2.4.24 first order ode separable

Table 2.1097: first order ode separable [1723]

#

ODE

CAS classification

Solved

Maple

Mma

Sympy

time(sec)

27

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

[_separable]

2.416

28

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

[_separable]

1.864

33

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

[_separable]

2.164

34

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

[_separable]

1.980

41

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

[_separable]

1.985

42

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

[_separable]

2.858

43

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

[_separable]

2.338

44

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

[_separable]

2.520

45

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

[_separable]

2.340

48

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

[_separable]

1.812

49

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

[_separable]

2.177

50

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

[_separable]

3.480

51

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

[_separable]

3.207

52

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

[_separable]

2.450

53

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

[_separable]

3.907

54

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

[_separable]

2.345

55

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

[_separable]

2.622

56

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

[_separable]

2.155

57

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

[_separable]

2.371

58

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

[_separable]

3.529

59

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

[_separable]

3.670

60

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

[_separable]

3.790

61

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

[_separable]

4.478

62

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

[_separable]

3.086

64

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

[_separable]

1.716

65

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

[_separable]

2.590

66

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

[_separable]

2.297

67

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

[_separable]

1.580

68

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

[_separable]

2.507

83

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

[_separable]

2.482

87

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

[_separable]

1.423

88

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

[_separable]

1.884

92

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

[_separable]

1.450

96

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

[_separable]

2.793

103

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

[_separable]

1.296

124

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

[_separable]

1.638

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]

2.213

180

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

[_separable]

1.975

183

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

[_separable]

1.852

184

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

[_separable]

1.937

188

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

[_separable]

2.375

191

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

[_separable]

1.962

197

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

[_separable]

1.967

202

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

[_separable]

2.519

209

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

[_separable]

1.556

210

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

[_separable]

4.663

213

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

[_separable]

1.622

214

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

[_separable]

9.522

669

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

[_separable]

2.378

670

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

[_separable]

1.085

673

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

[_separable]

2.109

674

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

[_separable]

2.910

677

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

[_separable]

1.570

678

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

[_separable]

2.319

679

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

[_separable]

1.861

680

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

[_separable]

1.790

681

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

[_separable]

1.825

684

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

[_separable]

1.602

685

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

[_separable]

1.932

686

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

[_separable]

3.063

687

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

[_separable]

2.922

688

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

[_separable]

2.205

689

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

[_separable]

2.318

690

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

[_separable]

2.332

691

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

[_separable]

2.095

692

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

[_separable]

1.954

693

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

[_separable]

3.131

694

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

[_separable]

2.261

695

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

[_separable]

3.048

696

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

[_separable]

2.940

697

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

[_separable]

2.722

699

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

[_separable]

2.343

700

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

[_separable]

2.474

701

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

[_separable]

2.895

702

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

[_separable]

2.120

703

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

[_separable]

2.790

714

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

[_separable]

1.960

718

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

[_separable]

2.041

719

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

[_separable]

3.537

723

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

[_separable]

2.196

727

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

[_separable]

2.878

748

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

[_separable]

1.650

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]

2.186

772

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

[_separable]

1.987

775

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

[_separable]

1.929

776

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

[_separable]

2.016

780

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

[_separable]

2.441

789

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

[_separable]

2.013

794

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

[_separable]

2.504

800

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

[_separable]

1.589

801

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

[_separable]

1.437

802

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

[_separable]

3.477

805

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

[_separable]

1.674

806

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

[_separable]

8.562

1129

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

[_separable]

2.075

1130

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

[_separable]

1.559

1131

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

[_separable]

2.263

1132

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

[_separable]

1.911

1133

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

[_separable]

2.664

1134

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

[_separable]

3.070

1136

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

[_separable]

1.312

1137

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

[_separable]

2.228

1138

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

[_separable]

2.275

1139

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

[_separable]

1.892

1140

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

[_separable]

3.218

1141

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

[_separable]

1.792

1142

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

[_separable]

2.846

1143

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

[_separable]

2.037

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]

1.822

1145

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

[_separable]

2.267

1146

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

[_separable]

3.211

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]

26.733

1148

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

[_separable]

3.464

1149

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

[_separable]

1.898

1150

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

[_separable]

1.572

1151

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

[_separable]

2.292

1152

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

[_separable]

2.131

1153

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

[_separable]

2.328

1154

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

[_separable]

2.876

1155

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

[_separable]

2.715

1156

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

[_separable]

3.409

1167

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

[_separable]

2.045

1172

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

[_separable]

1.639

1173

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

[_separable]

2.295

1174

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

[_separable]

3.226

1175

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

[_separable]

2.556

1177

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

[_separable]

1.585

1178

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

[_separable]

2.639

1193

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

[_separable]

3.441

1204

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

[_separable]

3.998

1207

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

[_separable]

1.812

1209

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

[_separable]

2.371

1219

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

[_separable]

3.103

1221

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

[_separable]

1.744

1224

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

[_separable]

1.562

1227

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

[_separable]

2.451

1230

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

[_separable]

2.346

1232

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

[_separable]

2.868

1237

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

[_separable]

1.374

1239

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

[_separable]

0.893

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]

