^{\prime }-2 x \cos \left (t \right )&=\cos \left (t \right ) \\ x \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}

[_separable]

4.665

21009

\begin{align*} x^{\prime }+\frac {x}{t^{2}-1}&=0 \\ x \left (-2\right ) &= 1 \\ \end{align*}

[_separable]

4.472

21013

\begin{align*} x^{\prime }&=2 x t \\ x \left (0\right ) &= 4 \\ \end{align*}

[_separable]

4.064

21014

\begin{align*} x^{\prime }&=-x t^{2} \\ \end{align*}

[_separable]

4.046

21024

\begin{align*} x^{\prime }&=\frac {x}{t^{2}+1} \\ x \left (0\right ) &= 1 \\ \end{align*}

[_separable]

4.264

21031

\begin{align*} x^{\prime }+\frac {\sin \left (t \right ) x}{1+{\mathrm e}^{t}}&=0 \\ \end{align*}

[_separable]

5.748

21054

\begin{align*} x^{\prime }&=4 t^{3} x^{4} \\ \end{align*}

[_separable]

10.135

21055

\begin{align*} x^{\prime }&=-t x^{2} \\ \end{align*}

[_separable]

13.230

21056

\begin{align*} x^{\prime }&={\mathrm e}^{t} \left (x^{2}+1\right ) \\ x \left (0\right ) &= 0 \\ \end{align*}

[_separable]

5.875

21057

\begin{align*} x^{\prime }&=\frac {t}{x} \\ x \left (\sqrt {2}\right ) &= 1 \\ \end{align*}

[_separable]

19.966

21058

\begin{align*} x^{\prime }&=-\frac {t}{4 x^{3}} \\ x \left (1\right ) &= 1 \\ \end{align*}

[_separable]

7.780

21059

\begin{align*} x^{\prime }&=-t^{2} x^{2} \\ x \left (1\right ) &= 2 \\ \end{align*}

[_separable]

13.530

21060

\begin{align*} x^{\prime }&=5 t \sqrt {x} \\ x \left (0\right ) &= 1 \\ \end{align*}

[_separable]

20.065

21061

\begin{align*} x^{\prime }&=4 t^{3} \sqrt {x} \\ x \left (0\right ) &= 1 \\ \end{align*}

[_separable]

20.529

21062

\begin{align*} x^{\prime }&=2 t \sqrt {x} \\ x \left (a \right ) &= 0 \\ \end{align*}

[_separable]

33.448

21063

\begin{align*} x^{\prime }&=-\left (1+p \right ) t^{p} x^{2} \\ \end{align*}

[_separable]

7.784

21065

\begin{align*} 2 x^{2}+1&=\left (y^{5}-1\right ) y^{\prime } \\ \end{align*}

[_separable]

3.256

21075

\begin{align*} x -2 y^{3} y^{\prime }&=0 \\ \end{align*}

[_separable]

6.950

21083

\begin{align*} x y y^{\prime }+1+y^{2}&=0 \\ \end{align*}

[_separable]

7.589

21092

\begin{align*} x^{\prime }+2 x t&=-4 t x^{3} \\ \end{align*}

[_separable]

15.328

21333

\begin{align*} y^{\prime }&=f \left (x \right ) g \left (y\right ) \\ \end{align*}

[_separable]

2.065

21334

\begin{align*} x y^{\prime }-y&=0 \\ \end{align*}

[_separable]

3.565

21336

\begin{align*} y y^{\prime }+x&=0 \\ \end{align*}

[_separable]

10.963

21337

\begin{align*} x y^{\prime }+y&=0 \\ \end{align*}

[_separable]

5.042

21338

\begin{align*} x y^{\prime }-2 y&=0 \\ \end{align*}

[_separable]

6.542

21340

\begin{align*} 2 x \left (y+1\right )-y y^{\prime }&=0 \\ y \left (0\right ) &= -2 \\ \end{align*}

[_separable]

5.399

21341

\begin{align*} y^{\prime }&=-\frac {x}{y} \\ \end{align*}

[_separable]

8.774

21342

\begin{align*} y^{\prime }&=\frac {2 y}{x} \\ \end{align*}

[_separable]

4.783

21343

\begin{align*} -2+2 y+x^{2} \sin \left (y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

4.606

21344

\begin{align*} y^{\prime }&=\frac {x +1}{1+y^{2}} \\ \end{align*}

[_separable]

2.885

21345

\begin{align*} y^{\prime }&=\frac {a x +b}{y^{n}+d} \\ \end{align*}

[_separable]

3.655

21346

\begin{align*} y^{\prime }&=-\frac {x}{y} \\ y \left (0\right ) &= a_{0} \\ \end{align*}

[_separable]

11.514

21347

\begin{align*} y^{\prime }&=x^{2} y \\ \end{align*}

[_separable]

4.405

21348

\begin{align*} y^{\prime }&=\frac {1+y^{2}}{x^{2}+1} \\ \end{align*}

[_separable]

4.786

21349

\begin{align*} x \cos \left (x \right )+\left (1-6 y^{5}\right ) y^{\prime }&=0 \\ y \left (\pi \right ) &= 0 \\ \end{align*}

[_separable]

4.611

21350

\begin{align*} y^{\prime }&=\frac {x}{y^{3}} \\ \end{align*}

[_separable]

5.296

21351

\begin{align*} y^{\prime }&=\frac {x}{y^{2} \sqrt {x^{2}+1}} \\ \end{align*}

[_separable]

3.904

21352

\begin{align*} y^{\prime }&=2 y x \\ y \left (0\right ) &= 5 \\ \end{align*}

[_separable]

4.319

21353

\begin{align*} x y^{2}-x +\left (y+x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

4.492

21354

\begin{align*} y^{\prime }&=x^{2} y^{3} \\ \end{align*}

[_separable]

10.948

21355

\begin{align*} y^{\prime }&=\frac {y \ln \left (x \right )}{x} \\ \end{align*}

[_separable]

5.922

21356

\begin{align*} y^{\prime }&=x^{2} y \\ \end{align*}

[_separable]

4.442

21357

\begin{align*} {\mathrm e}^{x}-y y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

4.323

21371

\begin{align*} \left (x -4\right ) y^{4}-x^{3} \left (y^{2}-3\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

3.931

21372

\begin{align*} 1+y^{2}+\left (x^{2}+1\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

5.128

21373

\begin{align*} \sin \left (y\right ) x +\left (x^{2}+1\right ) \cos \left (y\right ) y^{\prime }&=0 \\ y \left (1\right ) &= \frac {\pi }{2} \\ \end{align*}

[_separable]

4.157

21401

\begin{align*} y^{\prime }+2 y x&=0 \\ \end{align*}

[_separable]

4.225

21406

\begin{align*} y^{\prime }&=2 y x -x \\ \end{align*}

[_separable]

3.800

21411

\begin{align*} -x y^{\prime }+y&=0 \\ \end{align*}

[_separable]

3.802

21412

\begin{align*} x y^{\prime }-y+y^{2}&=0 \\ \end{align*}

[_separable]

5.599

21427

\begin{align*} \frac {y^{\prime }}{x}-\frac {y}{x^{2}}&=0 \\ \end{align*}

[_separable]

4.240

21432

\begin{align*} y^{\prime }+q \left (x \right ) y&=0 \\ y \left (\textit {x\_0} \right ) &= y_{0} \\ \end{align*}

[_separable]

4.694

21439

\begin{align*} \left (x^{2}+1\right ) y^{\prime }+4 y x&=x \\ y \left (2\right ) &= 1 \\ \end{align*}

[_separable]

4.497

21442

\begin{align*} y^{\prime }-2 y x&=x \\ \end{align*}

[_separable]

4.302

21458

\begin{align*} y^{\prime }+y x&=x y^{2} \\ \end{align*}

[_separable]

8.438

21791

\begin{align*} y y^{\prime }+x&=0 \\ \end{align*}

[_separable]

12.487

21795

\begin{align*} y^{\prime }&=-\frac {x}{4 y} \\ \end{align*}

[_separable]

10.782

21796

\begin{align*} y^{\prime }&=\frac {x}{y} \\ \end{align*}

[_separable]

14.915

21797

\begin{align*} 3 x^{2}-2 y^{3} y^{\prime }&=0 \\ \end{align*}

[_separable]

7.895

21798

\begin{align*} 1+y+y^{2}+x \left (x^{2}-4\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

8.018

21799

\begin{align*} r^{\prime } \sin \left (t \right )+r \cos \left (t \right )&=0 \\ \end{align*}

[_separable]

6.407

21801

\begin{align*} y y^{\prime }+x&=0 \\ y \left (1\right ) &= 2 \\ \end{align*}

[_separable]

13.566

21802

\begin{align*} r^{\prime }&=r \tan \left (t \right ) \\ r \left (0\right ) &= 1 \\ \end{align*}

[_separable]

6.412

21814

\begin{align*} \sec \left (x \right )^{2} \tan \left (y\right )+\sec \left (y\right )^{2} \tan \left (x \right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

26.224

21821

\begin{align*} x^{3} y^{\prime }-x^{2} y&=x^{5} y \\ \end{align*}

[_separable]

5.023

21842

\begin{align*} x y^{\prime }-y&=y^{3} \\ \end{align*}

[_separable]

15.526

21843

\begin{align*} y^{\prime }+3 x^{2} y&=3 x^{2} \\ \end{align*}

[_separable]

4.785

21844

\begin{align*} 4 x^{2} y^{2} y^{\prime }-3 x y^{3}&=x^{2} y^{3}+2 x^{2} y^{\prime } \\ \end{align*}

[_separable]

5.694

21926

\begin{align*} x^{2} y^{\prime }+y^{2}&=x^{2} y y^{\prime }-x y^{2} \\ \end{align*}

[_separable]

10.346

21965

\begin{align*} y^{\prime }+2 x y^{2}&=0 \\ \end{align*}

[_separable]

11.209

21977

\begin{align*} y^{\prime }&=\frac {y^{2}}{x} \\ \end{align*}

[_separable]

5.119

21980

\begin{align*} \sin \left (x \right )+y^{2} y^{\prime }&=0 \\ \end{align*}

[_separable]

4.453

21986

\begin{align*} y^{\prime }&=y x \\ \end{align*}

[_separable]

5.540

21988

\begin{align*} y^{\prime }&=\frac {x^{2}}{y^{2}} \\ \end{align*}

[_separable]

15.181

21989

\begin{align*} y^{\prime }&=-\frac {2 y}{x} \\ \end{align*}

[_separable]

7.689

21991

\begin{align*} x -y^{2} y^{\prime }&=0 \\ \end{align*}

[_separable]

8.061

21992

\begin{align*} y^{\prime }&=x^{3} y^{2} \\ \end{align*}

[_separable]

13.472

21994

\begin{align*} y^{\prime }&=\frac {x +1}{1+y^{4}} \\ \end{align*}

[_separable]

3.655

21995

\begin{align*} {\mathrm e}^{x}-y y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

5.832

21996

\begin{align*} x \cos \left (x \right )+\left (1-6 y^{5}\right ) y^{\prime }&=0 \\ y \left (\pi \right ) &= 0 \\ \end{align*}

[_separable]

5.171

21997

\begin{align*} y y^{\prime }+x&=0 \\ \end{align*}

[_separable]

12.655

21998

\begin{align*} \frac {1}{x}-\frac {y^{\prime }}{y}&=0 \\ \end{align*}

[_separable]

5.012

22000

\begin{align*} x +\frac {y^{\prime }}{y}&=0 \\ \end{align*}

[_separable]

5.390

22001

\begin{align*} x^{2}+1+\left (y^{2}+y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

4.593

22002

\begin{align*} \sin \left (x \right )+y y^{\prime }&=0 \\ y \left (0\right ) &= -2 \\ \end{align*}

[_separable]

5.247

22003

\begin{align*} x^{2}+1+\frac {y^{\prime }}{y}&=0 \\ y \left (-1\right ) &= 1 \\ \end{align*}

[_separable]

6.925

22004

\begin{align*} x \,{\mathrm e}^{x}+\left (y^{5}-1\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

4.088

22005

\begin{align*} y^{\prime }&=\frac {y}{x} \\ \end{align*}

[_separable]

4.267

22006

\begin{align*} y^{\prime }&=\frac {x \,{\mathrm e}^{x}}{2 y} \\ \end{align*}

[_separable]

3.573

22007

\begin{align*} y^{\prime }&=\frac {x^{2} y-y}{y+1} \\ y \left (3\right ) &= -1 \\ \end{align*}

[_separable]

6.846

22011

\begin{align*} y^{\prime }&=y x \\ y \left (1\right ) &= -2 \\ \end{align*}

[_separable]

5.579

22022

\begin{align*} \left (x^{2}+1\right ) y^{\prime }+2 y x&=0 \\ \end{align*}

[_separable]

3.772

22026

\begin{align*} y^{\prime }&=-\frac {2 x y}{x^{2}+1} \\ y \left (2\right ) &= -5 \\ \end{align*}

[_separable]

5.274

22032

\begin{align*} x y^{\prime }+y&=0 \\ \end{align*}

[_separable]

6.616

22034

\begin{align*} y \sin \left (x \right )+y \cos \left (x \right ) x +\left (x \sin \left (x \right )+1\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

23.178

22035

\begin{align*} -x y^{\prime }+y&=0 \\ \end{align*}

[_separable]

4.888

22036

\begin{align*} x y^{\prime }-y+y^{2}&=0 \\ \end{align*}

[_separable]

7.576

22039

\begin{align*} y^{\prime }&=2 y x -x \\ \end{align*}

[_separable]

4.969

22042

\begin{align*} y+1-x y^{\prime }&=0 \\ \end{align*}

[_separable]

5.685

22043

\begin{align*} \left (1-x \right ) y^{\prime }+y&=0 \\ \end{align*}

[_separable]

5.601

22047

\begin{align*} 3 x^{2} y-x^{2}+y^{\prime }&=0 \\ \end{align*}

[_separable]

4.967

22048

\begin{align*} 1-2 x y y^{\prime }&=0 \\ \end{align*}

[_separable]

7.983

22050

\begin{align*} 3 x y^{\prime }+y&=0 \\ \end{align*}

[_separable]

6.817

22051

\begin{align*} 2 x y^{2}+\frac {x}{y^{2}}+4 x^{2} y y^{\prime }&=0 \\ \end{align*}

[_separable]

10.912

22058

\begin{align*} y^{\prime }-2 y x&=x \\ \end{align*}

[_separable]

4.922

22063

\begin{align*} y^{\prime }+y x&=x y^{2} \\ \end{align*}

[_separable]

10.085

22068

\begin{align*} y^{\prime }+x^{2} y&=x^{2} \\ \end{align*}

[_separable]

5.388

22070

\begin{align*} y^{\prime }+6 y x&=0 \\ y \left (\pi \right ) &= 5 \\ \end{align*}

[_separable]

6.045

22071

\begin{align*} y^{\prime }-\frac {3 y}{x^{2}}&=\frac {1}{x^{2}} \\ \end{align*}

[_separable]

5.180

22075

\begin{align*} y^{\prime }+y x&=6 x \sqrt {y} \\ \end{align*}

[_separable]

10.457

22087

\begin{align*} y^{\prime }-2 y&=y x \\ \end{align*}

[_separable]

6.350

22090

\begin{align*} y^{\prime }-\frac {2 y}{x}&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

9.093

22091

\begin{align*} y^{\prime }-\frac {2 y}{x}&=0 \\ y \left (1\right ) &= 3 \\ \end{align*}

[_separable]

8.174

22319

\begin{align*} y^{\prime }&=\frac {-x +3}{y+5} \\ \end{align*}

[_separable]

15.756

22326

\begin{align*} y^{\prime }+y \tan \left (x \right )&=0 \\ y \left (\pi \right ) &= 4 \\ \end{align*}

[_separable]

6.898

22352

\begin{align*} y^{\prime }&=\frac {y}{x} \\ \end{align*}

[_separable]

5.055

22359

\begin{align*} y^{\prime }&=-\frac {x}{y} \\ y \left (1\right ) &= 2 \\ \end{align*}

[_separable]

17.495

22360

\begin{align*} y^{\prime }&=-\frac {y}{x} \\ y \left (1\right ) &= 3 \\ \end{align*}

[_separable]

7.937

22361

\begin{align*} 3 x \left (1+y^{2}\right )+y \left (x^{2}+2\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

8.542

22362

\begin{align*} 2 y+{\mathrm e}^{-3 x} y^{\prime }&=0 \\ \end{align*}

[_separable]

7.045

22363

\begin{align*} y^{\prime }&=\frac {x y^{2}+x}{4 y} \\ y \left (1\right ) &= 0 \\ \end{align*}