2.643

1521

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

[_separable]

1.336

1522

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

[_separable]

2.073

1523

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

[_separable]

2.003

1532

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

[_separable]

2.336

1533

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

[_separable]

2.444

1538

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

[_separable]

1.502

1539

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

[_separable]

1.750

1540

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

[_separable]

1.909

1541

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

[_separable]

1.550

1542

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

[_separable]

2.100

1543

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

[_separable]

1.952

1544

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

[_separable]

2.266

1545

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

[_separable]

1.666

1546

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

[_separable]

2.124

1569

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

[_separable]

1.775

1573

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

[_separable]

4.023

1578

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

[_separable]

2.080

1579

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

[_separable]

3.586

1580

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

[_separable]

2.670

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]

3.541

1582

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

[_separable]

5.943

1583

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

[_separable]

2.532

1584

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

[_separable]

1.830

1585

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

[_separable]

3.971

1586

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

[_separable]

2.185

1587

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

[_separable]

2.284

1588

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

[_separable]

3.974

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]

4.431

1590

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

[_separable]

1.595

1591

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

[_separable]

1.965

1592

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

[_separable]

6.231

1593

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

[_separable]

3.853

1594

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

[_separable]

5.102

1595

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

[_separable]

3.280

1597

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

[_separable]

4.931

1598

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

[_separable]

4.762

1599

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

[_separable]

2.613

1600

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

[_separable]

2.902

1601

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

[_separable]

14.037

1602

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

[_separable]

2.592

1613

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

[_separable]

2.504

1617

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

[_separable]

2.471

1620

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

[_separable]

3.731

1622

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

[_separable]

8.767

1623

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

[_separable]

7.437

1624

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

[_separable]

5.510

1636

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

[_separable]

3.359

1690

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

[_separable]

2.368

1692

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

[_separable]

3.704

1698

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

[_separable]

2.931

1700

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

[_separable]

2.444

1711

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

[_separable]

2.517

1712

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

[_separable]

1.579

1713

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

[_separable]

2.112

1721

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

[_separable]

2.434

1722

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

[_separable]

1.852

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]

3.925

1726

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

[_separable]

3.047

1728

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

[_separable]

2.861

1731

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

[_separable]

3.691

2298

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

[_separable]

1.912

2299

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

[_separable]

2.773

2303

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

[_separable]

1.653

2305

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

[_separable]

2.373

2306

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

[_separable]

2.506

2307

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

[_separable]

1.543

2312

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

[_separable]

1.988

2317

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

[_separable]

2.372

2318

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

[_separable]

1.740

2319

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

[_separable]

2.578

2320

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

[_separable]

1.342

2321

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

[_separable]

2.446

2322

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

[_separable]

2.105

2323

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

[_separable]

2.913

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]

3.210

2325

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

[_separable]

2.900

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]

2.342

2328

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

[_separable]

2.520

2359

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

[_separable]

1.793

2360

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

[_separable]

7.780

2471

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

[_separable]

2.086

2472

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

[_separable]

3.041

2476

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

[_separable]

1.911

2478

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

[_separable]

2.361

2479

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

[_separable]

3.156

2480

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

[_separable]

2.471

2481

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

[_separable]

1.856

2486

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

[_separable]

2.290

2488

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

[_separable]

2.707

2489

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

[_separable]

1.957

2490

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

[_separable]

2.780

2491

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

[_separable]

1.388

2492

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

[_separable]

2.682

2493

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

[_separable]

2.219

2494

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

[_separable]

1.907

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]

4.156

2496

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

[_separable]

2.046

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]

2.346

2499

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

[_separable]

2.701

2518

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

[_separable]

1.664

2534

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

[_separable]

1.442

2535

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

[_separable]

19.727

2536

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

[_separable]

11.058

2840

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

[_separable]

2.011

2841

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

[_separable]

4.849

2842

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

[_separable]

2.830

2843

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

[_separable]

2.301

2844

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

[_separable]

1.996

2845

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

[_separable]

2.517

2846

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

[_separable]

3.828

2847

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

[_separable]

2.194

2848

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

[_separable]

2.240

2849

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

[_separable]

2.472

2850

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

[_separable]

4.572

2852

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

[_separable]

3.483

2853

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

[_separable]

3.972

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]

8.708

2855

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

[_separable]

2.563

2856

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

[_separable]

2.494

2857

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

[_separable]

2.254

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]

8.823

2859

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

[_separable]

8.181

2860

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

[_separable]

2.248

2861

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

[_separable]

4.928

2862

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

[_separable]

3.149

2863

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

[_separable]

4.070

2866

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

[_separable]

3.991

2867

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

[_separable]

12.391

2868

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

[_separable]

7.496

2869

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

[_separable]

5.473

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]

3.158

2938

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

[_separable]

4.773

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]

2.670

2990

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

[_separable]

2.745

2992

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

[_separable]

2.829

2995

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

[_separable]

34.183

3003

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

[_separable]

2.499

3010

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

[_separable]

5.603

3014

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

[_separable]

4.411

3015

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

[_separable]

3.720

3019

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

[_separable]

2.233

3023

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

[_separable]

3.024

3027

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

[_separable]