[_separable]

5.670

22364

\begin{align*} x y^{\prime }&=1+y^{2} \\ \end{align*}

[_separable]

8.016

22365

\begin{align*} \sin \left (y\right )^{2}+\cos \left (x \right )^{2} y^{\prime }&=0 \\ y \left (\frac {\pi }{4}\right ) &= \frac {\pi }{4} \\ \end{align*}

[_separable]

6.239

22366

\begin{align*} x \sqrt {1+y^{2}}&=y y^{\prime } \sqrt {x^{2}+1} \\ \end{align*}

[_separable]

10.897

22367

\begin{align*} 2 \cos \left (x \right ) y+3 \sin \left (x \right ) y^{\prime }&=0 \\ y \left (\frac {\pi }{2}\right ) &= 2 \\ \end{align*}

[_separable]

8.782

22368

\begin{align*} y^{\prime }&=8 y x +3 y \\ \end{align*}

[_separable]

6.680

22370

\begin{align*} y+\left (x^{3}+x^{3} y^{2}\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

9.478

22371

\begin{align*} y^{\prime }&=-\frac {3 x +x y^{2}}{x^{2} y+2 y} \\ \end{align*}

[_separable]

7.667

22372

\begin{align*} y^{\prime }&=\frac {\left (-1+y\right ) \left (y+3\right )}{\left (-2+y\right ) \left (x +3\right )} \\ \end{align*}

[_separable]

19.217

22373

\begin{align*} r^{\prime }&=\frac {\sin \left (t \right )+{\mathrm e}^{r} \sin \left (t \right )}{3 \,{\mathrm e}^{r}+{\mathrm e}^{r} \cos \left (2 t \right )} \\ r \left (\frac {\pi }{2}\right ) &= 0 \\ \end{align*}

[_separable]

10.088

22374

\begin{align*} r^{\prime }&=\frac {\sin \left (t \right )+{\mathrm e}^{r} \sin \left (t \right )}{3 \,{\mathrm e}^{r}+{\mathrm e}^{r} \cos \left (2 t \right )} \\ r \left (\frac {\pi }{2}\right ) &= 0 \\ \end{align*}

[_separable]

8.866

22375

\begin{align*} x^{3} {\mathrm e}^{2 x^{2}+3 y^{2}}-y^{3} {\mathrm e}^{-x^{2}-2 y^{2}} y^{\prime }&=0 \\ \end{align*}

[_separable]

8.553

22410

\begin{align*} 3 x +4 y y^{\prime }&=0 \\ \end{align*}

[_separable]

20.371

22421

\begin{align*} \left (x^{2}+1\right ) y^{\prime }+2 y x&=0 \\ y \left (1\right ) &= -3 \\ \end{align*}

[_separable]

4.926

22439

\begin{align*} i^{\prime }&=\frac {t -i t}{t^{2}+1} \\ i \left (0\right ) &= 0 \\ \end{align*}

[_separable]

7.033

22508

\begin{align*} \left (x^{2}+1\right ) \left (y^{3}-1\right )&=x^{2} y^{2} y^{\prime } \\ \end{align*}

[_separable]

9.889

22512

\begin{align*} 3-y+2 x y^{\prime }&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}

[_separable]

13.102

22514

\begin{align*} s^{2} t s^{\prime }+t^{2}+4&=0 \\ \end{align*}

[_separable]

7.330

22538

\begin{align*} \sin \left (x \right ) \cos \left (y\right )+\cos \left (x \right ) \sin \left (y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

6.621

22543

\begin{align*} \left (y+1\right ) y^{\prime }&=x \sqrt {y} \\ \end{align*}

[_separable]

7.935

22544

\begin{align*} \tan \left (x \right ) \sin \left (y\right )+3 y^{\prime }&=0 \\ \end{align*}

[_separable]

6.931

22548

\begin{align*} x^{2} y+\left (x^{3}+1\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

8.542

22555

\begin{align*} q^{\prime }&=\frac {p \,{\mathrm e}^{p^{2}-q^{2}}}{q} \\ \end{align*}

[_separable]

10.206

22557

\begin{align*} \left (x +x \cos \left (y\right )\right ) y^{\prime }-\sin \left (y\right )-y&=0 \\ \end{align*}

[_separable]

15.060

22560

\begin{align*} r^{\prime }&=\frac {r \left (1+\ln \left (t \right )\right )}{t \left (1+\ln \left (r\right )\right )} \\ \end{align*}

[_separable]

12.393

22562

\begin{align*} u v-2 v+\left (-u^{2}+u \right ) v^{\prime }&=0 \\ \end{align*}

[_separable]

10.099

22566

\begin{align*} x \sqrt {1-y^{2}}+y \sqrt {-x^{2}+1}\, y^{\prime }&=0 \\ \end{align*}

[_separable]

23.494

22568

\begin{align*} y^{\prime }&=\frac {\left (y+3\right )^{2}}{4 x^{2}} \\ \end{align*}

[_separable]

19.984

22582

\begin{align*} {\mathrm e}^{2 x -y}+{\mathrm e}^{y-2 x} y^{\prime }&=0 \\ \end{align*}

[_separable]

9.953

22586

\begin{align*} y^{\prime } \sqrt {x^{3}+1}&=x^{2} y+x^{2} \\ \end{align*}

[_separable]

15.723

22592

\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{x -y}}{y} \\ \end{align*}

[_separable]

15.366

22594

\begin{align*} y^{\prime } \sqrt {-x^{2}+1}+\sqrt {1-y^{2}}&=0 \\ \end{align*}

[_separable]

69.458

22595

\begin{align*} 1+y^{2}+\left (x^{2}+1\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

11.714

22608

\begin{align*} y^{\prime }&=\frac {y}{x} \\ \end{align*}

[_separable]

7.496

22947

\begin{align*} y y^{\prime }&=x^{2} \\ \end{align*}

[_separable]

16.799

22948

\begin{align*} \left (x +1\right ) y^{\prime }&=y+1 \\ \end{align*}

[_separable]

9.490

22949

\begin{align*} 1+y^{2}&=\left (x^{2}+1\right ) y^{\prime } \\ \end{align*}

[_separable]

9.913

22950

\begin{align*} y^{\prime } \sin \left (y\right )&=\sec \left (x \right )^{2} \\ \end{align*}

[_separable]

5.165

22951

\begin{align*} x^{\prime }&=\frac {x}{t} \\ \end{align*}

[_separable]

7.656

22952

\begin{align*} \left (-x^{2}+1\right ) y^{\prime }&=1-y^{2} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

12.932

22953

\begin{align*} \frac {\tan \left (y\right )}{\cos \left (x \right )}&=\cos \left (x \right ) y^{\prime } \\ y \left (\frac {\pi }{4}\right ) &= \frac {\pi }{2} \\ \end{align*}

[_separable]

11.020

22954

\begin{align*} x y^{\prime }&=\left (x +1\right ) y^{2} \\ y \left (1\right ) &= 1 \\ \end{align*}

[_separable]

10.296

22955

\begin{align*} x \cos \left (y\right ) y^{\prime }-\left (x^{2}+1\right ) \sin \left (y\right )&=0 \\ y \left (1\right ) &= \frac {\pi }{2} \\ \end{align*}

[_separable]

9.661

22956

\begin{align*} \left (x^{2}-1\right ) y^{\prime }&=\left (-1+y\right ) x \\ \end{align*}

[_separable]

17.425

22957

\begin{align*} \left (y+2\right ) x +y \left (x +2\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

26.763

22958

\begin{align*} x y \left (x^{2}+1\right ) y^{\prime }-y^{2}&=1 \\ \end{align*}

[_separable]

24.758

22959

\begin{align*} x y^{\prime }+y&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}

[_separable]

11.985

22960

\begin{align*} x y^{\prime }-1+y&=0 \\ y \left (1\right ) &= 2 \\ \end{align*}

[_separable]

8.740

22962

\begin{align*} x^{2} y^{\prime }+2 y x&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}

[_separable]

13.663

22963

\begin{align*} x \cos \left (y\right ) y^{\prime }+\sin \left (y\right )&=5 \\ \end{align*}

[_separable]

16.299

22964

\begin{align*} y^{\prime }&=\frac {\sin \left (x \right ) \sin \left (y\right )}{\cos \left (x \right ) \cos \left (y\right )} \\ \end{align*}

[_separable]

6.385

22965

\begin{align*} x \sec \left (y\right )^{2} y^{\prime }+1+\tan \left (y\right )&=0 \\ \end{align*}

[_separable]

49.997

22966

\begin{align*} {\mathrm e}^{y} \left (x y^{\prime }+1\right )&=5 \\ \end{align*}

[_separable]

16.274

22977

\begin{align*} y^{\prime }+2 y x&=x \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

7.365

22978

\begin{align*} y^{\prime }-2 y x&=3 x \\ y \left (1\right ) &= 1 \\ \end{align*}

[_separable]

7.562

22986

\begin{align*} y^{\prime }-y \sin \left (x \right )&=\sin \left (x \right ) \\ y \left (0\right ) &= 2 \\ \end{align*}

[_separable]

9.102

22988

\begin{align*} \left (1+{\mathrm e}^{x}\right ) y^{\prime }+y \,{\mathrm e}^{x}&={\mathrm e}^{x} \\ y \left (0\right ) &= 2 \\ \end{align*}

[_separable]

10.290

23056

\begin{align*} \frac {r^{\prime }}{r}&=\tan \left (\theta \right ) \\ \end{align*}

[_separable]

2.847

23057

\begin{align*} \left (1+\cos \left (\theta \right )\right ) r^{\prime }&=-r \sin \left (\theta \right ) \\ \end{align*}

[_separable]

3.503

23058

\begin{align*} \cot \left (\theta \right ) r^{\prime }&=r+b \\ \end{align*}

[_separable]

2.109

23060

\begin{align*} r^{\prime } \left (1+\frac {\cos \left (\theta \right )}{2}\right )-r \sin \left (\theta \right )&=0 \\ r \left (\frac {\pi }{2}\right ) &= 2 a \\ \end{align*}

[_separable]

4.185

23064

\begin{align*} r^{\prime } \left (\sin \left (\theta \right )-m \cos \left (\theta \right )\right )+r \left (\cos \left (\theta \right )+m \sin \left (\theta \right )\right )&=0 \\ \end{align*}

[_separable]

4.280

23127

\begin{align*} x^{\prime }&=\frac {a x^{{5}/{6}}}{\left (-B t +b \right )^{{3}/{2}}} \\ \end{align*}

[_separable]

108.157

23128

\begin{align*} x y^{\prime }-y&=1 \\ y \left (2\right ) &= 3 \\ \end{align*}

[_separable]

3.039

23130

\begin{align*} x y^{\prime }+y^{2}&=1 \\ y \left (-2\right ) &= 1 \\ \end{align*}

[_separable]

6.333

23132

\begin{align*} y^{\prime }&=y x \\ y \left (1\right ) &= 2 \\ \end{align*}

[_separable]

2.414

23134

\begin{align*} x y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}

[_separable]

1.777

23137

\begin{align*} x y^{\prime }+y&=3 \\ \end{align*}

[_separable]

2.110

23142

\begin{align*} y^{\prime }&=x -y x -y+1 \\ \end{align*}

[_separable]

2.427

23143

\begin{align*} \left (x^{2}+4\right ) y^{\prime }+3 y x&=0 \\ \end{align*}

[_separable]

2.615

23147

\begin{align*} \left (1+y^{2}\right ) \cos \left (x \right )&=2 \left (1+\sin \left (x \right )^{2}\right ) y y^{\prime } \\ \end{align*}

[_separable]

10.415

23148

\begin{align*} y^{\prime }&=\frac {y \left (b_{2} x +b_{1} \right )}{x \left (a_{1} +a_{2} y\right )} \\ \end{align*}

[_separable]

3.076

23150

\begin{align*} y^{\prime }&=\frac {\left (-x +a \right ) y}{d \,x^{2}+c x +b} \\ \end{align*}

[_separable]

5.235

23151

\begin{align*} x y^{\prime }+y&=3 \\ \end{align*}

[_separable]

1.964

23154

\begin{align*} x y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}

[_separable]

1.578

23162

\begin{align*} y^{\prime }-\frac {x}{x^{2}+1}&=-\frac {x y}{x^{2}+1} \\ \end{align*}

[_separable]

2.207

23167

\begin{align*} y^{\prime }-2 y x&=4 x \sqrt {y} \\ \end{align*}

[_separable]

3.678

23171

\begin{align*} x y^{\prime }-\frac {y}{\ln \left (x \right )}&=0 \\ y \left ({\mathrm e}\right ) &= -1 \\ \end{align*}

[_separable]

3.324

23172

\begin{align*} \left (x^{2}+1\right ) y^{\prime }+2 y x&=-2 x \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

2.950

23185

\begin{align*} \cos \left (y\right )+\sin \left (x \right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

3.456

23194

\begin{align*} -x y^{\prime }+y&=0 \\ \end{align*}

[_separable]

2.772

23203

\begin{align*} x y^{\prime }+y&=3 \\ \end{align*}

[_separable]

2.602

23256

\begin{align*} 7 y^{\prime }-y x&=0 \\ \end{align*}

[_separable]

2.558

23269

\begin{align*} x y^{\prime }+y&=0 \\ \end{align*}

[_separable]

3.894

23849

\begin{align*} 2 x y^{\prime }+y&=0 \\ \end{align*}

[_separable]

3.658

23850

\begin{align*} \left (x^{2}+1\right ) y y^{\prime }+4&=0 \\ \end{align*}

[_separable]

3.260

23851

\begin{align*} x^{2} y+\left (x +1\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}

[_separable]

4.027

23852

\begin{align*} y x +{\mathrm e}^{x} y^{\prime }&=0 \\ \end{align*}

[_separable]

3.756

23853

\begin{align*} y^{3}+y^{\prime } \sqrt {-x^{2}+1}&=0 \\ \end{align*}

[_separable]

7.263

23854

\begin{align*} \cos \left (x \right ) \cot \left (y\right )+\sin \left (x \right ) \cos \left (y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

7.827

23855

\begin{align*} \left (x^{2}-1\right ) y+\left (1+y^{2}\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

2.727

23856

\begin{align*} y x +\ln \left (y\right ) y^{\prime }&=0 \\ y \left (2\right ) &= 1 \\ \end{align*}

[_separable]

2.575

23857

\begin{align*} \left (x^{3}+1\right ) y^{\prime }+x y^{2}&=0 \\ \end{align*}

[_separable]

3.287

23858

\begin{align*} y^{2} \sec \left (x \right )^{2} y^{\prime }+x&=0 \\ \end{align*}

[_separable]

3.774

23919

\begin{align*} y^{\prime }+y x&=y^{5} x \\ \end{align*}

[_separable]

3.847

23941

\begin{align*} y^{\prime }&=x^{2} y \\ \end{align*}

[_separable]

3.289

23946

\begin{align*} y^{5} x^{2}+{\mathrm e}^{x^{3}} y^{\prime }&=0 \\ y \left (0\right ) &= 2 \\ \end{align*}

[_separable]

3.059

23948

\begin{align*} x \sqrt {a^{2}+x^{2}}&=y \sqrt {y^{2}-a^{2}}\, y^{\prime } \\ \end{align*}

[_separable]

5.300

23956

\begin{align*} y^{\prime }&=\sin \left (y\right )^{3} \cos \left (x \right )^{2} \\ \end{align*}

[_separable]

4.708

23957

\begin{align*} y x -x&=\left (x y^{2}+x -y^{2}-1\right ) y^{\prime } \\ \end{align*}

[_separable]

2.589

23963

\begin{align*} {\mathrm e}^{2 x +3 y}+{\mathrm e}^{4 x -5 y} y^{\prime }&=0 \\ \end{align*}

[_separable]

2.946

23971

\begin{align*} y^{\prime }-y x&=x \\ \end{align*}

[_separable]

2.905

24120

\begin{align*} \left (1-x \right ) y^{\prime }&=y^{2} \\ \end{align*}

[_separable]

2.901

24121

\begin{align*} \sin \left (x \right ) \sin \left (y\right )+\cos \left (x \right ) \cos \left (y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

3.697

24122

\begin{align*} x y^{3}+{\mathrm e}^{x^{2}} y^{\prime }&=0 \\ \end{align*}

[_separable]

5.000

24123

\begin{align*} 2 y-3 x y^{\prime }&=0 \\ \end{align*}

[_separable]

4.426

24124

\begin{align*} m y-n x y^{\prime }&=0 \\ \end{align*}

[_separable]

4.055

24125

\begin{align*} y^{\prime }&=x y^{2} \\ \end{align*}

[_separable]