2.506

3030

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

[_separable]

7.810

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]

3.680

3039

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

[_separable]

4.411

3041

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

[_separable]

2.726

3051

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

[_separable]

3.567

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]

6.313

3408

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

[_separable]

2.862

3409

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

[_separable]

5.484

3410

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

[_separable]

3.345

3411

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

[_separable]

2.391

3412

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

[_separable]

6.215

3426

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

[_separable]

3.097

3430

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

[_separable]

2.464

3431

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

[_separable]

6.222

3437

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

[_separable]

3.218

3450

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

[_separable]

3.356

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]

3.687

3456

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

[_separable]

6.106

3457

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

[_separable]

5.194

3458

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

[_separable]

3.241

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]

4.504

3472

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

[_separable]

3.333

3514

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

[_separable]

1.221

3515

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

[_separable]

1.483

3516

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

[_separable]

1.087

3517

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

[_separable]

1.268

3518

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

[_separable]

1.282

3519

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

[_separable]

1.427

3520

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

[_separable]

1.442

3521

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

[_separable]

2.295

3522

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

[_separable]

2.968

3524

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

[_separable]

2.373

3525

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

[_separable]

2.389

3526

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

[_separable]

1.603

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]

3.043

3528

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

[_separable]

2.685

3561

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

[_separable]

2.193

3592

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

[_separable]

1.184

3593

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

[_separable]

1.497

3594

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

[_separable]

1.118

3595

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

[_separable]

1.211

3596

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

[_separable]

1.337

3597

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

[_separable]

1.447

3598

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

[_separable]

1.437

3599

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

[_separable]

2.648

3600

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

[_separable]

3.405

3601

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

[_separable]

1.679

3602

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

[_separable]

2.789

3603

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

[_separable]

2.137

3604

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

[_separable]

1.466

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]

3.147

3606

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

[_separable]

2.617

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]

6.295

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]

26.218

4093

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

[_separable]

1.855

4094

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

[_separable]

1.654

4095

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

[_separable]

1.767

4101

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

[_separable]

1.784

4104

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

[_separable]

2.053

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]

2.740

4110

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

[_separable]

3.091

4189

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

[_separable]

3.386

4212

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

[_separable]

1.815

4213

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

[_separable]

2.628

4214

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

[_separable]

1.473

4215

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

[_separable]

1.221

4216

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

[_separable]

1.356

4218

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

[_separable]

1.463

4219

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

[_separable]

1.404

4220

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

[_separable]

1.599

4221

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

[_separable]

1.603

4222

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

[_separable]

2.878

4223

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

[_separable]

1.683

4224

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

[_separable]

2.993

4225

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

[_separable]

3.191

4226

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

[_separable]

2.641

4227

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

[_separable]

1.010

4229

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

[_separable]

4.845

4230

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

[_separable]

3.565

4231

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

[_separable]

2.535

4232

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

[_separable]

1.829

4233

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

[_separable]

2.049

4234

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

[_separable]

2.424

4235

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

[_separable]

1.769

4236

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

[_separable]

1.873

4237

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

[_separable]

8.641

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]

2.067

4257

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

[_separable]

1.710

4264

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

[_separable]

2.652

4294

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

[_separable]

2.116

4300

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

[_separable]

2.068

4301

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

[_separable]

2.947

4302

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

[_separable]

2.763

4303

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

[_separable]

4.009

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]

4.703

4306

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

[_separable]

3.325

4307

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

[_separable]

2.748

4308

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

[_separable]

10.213

4309

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

[_separable]

2.826

4310

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

[_separable]

3.202

4311

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

[_separable]

27.336

4312

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

[_separable]

4.207

4360

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

[_separable]

2.000

4397

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

[_separable]

2.043

4411

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

[_separable]

2.114

4428

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

[_separable]

2.553

4618

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

[_separable]

2.378

4625

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

[_separable]

2.112

4628

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

[_separable]

3.914

4636

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

[_separable]

2.474

4638

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

[_separable]

2.255

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]

3.257

4676

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

[_separable]

4.095

4680

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

[_separable]

3.980

4681

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

[_separable]

5.339

4687

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

[_separable]

3.808

4689

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

[_separable]

6.622

4695

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

[_separable]

3.518

4701

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

[_separable]

4.470

4714

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

[_separable]

2.649

4715

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

[_separable]

2.329

4719

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

[_separable]

2.247

4720

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

[_separable]

2.948

4721

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

[_separable]

2.421

4722

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

[_separable]

4.256

4723

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

[_separable]

1.643

4724

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

[_separable]

1.704

4725

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

[_separable]

1.852

4727

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

[_separable]

1.668

4728

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

[_separable]

1.838

4732

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

[_separable]

3.477

4735

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

[_separable]

1.149

4736

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

[_separable]

2.179

4737

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

[_separable]

1.780

4741

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

[_separable]

1.404

4760

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

[_separable]

1.877

4761

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

[_separable]

1.826

4768

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

[_separable]

1.128

4771

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

[_separable]

1.833

4775

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

[_separable]

2.344

4796

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

[_separable]

3.606

4803

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

[_separable]

3.976

4804

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

[_separable]