8.175

24126

\begin{align*} v^{\prime }&=-\frac {v}{p} \\ \end{align*}

[_separable]

3.933

24127

\begin{align*} y \,{\mathrm e}^{2 x}-\left (4+{\mathrm e}^{2 x}\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

5.441

24128

\begin{align*} 1&=b \left (\cos \left (y\right )+x \sin \left (y\right ) y^{\prime }\right ) \\ \end{align*}

[_separable]

5.968

24129

\begin{align*} y x -\left (x +2\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

3.654

24130

\begin{align*} x^{2}+y \left (x -1\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

3.151

24131

\begin{align*} y x +x -\left (1+x^{2}+y^{2}+x^{2} y^{2}\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

2.969

24132

\begin{align*} x \cos \left (y\right )^{2}+\tan \left (y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

34.673

24133

\begin{align*} x y^{3}+\left (y+1\right ) {\mathrm e}^{-x} y^{\prime }&=0 \\ \end{align*}

[_separable]

7.005

24134

\begin{align*} \theta ^{\prime }&=z \left (-z^{2}+1\right ) \sec \left (\theta \right )^{2} \\ \end{align*}

[_separable]

2.937

24135

\begin{align*} x^{\prime }&=\sin \left (x\right )^{2} \cos \left (t \right )^{3} \\ \end{align*}

[_separable]

4.404

24136

\begin{align*} x y^{\prime }+y+x y \left (y^{\prime }+1\right )&=0 \\ \end{align*}

[_separable]

4.203

24137

\begin{align*} \cos \left (y\right )&=x y^{\prime } \\ \end{align*}

[_separable]

4.202

24142

\begin{align*} y-\left ({\mathrm e}^{3 x}+1\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

5.401

24143

\begin{align*} y \ln \left (x \right ) \ln \left (y\right )+y^{\prime }&=0 \\ \end{align*}

[_separable]

3.664

24144

\begin{align*} x y y^{\prime }-y^{2}&=1 \\ y \left (2\right ) &= 1 \\ \end{align*}

[_separable]

6.803

24145

\begin{align*} r^{\prime }&=-2 r t \\ r \left (0\right ) &= r_{0} \\ \end{align*}

[_separable]

3.265

24146

\begin{align*} x y^{2}+{\mathrm e}^{x} y^{\prime }&=0 \\ y \left (\infty \right ) &= {\frac {1}{2}} \\ \end{align*}

[_separable]

4.170

24147

\begin{align*} \left (2 a^{2}-r^{2}\right ) r^{\prime }&=r^{3} \sin \left (\theta \right ) \\ r \left (0\right ) &= a \\ \end{align*}

[_separable]

4.625

24148

\begin{align*} y^{\prime }&=x \,{\mathrm e}^{-y-x^{2}} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

2.497

24187

\begin{align*} 2 y x -y+\left (x^{2}+x \right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

3.689

24190

\begin{align*} 1+y^{2}+\left (y+x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

6.145

24212

\begin{align*} y \left (1+y^{2}\right )+x \left (y^{2}-1\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

12.860

24243

\begin{align*} y^{\prime }&=-2 y x +x \\ \end{align*}

[_separable]

3.394

24268

\begin{align*} y^{\prime }&={\mathrm e}^{x +y} \\ \end{align*}

[_separable]

3.276

24271

\begin{align*} x^{2}+1+x^{2} y^{2} y^{\prime }&=0 \\ \end{align*}

[_separable]

2.989

24274

\begin{align*} y^{\prime }-\cos \left (x \right )&=\tan \left (y\right )^{2} \cos \left (x \right ) \\ \end{align*}

[_separable]

3.052

24278

\begin{align*} y^{\prime }&=\sec \left (x \right )^{2} \sec \left (y\right )^{3} \\ \end{align*}

[_separable]

3.207

24281

\begin{align*} y x +\sqrt {x^{2}+1}\, y^{\prime }&=0 \\ \end{align*}

[_separable]

4.507

24286

\begin{align*} x^{\prime }&=\cos \left (x\right ) \cos \left (t \right )^{2} \\ \end{align*}

[_separable]

3.983

24292

\begin{align*} a^{2} \left (y^{\prime }-1\right )&=x^{2} y^{\prime }+y^{2} \\ \end{align*}

[_separable]

5.727

24296

\begin{align*} y^{\prime } \sqrt {-x^{2}+1}+\sqrt {1-y^{2}}&=0 \\ y \left (0\right ) &= \frac {\sqrt {3}}{2} \\ \end{align*}

[_separable]

17.394

24297

\begin{align*} y^{\prime } \sqrt {-x^{2}+1}+\sqrt {1-y^{2}}&=0 \\ y \left (0\right ) &= -\frac {\sqrt {3}}{2} \\ \end{align*}

[_separable]

17.764

24298

\begin{align*} \sqrt {1-y^{2}}-y^{\prime } \sqrt {-x^{2}+1}&=0 \\ y \left (0\right ) &= \frac {\sqrt {3}}{2} \\ \end{align*}

[_separable]

15.612

24299

\begin{align*} \sqrt {1-y^{2}}-y^{\prime } \sqrt {-x^{2}+1}&=0 \\ y \left (0\right ) &= -\frac {\sqrt {3}}{2} \\ \end{align*}

[_separable]

14.724

24337

\begin{align*} x y^{\prime }-y&=x^{k} y \\ \end{align*}

[_separable]

5.331

24338

\begin{align*} x y^{\prime }-y&=y \\ \end{align*}

[_separable]

5.753

24909

\begin{align*} t y^{\prime }&=y \\ \end{align*}

[_separable]

3.743

24918

\begin{align*} y^{\prime }&=2 y t \\ \end{align*}

[_separable]

4.427

24920

\begin{align*} \left (t +1\right ) y^{\prime }+y&=0 \\ \end{align*}

[_separable]

3.821

24931

\begin{align*} \left (t +1\right ) y^{\prime }+y&=0 \\ y \left (1\right ) &= -9 \\ \end{align*}

[_separable]

4.217

24940

\begin{align*} y^{\prime }&=-y t \\ \end{align*}

[_separable]

4.408

24942

\begin{align*} y^{\prime }&=t y^{2} \\ \end{align*}

[_separable]

10.025

24943

\begin{align*} y^{\prime }&=\frac {t y}{1+y} \\ \end{align*}

[_separable]

4.971

24952

\begin{align*} t y^{\prime }&=y-2 y t \\ \end{align*}

[_separable]

3.249

24953

\begin{align*} y^{\prime }&=t y^{2}-y^{2}+t -1 \\ \end{align*}

[_separable]

5.442

24956

\begin{align*} {\mathrm e}^{t} y^{\prime }&=y^{3}-y \\ \end{align*}

[_separable]

9.739

24957

\begin{align*} y y^{\prime }&=t \\ y \left (2\right ) &= -1 \\ \end{align*}

[_separable]

17.621

24958

\begin{align*} 1-y^{2}-t y y^{\prime }&=0 \\ \end{align*}

[_separable]

19.438

24959

\begin{align*} y^{3} y^{\prime }&=t \\ \end{align*}

[_separable]

6.586

24960

\begin{align*} y^{4} y^{\prime }&=t +2 \\ \end{align*}

[_separable]

4.258

24961

\begin{align*} y^{\prime }&=t y^{2} \\ \end{align*}

[_separable]

7.888

24962

\begin{align*} \tan \left (t \right ) y+y^{\prime }&=\tan \left (t \right ) \\ \end{align*}

[_separable]

4.625

24963

\begin{align*} y^{\prime }&=t^{m} y^{n} \\ \end{align*}

[_separable]

45.994

24967

\begin{align*} t y y^{\prime }+t^{2}+1&=0 \\ \end{align*}

[_separable]

4.097

24968

\begin{align*} y+1+\left (-1+y\right ) \left (t^{2}+1\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

7.473

24969

\begin{align*} 2 y y^{\prime }&={\mathrm e}^{t} \\ \end{align*}

[_separable]

4.184

24970

\begin{align*} \left (1-t \right ) y^{\prime }&=y^{2} \\ \end{align*}

[_separable]

3.830

24972

\begin{align*} y^{\prime }&=4 t y^{2} \\ y \left (1\right ) &= 0 \\ \end{align*}

[_separable]

23.362

24973

\begin{align*} y^{\prime }&=\frac {y x +2 y}{x} \\ y \left (1\right ) &= {\mathrm e} \\ \end{align*}