4.494

4805

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

[_separable]

4.484

4815

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

[_separable]

3.214

4822

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

[_separable]

3.243

4828

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

[_separable]

3.200

4845

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

[_separable]

3.539

4846

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

[_separable]

3.562

4848

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

[_separable]

4.418

4852

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

[_separable]

2.633

4853

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

[_separable]

7.075

4855

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

[_separable]

8.408

4856

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

[_separable]

8.236

4858

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

[_separable]

4.266

4864

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

[_separable]

3.497

4869

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

[_separable]

3.904

4874

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

[_separable]

4.404

4902

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

[_separable]

1.622

4907

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

[_separable]

1.605

4913

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

[_separable]

2.392

4914

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

[_separable]

3.310

4915

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

[_separable]

2.338

4916

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

[_separable]

3.707

4917

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

[_separable]

3.687

4920

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

[_separable]

4.642

4921

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

[_separable]

5.970

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]

8.093

4931

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

[_separable]

7.030

4932

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

[_separable]

6.551

4936

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

[_separable]

1.865

4942

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

[_separable]

6.996

4943

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

[_separable]

3.385

4945

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

[_separable]

5.441

4947

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

[_separable]

4.620

4948

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

[_separable]

10.528

4950

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

[_separable]

2.947

4962

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

[_separable]

4.829

4963

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

[_separable]

4.665

4964

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

[_separable]

4.068

4965

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

[_separable]

1.984

4972

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

[_separable]

2.045

4980

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

[_separable]

1.884

4981

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

[_separable]

2.131

4995

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

[_separable]

3.471

4999

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

[_separable]

2.273

5011

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

[_separable]

3.935

5012

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

[_separable]

3.243

5014

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

[_separable]

42.672

5015

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

[_separable]

41.144

5016

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

[_separable]

6.352

5017

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

[_separable]

10.260

5019

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

[_separable]

3.260

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]

7.592

5021

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

[_separable]

3.164

5022

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

[_separable]

4.039

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]

4.304

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]

8.710

5026

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

[_separable]

2.737

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]

3.529

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]

13.507

5030

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

[_separable]

3.743

5031

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

[_separable]

3.467

5035

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

[_separable]

3.723

5036

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

[_separable]

1.766

5039

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

[_separable]

4.411

5045

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

[_separable]

3.220

5051

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

[_separable]

2.544

5094

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

[_separable]

8.619

5095

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

[_separable]

2.233

5123

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

[_separable]

2.253

5130

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

[_separable]

2.636

5132

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

[_separable]

2.082

5136

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

[_separable]

1.639

5137

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

[_separable]

1.764

5138

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

[_separable]

1.747

5143

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

[_separable]

2.026

5155

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

[_separable]

1.908

5156

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

[_separable]

2.565

5158

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

[_separable]

1.487

5178

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

[_separable]

3.361

5186

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

[_separable]

2.957

5187

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

[_separable]

2.810

5188

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

[_separable]

3.785

5195

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

[_separable]

3.376

5203

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

[_separable]

5.936

5206

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

[_separable]

2.882

5207

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

[_separable]

4.273

5208

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

[_separable]

1.576

5209

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

[_separable]

1.553

5223

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

[_separable]

1.810

5251

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

[_separable]

2.740

5258

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

[_separable]

3.510

5275

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

[_separable]

2.131

5280

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

[_separable]

2.348

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]

3.891

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]

2.874

5285

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

[_separable]

3.730

5297

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

[_separable]

2.252

5303

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

[_separable]

3.313

5333

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

[_separable]

3.411

5334

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

[_separable]

3.967

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]

4.192

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]

3.773

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]

5.862

5684

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

[_separable]

3.832

5706

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

[_separable]

19.543

6824

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

[_separable]

1.971

6825

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

[_separable]

2.598

6826

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

[_separable]

3.641

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]

3.776

6828

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

[_separable]

2.615

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]

26.371

6842

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

[_separable]

3.769

6873

\begin{align*} \frac {\sqrt {f \,x^{4}+c \,x^{3}+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]

9.562

6894

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

[_separable]

0.563

6915

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

[_separable]

2.350

6983

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

[_separable]

7.103

6994

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

[_separable]

30.441

7004

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

[_separable]

2.806

7010

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

[_separable]

3.124

7023

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

[_separable]

4.623

7024

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

[_separable]

4.029

7038

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

[_separable]

2.156

7039

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

[_separable]

2.468

7149

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

[_separable]

1.697

7155

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

[_separable]

2.376

7156

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

[_separable]

3.461

7157

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

[_separable]

3.002

7158

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

[_separable]

4.095

7159

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

[_separable]

1.957

7161

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

[_separable]

2.431

7162

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

[_separable]

2.612

7163

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

[_separable]

4.372

7217

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

[_separable]

3.977

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]

5.645

7219

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

[_separable]

2.809

7220

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

[_separable]

4.123

7222

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

[_separable]

4.629

7223

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

[_separable]

2.348

7224

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

[_separable]

4.457

7226

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

[_separable]

1.721

7228

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

[_separable]

5.144

7245

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

[_separable]

2.970

7333

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

[_separable]