[_separable]

4.879

24974

\begin{align*} 2 y t +y^{\prime }&=0 \\ y \left (0\right ) &= 4 \\ \end{align*}

[_separable]

4.499

24975

\begin{align*} y^{\prime }&=\frac {\cot \left (y\right )}{t} \\ y \left (1\right ) &= \frac {\pi }{4} \\ \end{align*}

[_separable]

9.899

24976

\begin{align*} \frac {\left (u^{2}+1\right ) y^{\prime }}{y}&=u \\ y \left (0\right ) &= 2 \\ \end{align*}

[_separable]

5.239

24977

\begin{align*} y t -\left (t +2\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

5.262

24978

\begin{align*} y^{\prime }&=\frac {1+y^{2}}{t} \\ y \left (1\right ) &= \sqrt {3} \\ \end{align*}

[_separable]

5.843

24987

\begin{align*} t \left (t +1\right ) y^{\prime }&=y+2 \\ \end{align*}

[_separable]

3.998

24990

\begin{align*} \cos \left (t \right ) y+y^{\prime }&=\cos \left (t \right ) \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

4.658

24997

\begin{align*} t y^{\prime }+2 \ln \left (t \right ) y&=4 \ln \left (t \right ) \\ \end{align*}

[_separable]

6.638

25013

\begin{align*} y t +y^{\prime }&=t y^{3} \\ \end{align*}

[_separable]

10.927

25015

\begin{align*} \left (-t^{2}+1\right ) y^{\prime }-y t&=5 t y^{2} \\ \end{align*}

[_separable]

10.315

25017

\begin{align*} y y^{\prime }+t y^{2}&=t \\ y \left (0\right ) &= -2 \\ \end{align*}

[_separable]

4.959

25038

\begin{align*} y^{\prime }&=y t \\ y \left (1\right ) &= 1 \\ \end{align*}

[_separable]

5.570

25042

\begin{align*} y^{\prime }&=y t \\ y \left (1\right ) &= 1 \\ \end{align*}

[_separable]

4.885

25398

\begin{align*} y^{\prime }&=a \left (t \right ) y \\ \end{align*}

[_separable]

5.296

25430

\begin{align*} y^{\prime }-a \left (t \right ) y&=0 \\ \end{align*}

[_separable]

5.145

25465

\begin{align*} y^{\prime }&=\sin \left (t \right ) y+Q \sin \left (t \right ) \\ \end{align*}

[_separable]

4.786

25466

\begin{align*} y^{\prime }&=\sin \left (t \right ) y \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

6.022

25468

\begin{align*} y^{\prime }&=\frac {y}{t +1} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

5.401

25490

\begin{align*} y^{\prime }&=a \left (t \right ) y \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

12.191

25491

\begin{align*} y^{\prime }&=y t \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

10.610

25492

\begin{align*} y^{\prime }&=t^{m} y^{n} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

166.520

25493

\begin{align*} y^{\prime }&=a \left (t \right ) y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

5.511

25495

\begin{align*} y^{\prime }&=\frac {y}{t} \\ \end{align*}

[_separable]

4.493

25497

\begin{align*} y^{\prime }&=\frac {y^{2}}{t^{2}} \\ \end{align*}

[_separable]

10.564

25498

\begin{align*} y^{\prime }&={\mathrm e}^{t +y} \\ \end{align*}

[_separable]

4.407

25499

\begin{align*} y^{\prime }&=y t +t +y+1 \\ \end{align*}

[_separable]

5.372

25500

\begin{align*} y^{\prime }&=\left (y+4\right ) \cos \left (t \right ) \\ \end{align*}

[_separable]

5.148

25501

\begin{align*} y^{\prime }&={\mathrm e}^{t} y \\ \end{align*}

[_separable]

5.278

25502

\begin{align*} y^{\prime }&=-4 y t \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

5.008

25503

\begin{align*} y^{\prime }&=t y^{3} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

13.158

25504

\begin{align*} \left (t +1\right ) y^{\prime }&=4 y \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

7.372

25656

\begin{align*} y^{2}-1+x y^{\prime }&=0 \\ \end{align*}

[_separable]

9.536

25663

\begin{align*} y^{\prime }&=2 x y^{2} \\ \end{align*}

[_separable]

12.248

25664

\begin{align*} 2 y^{\prime }&=y^{3} \cos \left (x \right ) \\ \end{align*}

[_separable]

7.861

25675

\begin{align*} x y^{\prime }-2 y&=0 \\ \end{align*}

[_separable]

7.974

25676

\begin{align*} y^{\prime }&=-\frac {x}{y} \\ \end{align*}

[_separable]

13.327

25683

\begin{align*} 3 x y^{\prime }+5 y&=10 \\ \end{align*}

[_separable]

8.391

25693

\begin{align*} y^{\prime }+2 x y^{2}&=0 \\ y \left (2\right ) &= {\frac {1}{3}} \\ \end{align*}

[_separable]

12.695

25694

\begin{align*} y^{\prime }+2 x y^{2}&=0 \\ y \left (-2\right ) &= {\frac {1}{2}} \\ \end{align*}

[_separable]

10.764

25695

\begin{align*} y^{\prime }+2 x y^{2}&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

10.377

25696

\begin{align*} y^{\prime }+2 x y^{2}&=0 \\ y \left (\frac {1}{2}\right ) &= -4 \\ \end{align*}

[_separable]

10.834

25706

\begin{align*} x y^{\prime }&=2 y \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

7.024

25709

\begin{align*} x y^{\prime }&=y \\ \end{align*}

[_separable]

4.578

25711

\begin{align*} \left (4-y^{2}\right ) y^{\prime }&=x^{2} \\ \end{align*}

[_separable]

4.029

25712

\begin{align*} \left (y^{3}+1\right ) y^{\prime }&=x^{2} \\ \end{align*}

[_separable]

3.859

25719

\begin{align*} x y^{\prime }&=y \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

4.826

25722

\begin{align*} y y^{\prime }&=3 x \\ y \left (-2\right ) &= 3 \\ \end{align*}

[_separable]

19.938

25723

\begin{align*} y y^{\prime }&=3 x \\ y \left (2\right ) &= -4 \\ \end{align*}

[_separable]

18.672

25732

\begin{align*} y^{\prime }&=x \sqrt {y} \\ y \left (2\right ) &= 1 \\ \end{align*}

[_separable]

25.421

25735

\begin{align*} x y^{\prime }&=2 y \\ \end{align*}

[_separable]

8.296

25736

\begin{align*} x y^{\prime }&=2 y \\ \end{align*}

[_separable]

6.597

25738

\begin{align*} x y^{\prime }&=y \\ \end{align*}

[_separable]

4.850

25743

\begin{align*} 3 x y^{\prime }-2 y&=0 \\ \end{align*}

[_separable]

8.202

25744

\begin{align*} \left (-2+2 y\right ) y^{\prime }&=2 x -1 \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

21.074

25757

\begin{align*} x y^{\prime }+y&=\frac {1}{y^{2}} \\ \end{align*}

[_separable]

13.336

25779

\begin{align*} y^{\prime }&=\sin \left (x \right ) \cos \left (y\right ) \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

9.664

25780

\begin{align*} y^{\prime }&=\sin \left (x \right ) \cos \left (y\right ) \\ y \left (1\right ) &= 0 \\ \end{align*}

[_separable]

5.474

25781

\begin{align*} y^{\prime }&=\sin \left (x \right ) \cos \left (y\right ) \\ y \left (3\right ) &= 3 \\ \end{align*}

[_separable]

9.382

25782

\begin{align*} y^{\prime }&=\sin \left (x \right ) \cos \left (y\right ) \\ y \left (0\right ) &= -{\frac {5}{2}} \\ \end{align*}

[_separable]

8.770

25787

\begin{align*} y y^{\prime }&=-x \\ y \left (1\right ) &= 1 \\ \end{align*}

[_separable]

18.670

25788

\begin{align*} y y^{\prime }&=-x \\ y \left (0\right ) &= 4 \\ \end{align*}

[_separable]

61.079

25793

\begin{align*} y^{\prime }&=x \,{\mathrm e}^{y} \\ y \left (0\right ) &= -2 \\ \end{align*}

[_separable]

6.059

25794

\begin{align*} y^{\prime }&=x \,{\mathrm e}^{y} \\ y \left (1\right ) &= {\frac {5}{2}} \\ \end{align*}

[_separable]