2.549

7341

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

[_separable]

3.731

7352

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

[_separable]

2.142

7356

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

[_separable]

2.668

7361

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

[_separable]

1.040

7363

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

[_separable]

1.838

7365

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

[_separable]

1.721

7383

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

[_separable]

2.335

7384

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

[_separable]

1.838

7386

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

[_separable]

2.242

7387

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

[_separable]

1.981

7388

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

[_separable]

2.036

7389

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

[_separable]

2.181

7390

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

[_separable]

5.564

7391

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

[_separable]

3.204

7392

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

[_separable]

8.778

7394

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

[_separable]

3.138

7395

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

[_separable]

3.148

7396

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

[_separable]

5.653

7397

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

[_separable]

2.043

7398

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

[_separable]

3.567

7399

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

[_separable]

5.197

7400

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

[_separable]

3.968

7401

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

[_separable]

6.987

7402

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

[_separable]

2.068

7403

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

[_separable]

2.917

7404

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

[_separable]

2.898

7405

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

[_separable]

6.318

7407

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

[_separable]

3.496

7408

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

[_separable]

25.092

7409

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

[_separable]

2.454

7412

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

[_separable]

5.408

7413

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

[_separable]

4.257

7414

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

[_separable]

6.233

7415

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

[_separable]

5.121

7416

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

[_separable]

5.177

7420

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

[_separable]

2.655

7432

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

[_separable]

1.941

7448

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

[_separable]

6.199

7467

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

[_separable]

3.500

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]

4.931

7525

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

[_separable]

3.036

7529

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

[_separable]

4.352

7530

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

[_separable]

3.234

7549

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

[_separable]

2.146

7561

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

[_separable]

4.895

7562

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

[_separable]

4.148

7682

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

[_separable]

4.115

7696

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

[_separable]

3.200

7700

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

[_separable]

8.136

7702

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

[_separable]

2.668

7707

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

[_separable]

6.270

7708

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

[_separable]

2.680

7709

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

[_separable]

2.628

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]

3.520

7711

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

[_separable]

2.164

7733

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

[_separable]

2.918

7735

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

[_separable]

2.301

7738

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

[_separable]

2.125

7741

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

[_separable]

3.309

7748

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

[_separable]

4.434

7751

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

[_separable]

5.646

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]

4.586

7845

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

[_separable]

3.133

7846

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

[_separable]

5.546

7855

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

[_separable]

3.108

7856

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

[_separable]

5.572

7857

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

[_separable]

4.369

7858

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

[_separable]

2.574

7864

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

[_separable]

3.168

7865

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

[_separable]

2.152

7869

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

[_separable]

3.612

7872

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

[_separable]

3.591

7875

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

[_separable]

3.465

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]

4.169

7908

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

[_separable]

3.914

7918

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

[_separable]

2.694

7927

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

[_separable]

3.474

8160

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

[_separable]

2.825

8167

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

[_separable]

2.750

8168

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

[_separable]

3.996

8179

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

[_separable]

2.418

8180

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

[_separable]

3.507

8189

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

[_separable]

2.705

8210

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

[_separable]

4.046

8211

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

[_separable]

2.707

8212

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

[_separable]

3.253

8213

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

[_separable]

4.761

8223

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

[_separable]

2.990

8226

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

[_separable]

1.362

8228

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

[_separable]

1.290

8229

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

[_separable]

1.317

8236

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

[_separable]

2.247

8243

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

[_separable]

4.076

8244

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

[_separable]

4.869

8245

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

[_separable]

6.617

8256

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

[_separable]

9.802

8260

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

[_separable]

1.460

8265

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

[_separable]

2.566

8266

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

[_separable]

4.891

8279

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

[_separable]

3.280

8301

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

[_separable]

3.292

8302

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

[_separable]

2.463

8303

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

[_separable]

3.970

8304

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

[_separable]

2.998

8309

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

[_separable]

3.549

8310

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

[_separable]

4.682

8315

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

[_separable]

2.122

8316

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

[_separable]

2.171

8342

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

[_separable]

2.158

8343

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

[_separable]

2.687

8344

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

[_separable]

1.507

8345

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

[_separable]

2.859

8346

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

[_separable]

3.251

8347

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

[_separable]

3.928

8348

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

[_separable]

2.474

8349

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

[_separable]

4.866

8350

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

[_separable]

4.167

8351

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

[_separable]

3.204

8355

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

[_separable]

2.297

8356

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

[_separable]

3.873

8357

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

[_separable]

2.672

8358

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

[_separable]

0.221

8359

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

[_separable]

2.979

8361

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

[_separable]

3.093

8362

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

[_separable]

2.514

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]

11.662

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]

3.329

8367

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

[_separable]

5.230

8368

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

[_separable]

4.447

8369

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

[_separable]

4.195

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]

42.881

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]

3.065

8372

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

[_separable]

3.492

8373

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

[_separable]

3.135

8374

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

[_separable]

1.939

8375

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

[_separable]

2.302

8379

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

[_separable]

5.456

8380

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

[_separable]

5.503

8381

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

[_separable]

3.368

8382

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

[_separable]

3.418

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]

3.796

8397

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

[_separable]

3.492

8398

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

[_separable]

5.869

8400

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

[_separable]

3.317

8401

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

[_separable]

2.931

8402

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

[_separable]

6.296

8403

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

[_separable]

6.026

8406

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

[_separable]

3.362

8413

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

[_separable]

0.588

8414

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

[_separable]

0.856

8415

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

[_separable]

0.818

8416

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

[_separable]

0.584

8417

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

[_separable]

2.022

8418

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

[_separable]

3.454

8419

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

[_separable]

2.353

8424

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

[_separable]

2.075

8429

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

[_separable]

2.994

8441

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

[_separable]

2.353

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]

2.796

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]

2.122

8467

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

[_separable]

4.091

8475

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

[_separable]

5.144

8657

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

[_separable]

3.300

8658

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

[_separable]

2.039

8659

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

[_separable]

2.371

8660

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

[_separable]

4.812

8661

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

[_separable]

1.753

8662

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

[_separable]

5.273

8663

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

[_separable]

3.050

8665

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

[_separable]

3.980

8666

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

[_separable]

3.814

8667

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

[_separable]

3.523

8669

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

[_separable]

3.293

8670

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

[_separable]

4.069

8671

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

[_separable]

5.096

8672

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

[_separable]

2.615

8673

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

[_separable]

12.152

8674

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

[_separable]

7.463

8675

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

[_separable]

3.447

8676

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

[_separable]

2.306

8677

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

[_separable]

1.766

8678

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

[_separable]

10.644

8679

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

[_separable]

4.092

8680

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

[_separable]

2.363

8690

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

[_separable]

4.062

8691

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

[_separable]

3.527

8693

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

[_separable]

2.799

8751

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

[_separable]

3.108

8777

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

[_separable]

2.790

8778

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

[_separable]

1.460

8779

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

[_separable]

2.691

8787

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

[_separable]

3.972

8858

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

[_separable]

2.408

8876

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

[_separable]

2.203

8878

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

[_separable]

2.418

9006

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

[_separable]

1.573

9007

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

[_separable]

3.650

9008

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

[_separable]

1.631

9009

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

[_separable]

1.643

9010

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

[_separable]

3.261

9049

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

[_separable]

2.045

9050

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

[_separable]

1.606

9082

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

[_separable]

4.726

9083

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

[_separable]

1.579

9084

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

[_separable]

1.554

9085

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

[_separable]

2.400

9086

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

[_separable]

2.291

9087

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

[_separable]

2.183

9088

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

[_separable]

1.615

9089

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

[_separable]

1.649

9090

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

[_separable]

2.697

9091

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

[_separable]

1.800

9092

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

[_separable]

1.916

9093

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

[_separable]

2.658

9094

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

[_separable]

2.600

9095

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

[_separable]

1.967

9096

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

[_separable]

4.164

9097

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

[_separable]

1.737

9119

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

[_separable]

2.560

9123

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

[_separable]

2.569

9133

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

[_separable]

1.806

9139

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

[_separable]

2.657

9194

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

[_separable]

1.966

9195

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

[_separable]

2.014

9198

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

[_separable]

2.337

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]

2.697

9202

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

[_separable]

4.175

9203

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

[_separable]

2.417

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]

8.351

9207

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

[_separable]

1.899

9348

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

[_separable]

1.816

9360

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

[_separable]

1.724

9362

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

[_separable]

1.858

9971

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

[_separable]

2.331

9972

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

[_separable]

3.612

9987

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

[_separable]

3.849

9988

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

[_separable]

2.133

9989

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

[_separable]

4.019

9990

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

[_separable]

15.136

9998

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

[_separable]

4.921

9999

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

[_separable]

2.832

10000

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

[_separable]

2.752

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]

132.826

10256

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

[_separable]

2.258

10264

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

[_separable]

1.635

10324

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

[_separable]

1.369

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]

4.319

11331

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

[_separable]

5.506

11333

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

[_separable]

2.663

11337

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

[_separable]

6.823

11361

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

[_separable]

16.304

11362

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

[_separable]

2.540

11364

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

[_separable]

49.078

11367

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

[_separable]

29.106

11368

\begin{align*} y^{\prime }-\frac {\sqrt {1-y^{4}}}{\sqrt {-x^{4}+1}}&=0 \\ \end{align*}

[_separable]

12.329

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]

4.062

11376

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

[_separable]

2.113

11396

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

[_separable]

2.603

11417

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

[_separable]

2.602

11430

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

[_separable]

3.372

11434

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

[_separable]

2.262

11457

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

[_separable]

4.782

11458

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

[_separable]

4.052

11473

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

[_separable]

2.110

11482

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

[_separable]

2.319

11489

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

[_separable]

16.737

11490

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

[_separable]

18.324

11498

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

[_separable]

15.974

11508

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

[_separable]

3.360

11539

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

[_separable]

4.580

11552

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

[_separable]

4.995

11603

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

[_separable]

3.330

11628

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

[_separable]

10.755

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]

6.256

11646

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

[_separable]

8.626

11651

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

[_separable]

3.582

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]

6.960

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]

23.066

11851

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

[_separable]