6.238

25819

\begin{align*} x y^{\prime }&=4 y \\ \end{align*}

[_separable]

8.710

25820

\begin{align*} y^{\prime }+2 x y^{2}&=0 \\ \end{align*}

[_separable]

12.817

25821

\begin{align*} y^{\prime }&={\mathrm e}^{3 x +2 y} \\ \end{align*}

[_separable]

5.145

25822

\begin{align*} y \,{\mathrm e}^{x} y^{\prime }&={\mathrm e}^{-y}+{\mathrm e}^{-2 x -y} \\ \end{align*}

[_separable]

6.587

25823

\begin{align*} y^{\prime }&=\frac {y \ln \left (x \right ) x^{2}}{\left (y+1\right )^{2}} \\ \end{align*}

[_separable]

5.948

25824

\begin{align*} y^{\prime }&=\frac {\left (3+2 y\right )^{2}}{\left (5+4 x \right )^{2}} \\ \end{align*}

[_separable]

13.648

25825

\begin{align*} \csc \left (y\right )+\sec \left (x \right )^{2} y^{\prime }&=0 \\ \end{align*}

[_separable]

4.431

25826

\begin{align*} \sin \left (3 x \right )+2 y \cos \left (3 x \right )^{3} y^{\prime }&=0 \\ \end{align*}

[_separable]

11.081

25827

\begin{align*} \left (1+{\mathrm e}^{y}\right )^{2} {\mathrm e}^{-y}+\left (1+{\mathrm e}^{x}\right )^{3} {\mathrm e}^{-x} y^{\prime }&=0 \\ \end{align*}

[_separable]

6.030

25828

\begin{align*} x \sqrt {1+y^{2}}&=y y^{\prime } \sqrt {x^{2}+1} \\ \end{align*}

[_separable]

8.720

25830

\begin{align*} y^{\prime }&=\frac {y \left (x \cos \left (x \right )+\sin \left (x \right )-1\right )}{3 x -3 x \sin \left (x \right )} \\ \end{align*}

[_separable]

14.230

25833

\begin{align*} y y^{\prime }+x&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

60.362

25835

\begin{align*} y^{\prime }&=-\frac {2 x y}{x^{2}+1} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

3.950

25836

\begin{align*} y^{\prime }&=-\frac {y}{x -3} \\ y \left (-2\right ) &= 1 \\ \end{align*}

[_separable]

5.717

25837

\begin{align*} 2 x y y^{\prime }-1-y^{2}&=0 \\ y \left (2\right ) &= 3 \\ \end{align*}

[_separable]

11.188

25838

\begin{align*} x^{2} \left (1-y\right ) y^{\prime }+\left (1-x \right ) y&=0 \\ \end{align*}

[_separable]

12.588

25839

\begin{align*} 2 x y \left (4-y^{2}\right )+\left (-1+y\right ) \left (x^{2}+2\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

41.665

25840

\begin{align*} \left (2 x^{2}+1\right ) y y^{\prime }&=2 x \left (1+y^{2}\right ) \\ \end{align*}

[_separable]

11.868

25841

\begin{align*} x^{2} y+\left (x +1\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

8.343

25842

\begin{align*} y^{3}+y^{\prime } \sqrt {-x^{2}+1}&=0 \\ \end{align*}

[_separable]

10.964

25843

\begin{align*} y x -x +\left (y x +y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

7.633

25844

\begin{align*} y^{\prime }+\left (-1+y\right ) \cos \left (x \right )&=0 \\ \end{align*}

[_separable]

5.549

25852

\begin{align*} \sec \left (x \right )^{2} \tan \left (y\right )+\sec \left (y\right )^{2} \tan \left (x \right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

30.276

25855

\begin{align*} 3-2 y+\left (x^{2}-1\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

5.894

25889

\begin{align*} -x y^{\prime }+y&=a y^{2}+a y^{\prime } \\ \end{align*}

[_separable]

11.030

25895

\begin{align*} x y^{\prime }+y&=x y y^{\prime }-y x \\ \end{align*}

[_separable]

8.152

25898

\begin{align*} \sin \left (x \right ) \cos \left (y\right )^{2}+\cos \left (x \right )^{2} y^{\prime }&=0 \\ \end{align*}

[_separable]

5.997

26061

\begin{align*} y&=x y^{\prime }+y^{\prime }-1 \\ \end{align*}

[_separable]

2.705

26077

\begin{align*} y^{\prime }&=\left (-1+y\right ) x \\ \end{align*}

[_separable]

2.582

26078

\begin{align*} y^{\prime }&=2 y x \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

3.042

26079

\begin{align*} 2 x y y^{\prime }+1+y^{2}&=0 \\ \end{align*}

[_separable]

3.747

26080

\begin{align*} {\mathrm e}^{3 y} \sin \left (x \right )^{2}+\cos \left (x \right )^{2} y^{\prime }&=0 \\ \end{align*}

[_separable]

3.844

26147

\begin{align*} \left (-x^{2}+1\right ) y^{\prime }+y x&=2 x \\ \end{align*}

[_separable]

3.607

26148

\begin{align*} y y^{\prime }&=-2 x^{3}+x \\ \end{align*}

[_separable]

2.014

26149

\begin{align*} x y^{\prime }&=y \tan \left (\ln \left (y\right )\right ) \\ \end{align*}

[_separable]

5.801

26153

\begin{align*} y y^{\prime }+x&=0 \\ \end{align*}

[_separable]

4.868

26155

\begin{align*} -x y^{\prime }+y&=0 \\ \end{align*}

[_separable]

2.004

26160

\begin{align*} y^{\prime }-y \tan \left (x \right )&=0 \\ \end{align*}

[_separable]

2.649

26162

\begin{align*} y^{\prime }&={\mathrm e}^{x -y} \\ \end{align*}

[_separable]

1.730

26167

\begin{align*} x y^{\prime }+1&={\mathrm e}^{y} \\ \end{align*}

[_separable]

2.941

26175

\begin{align*} y^{\prime }&=\frac {x}{y} \\ \end{align*}

[_separable]

5.317

26189

\begin{align*} y^{\prime }&=\left (-1+y\right ) x \\ \end{align*}

[_separable]

2.033

26194

\begin{align*} y^{\prime }&=\frac {y+1}{x -1} \\ \end{align*}

[_separable]

2.164

26198

\begin{align*} y^{\prime }&=\left (1-y\right ) \left (1-x \right ) \\ \end{align*}

[_separable]

2.187

26202

\begin{align*} y^{\prime }&=\frac {x -1}{y} \\ \end{align*}

[_separable]

3.318

26203

\begin{align*} y^{\prime }&=-\frac {y}{x} \\ \end{align*}

[_separable]

2.619

26204

\begin{align*} y^{\prime }&=\frac {y}{x} \\ y \left (1\right ) &= 1 \\ \end{align*}

[_separable]

2.283

26205

\begin{align*} y^{\prime }&=\frac {y x}{2} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

2.390

26209

\begin{align*} 1+y^{2}+\left (x^{2}+1\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

2.927

26210

\begin{align*} x y y^{\prime }+1+y^{2}&=0 \\ \end{align*}

[_separable]

4.523

26211

\begin{align*} \left (y^{2}+x y^{2}\right ) y^{\prime }+x^{2}-x^{2} y&=0 \\ \end{align*}

[_separable]

1.982

26212

\begin{align*} 1+y^{2}&=x y^{\prime } \\ \end{align*}

[_separable]

3.199

26213

\begin{align*} y y^{\prime } \sqrt {x^{2}+1}+x \sqrt {1+y^{2}}&=0 \\ \end{align*}

[_separable]

3.672

26214

\begin{align*} x \sqrt {1-y^{2}}+y \sqrt {-x^{2}+1}\, y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

5.687

26216

\begin{align*} \ln \left (y\right ) y+x y^{\prime }&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}

[_separable]

3.901

26217

\begin{align*} y^{\prime }&=a^{x +y} \\ \end{align*}

[_separable]

1.707

26218

\begin{align*} {\mathrm e}^{y} \left (x^{2}+1\right ) y^{\prime }-2 x \left (1+{\mathrm e}^{y}\right )&=0 \\ \end{align*}

[_separable]

4.813

26219

\begin{align*} \left (1+{\mathrm e}^{x}\right ) y y^{\prime }&={\mathrm e}^{y} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

2.408

26220

\begin{align*} \left (1+y^{2}\right ) {\mathrm e}^{2 x}-\left (1+y^{2}\right ) {\mathrm e}^{y} y^{\prime }-\left (y+1\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

3.449

26221

\begin{align*} x y^{2}-y^{2}+x -1+\left (x^{2} y-2 y x +x^{2}+2 y-2 x +2\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

3.793

26226

\begin{align*} 1+y^{2}&=\left (y-\sqrt {1+y^{2}}\right ) \left (x^{2}+1\right )^{{3}/{2}} y^{\prime } \\ \end{align*}

[_separable]

5.992

26235

\begin{align*} -x y^{\prime }+y&=a \left (1+x^{2} y^{\prime }\right ) \\ \end{align*}

[_separable]

2.124

26236

\begin{align*} a^{2}+y^{2}+2 x \sqrt {a x -x^{2}}\, y^{\prime }&=0 \\ y \left (a \right ) &= 0 \\ \end{align*}

[_separable]

6.431

26237

\begin{align*} y^{\prime }+\sin \left (\frac {x}{2}+\frac {y}{2}\right )&=\sin \left (\frac {x}{2}-\frac {y}{2}\right ) \\ \end{align*}

[_separable]

6.744

26238

\begin{align*} y^{\prime }&=\frac {y}{x} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

2.325

26248

\begin{align*} x^{2} \cos \left (y\right ) y^{\prime }+1&=0 \\ y \left (\infty \right ) &= 2 \pi \\ \end{align*}

[_separable]

3.743

26251

\begin{align*} 2 \left (x^{2}+1\right ) y^{\prime }-\cos \left (2 y\right )^{2}&=0 \\ y \left (-\infty \right ) &= \frac {7 \pi }{2} \\ \end{align*}

[_separable]

4.450

26323

\begin{align*} \frac {x y}{\sqrt {x^{2}+1}}+2 y x -\frac {y}{x}+\left (\sqrt {x^{2}+1}+x^{2}-\ln \left (x \right )\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

30.147

26395

\begin{align*} y^{\prime }+\cos \left (\frac {x}{2}+\frac {y}{2}\right )&=\cos \left (\frac {x}{2}-\frac {y}{2}\right ) \\ \end{align*}

[_separable]

8.983

26404

\begin{align*} \left (x -1\right ) \left (y^{2}-y+1\right )&=\left (y+1\right ) \left (x^{2}+x +1\right ) y^{\prime } \\ \end{align*}

[_separable]

5.067

26857

\begin{align*} y^{\prime }&=\frac {2 x y}{-x^{2}+2} \\ \end{align*}

[_separable]

2.578

26860

\begin{align*} 3 y^{\prime }&=\frac {4 x}{y^{2}} \\ \end{align*}

[_separable]

3.126

26861

\begin{align*} x y^{\prime }+y&=0 \\ \end{align*}

[_separable]

2.890

26863

\begin{align*} {\mathrm e}^{x +y} y^{\prime }&=3 x \\ \end{align*}

[_separable]

2.048

26864

\begin{align*} x y^{\prime }+y&=y^{2} \\ \end{align*}

[_separable]

3.525

26866

\begin{align*} x \sin \left (y\right ) y^{\prime }&=\cos \left (y\right ) \\ \end{align*}

[_separable]

6.161

26867

\begin{align*} \frac {x y^{\prime }}{y}&=\frac {2 y^{2}+1}{x +1} \\ \end{align*}

[_separable]

4.945

26870

\begin{align*} x y^{2} y^{\prime }&=y+1 \\ y \left (3 \,{\mathrm e}^{2}\right ) &= 2 \\ \end{align*}

[_separable]

3.253

26871

\begin{align*} y^{\prime }&=3 x^{2} \left (y+2\right ) \\ y \left (2\right ) &= 8 \\ \end{align*}

[_separable]

8.835

26873

\begin{align*} 2 y y^{\prime }&={\mathrm e}^{x -y^{2}} \\ y \left (4\right ) &= -2 \\ \end{align*}

[_separable]

2.651

26874

\begin{align*} y y^{\prime }&=2 x \sec \left (3 y\right ) \\ y \left (\frac {2}{3}\right ) &= \frac {\pi }{3} \\ \end{align*}

[_separable]

9.985

26891

\begin{align*} 4 y^{4}-1+12 x y^{3} y^{\prime }&=0 \\ y \left (1\right ) &= 2 \\ \end{align*}

[_separable]

5.802

26895

\begin{align*} -x y^{\prime }+y&=0 \\ \end{align*}

[_separable]

2.178

26896

\begin{align*} y^{\prime }-\frac {y}{x}&=0 \\ \end{align*}

[_separable]

2.130

26901

\begin{align*} y^{\prime }+y x&=x y^{2} \\ \end{align*}

[_separable]

3.267

26904

\begin{align*} y^{\prime }&=\frac {y^{2}}{2 x}-\frac {y}{x}-\frac {4}{x} \\ \end{align*}

[_separable]

5.398

26909

\begin{align*} y^{\prime }&=-\frac {y^{2}}{x}+\frac {2 y}{x} \\ \end{align*}

[_separable]

4.374

26912

\begin{align*} y^{\prime }+\frac {2 y}{x}&=\frac {3 y^{2}}{x} \\ \end{align*}

[_separable]

4.358

27203

\begin{align*} y y^{\prime }+x&=0 \\ \end{align*}

[_separable]

5.293

27204

\begin{align*} x y^{\prime }&=2 y \\ \end{align*}

[_separable]

3.468

27205

\begin{align*} x y^{\prime }+y&=0 \\ \end{align*}

[_separable]

3.148

27207

\begin{align*} \left (1+y^{2}\right ) y^{\prime }+x&=0 \\ \end{align*}

[_separable]

1.746

27208

\begin{align*} y^{\prime }&=\frac {x}{y} \\ \end{align*}

[_separable]

5.177

27211

\begin{align*} x^{2}+y^{2} y^{\prime }&=1 \\ \end{align*}

[_separable]

2.113

27213

\begin{align*} \left (x +1\right ) y^{\prime }+y x&=0 \\ \end{align*}

[_separable]

2.802

27214

\begin{align*} \sqrt {1+y^{2}}&=x y y^{\prime } \\ \end{align*}

[_separable]

6.031

27215

\begin{align*} \left (x^{2}-1\right ) y^{\prime }+2 x y^{2}&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

7.161

27216

\begin{align*} \cot \left (x \right ) y^{\prime }+y&=2 \\ y \left (0\right ) &= -1 \\ \end{align*}

[_separable]

3.824

27218

\begin{align*} x y^{\prime }+y&=y^{2} \\ y \left (1\right ) &= {\frac {1}{2}} \\ \end{align*}

[_separable]

3.440

27219

\begin{align*} 2 x^{2} y y^{\prime }+y^{2}&=2 \\ \end{align*}

[_separable]

3.301

27220

\begin{align*} y^{\prime }-x y^{2}&=2 y x \\ \end{align*}

[_separable]

2.710

27222

\begin{align*} z^{\prime }&=10^{x +z} \\ \end{align*}

[_separable]

2.804

27223

\begin{align*} x x^{\prime }+t&=1 \\ \end{align*}

[_separable]

2.460

27230

\begin{align*} y^{\prime }&=\left (\frac {1+y^{2}}{x^{4}+1}\right )^{{1}/{3}} \\ \end{align*}

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

3.185

27399

\begin{align*} y&=x y^{\prime }-y^{\prime }-2 \\ \end{align*}

[_separable]

3.902

27408

\begin{align*} 2 x y^{\prime }+y^{2}&=1 \\ \end{align*}

[_separable]

5.702

27411

\begin{align*} y-y^{\prime }&=x y^{\prime }+y^{2} \\ \end{align*}

[_separable]

9.337

27415

\begin{align*} \left (-x^{2}+1\right ) y^{\prime }+y x&=0 \\ \end{align*}

[_separable]

4.305

27418

\begin{align*} x^{2} y^{\prime }-2 y x&=3 y \\ \end{align*}

[_separable]

5.474

27428

\begin{align*} x y^{\prime }&={\mathrm e}^{y}+2 y^{\prime } \\ \end{align*}

[_separable]

3.757

27430

\begin{align*} y^{\prime }+y x -x y^{3}&=0 \\ \end{align*}

[_separable]

14.389

27435

\begin{align*} \left (-x^{2}+1\right ) y^{\prime }-2 x y^{2}&=y x \\ \end{align*}

[_separable]

11.262

27437

\begin{align*} x y^{2}-x +\left (y x +y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

7.655