5.069

13203

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

[_separable]

1.536

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]

8.740

13972

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

[_separable]

3.016

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]

5.314

13974

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

[_separable]

4.696

13979

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

[_separable]

9.399

13993

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

[_separable]

4.166

13994

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

[_separable]

34.774

14015

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

[_separable]

5.466

14016

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

[_separable]

7.421

14020

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

[_separable]

4.303

14027

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

[_separable]

2.890

14033

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

[_separable]

2.045

14034

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

[_separable]

2.405

14192

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

[_separable]

4.842

14193

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

[_separable]

7.745

14198

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

[_separable]

4.804

14219

\begin{align*} x^{\prime }&=\frac {2 x}{t +1} \\ \end{align*}

[_separable]

5.404

14220

\begin{align*} \theta ^{\prime }&=t \sqrt {t^{2}+1}\, \sec \left (\theta \right ) \\ \end{align*}

[_separable]

4.402

14221

\begin{align*} \left (2 u+1\right ) u^{\prime }-t -1&=0 \\ \end{align*}

[_separable]

8.071

14222

\begin{align*} R^{\prime }&=\left (t +1\right ) \left (1+R^{2}\right ) \\ \end{align*}

[_separable]

7.244

14224

\begin{align*} \left (t +1\right ) x^{\prime }+x^{2}&=0 \\ \end{align*}

[_separable]

5.314

14227

\begin{align*} x^{\prime }&=2 t x^{2} \\ x \left (0\right ) &= 1 \\ \end{align*}

[_separable]

9.395

14228

\begin{align*} x^{\prime }&=t^{2} {\mathrm e}^{-x} \\ x \left (0\right ) &= \ln \left (2\right ) \\ \end{align*}

[_separable]

6.002

14230

\begin{align*} x^{\prime }&={\mathrm e}^{t +x} \\ x \left (0\right ) &= 0 \\ \end{align*}

[_separable]

5.367

14231

\begin{align*} T^{\prime }&=2 a t \left (T^{2}-a^{2}\right ) \\ T \left (0\right ) &= 0 \\ \end{align*}

[_separable]

9.231

14232

\begin{align*} y^{\prime }&=t^{2} \tan \left (y\right ) \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

6.517

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]

5.700

14234

\begin{align*} y^{\prime }&=\frac {2 t y^{2}}{t^{2}+1} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

7.325

14235

\begin{align*} x^{\prime }&=\frac {t^{2}}{1-x^{2}} \\ x \left (1\right ) &= 1 \\ \end{align*}

[_separable]

6.632

14236

\begin{align*} x^{\prime }&=6 t \left (x-1\right )^{{2}/{3}} \\ \end{align*}

[_separable]

7.812

14241

\begin{align*} y^{\prime }&=-y^{2} {\mathrm e}^{-t^{2}} \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}

[_separable]

7.598

14243

\begin{align*} \cos \left (t \right ) x^{\prime }-2 x \sin \left (x\right )&=0 \\ \end{align*}

[_separable]

4.954

14253

\begin{align*} \left (t^{2}+1\right ) x^{\prime }&=-3 t x+6 t \\ \end{align*}

[_separable]

1.828

14255

\begin{align*} x^{\prime }&=\left (a +\frac {b}{t}\right ) x \\ x \left (1\right ) &= 1 \\ \end{align*}

[_separable]

1.300

14258

\begin{align*} \cos \left (\theta \right ) v^{\prime }+v&=3 \\ \end{align*}

[_separable]

2.390

14261

\begin{align*} x^{\prime }&=2 t x \\ \end{align*}

[_separable]

1.474

14266

\begin{align*} x^{\prime }+p \left (t \right ) x&=0 \\ \end{align*}

[_separable]

1.579

14269

\begin{align*} x^{\prime }&=-\frac {x}{t}+\frac {1}{t x^{2}} \\ \end{align*}

[_separable]

2.976

14277

\begin{align*} x^{2}-t^{2} x^{\prime }&=0 \\ \end{align*}

[_separable]

2.219

14278

\begin{align*} t \cot \left (x\right ) x^{\prime }&=-2 \\ \end{align*}

[_separable]

2.551

14420

\begin{align*} y^{\prime }+4 y x&=8 x \\ \end{align*}

[_separable]

1.700

14436

\begin{align*} y^{\prime }&=x^{2} \sin \left (y\right ) \\ y \left (1\right ) &= -2 \\ \end{align*}

[_separable]

5.120

14437

\begin{align*} y^{\prime }&=\frac {y^{2}}{x -2} \\ y \left (1\right ) &= 0 \\ \end{align*}

[_separable]

3.109

14446

\begin{align*} \frac {\left (2 s-1\right ) s^{\prime }}{t}+\frac {s-s^{2}}{t^{2}}&=0 \\ \end{align*}

[_separable]

4.269

14457

\begin{align*} \left (x^{2}+1\right ) y^{\prime }+4 y x&=0 \\ \end{align*}

[_separable]

1.744

14458

\begin{align*} y x +2 x +y+2+\left (x^{2}+2 x \right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

2.213

14459

\begin{align*} 2 r \left (s^{2}+1\right )+\left (r^{4}+1\right ) s^{\prime }&=0 \\ \end{align*}

[_separable]

2.829

14460

\begin{align*} \csc \left (y\right )+\sec \left (x \right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

2.235

14461

\begin{align*} \tan \left (\theta \right )+2 r \theta ^{\prime }&=0 \\ \end{align*}

[_separable]

3.107

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]

2.682

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]

2.996

14471

\begin{align*} y+2+y \left (x +4\right ) y^{\prime }&=0 \\ y \left (-3\right ) &= -1 \\ \end{align*}

[_separable]

4.819

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]

2.853

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]

3.356

14484

\begin{align*} y^{\prime }+4 y x&=8 x \\ \end{align*}

[_separable]

1.730

14485

\begin{align*} x^{\prime }+\frac {x}{t^{2}}&=\frac {1}{t^{2}} \\ \end{align*}

[_separable]

1.780

14486

\begin{align*} \left (u^{2}+1\right ) v^{\prime }+4 u v&=3 u \\ \end{align*}

[_separable]

2.103

14495

\begin{align*} y^{\prime }-\frac {y}{x}&=-\frac {y^{2}}{x} \\ \end{align*}

[_separable]

2.013

14497

\begin{align*} y^{\prime }+\left (4 y-\frac {8}{y^{3}}\right ) x&=0 \\ \end{align*}

[_separable]

2.638

14498

\begin{align*} x^{\prime }+\frac {\left (t +1\right ) x}{2 t}&=\frac {t +1}{t x} \\ \end{align*}

[_separable]

2.391

14500

\begin{align*} y^{\prime }+3 x^{2} y&=x^{2} \\ y \left (0\right ) &= 2 \\ \end{align*}

[_separable]

1.923

14502

\begin{align*} 2 x \left (1+y\right )-\left (x^{2}+1\right ) y^{\prime }&=0 \\ y \left (1\right ) &= -5 \\ \end{align*}

[_separable]

1.951

14514

\begin{align*} \left (1+y\right ) y^{\prime }+x \left (y^{2}+2 y\right )&=x \\ \end{align*}

[_separable]

2.917

14518

\begin{align*} 6 x^{2} y-\left (x^{3}+1\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

1.918

14520

\begin{align*} y-1+x \left (x +1\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

1.886

14524

\begin{align*} 8 x^{3} y-12 x^{3}+\left (x^{4}+1\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

2.303

14529

\begin{align*} y x +x^{2} y^{\prime }&=x y^{3} \\ \end{align*}

[_separable]

6.632

14530

\begin{align*} \left (x^{3}+1\right ) y^{\prime }+6 x^{2} y&=6 x^{2} \\ \end{align*}

[_separable]

2.332

14533

\begin{align*} 8+2 y^{2}+\left (-x^{2}+1\right ) y y^{\prime }&=0 \\ y \left (3\right ) &= 0 \\ \end{align*}

[_separable]

3.431

14536

\begin{align*} 4 x y^{\prime } y&=1+y^{2} \\ y \left (2\right ) &= 1 \\ \end{align*}

[_separable]

4.625

14538

\begin{align*} y^{\prime }&=\frac {x y}{x^{2}+1} \\ y \left (\sqrt {15}\right ) &= 2 \\ \end{align*}

[_separable]

2.891

14886

\begin{align*} x^{\prime }&=t^{3} \left (1-x\right ) \\ x \left (0\right ) &= 3 \\ \end{align*}

[_separable]

2.108

14887

\begin{align*} y^{\prime }&=\left (1+y^{2}\right ) \tan \left (x \right ) \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

5.947

14888

\begin{align*} x^{\prime }&=t^{2} x \\ \end{align*}

[_separable]

1.992

14890

\begin{align*} y^{\prime }&=y^{2} {\mathrm e}^{-t^{2}} \\ \end{align*}

[_separable]

2.701

14892

\begin{align*} y^{\prime } x&=k y \\ \end{align*}

[_separable]

2.506

14893

\begin{align*} i^{\prime }&=p \left (t \right ) i \\ \end{align*}

[_separable]

2.113

14899

\begin{align*} x^{\prime }+t x&=4 t \\ x \left (0\right ) &= 2 \\ \end{align*}

[_separable]

2.120

14912

\begin{align*} V^{\prime }\left (x \right )+2 y^{\prime } y&=0 \\ \end{align*}

[_separable]

0.831

14913

\begin{align*} \left (\frac {1}{y}-a \right ) y^{\prime }+\frac {2}{x}-b&=0 \\ \end{align*}

[_separable]

4.066

15015

\begin{align*} \tan \left (y\right )-\cot \left (x \right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

2.534

15022

\begin{align*} y^{\prime }&={\mathrm e}^{x -y} \\ \end{align*}

[_separable]

1.997

15029

\begin{align*} y&=y^{\prime } x +\frac {1}{y} \\ \end{align*}

[_separable]

14.874

15115

\begin{align*} y^{\prime }&=y \,{\mathrm e}^{x +y} \left (x^{2}+1\right ) \\ \end{align*}

[_separable]

1.657

15116

\begin{align*} x^{2} y^{\prime }&=1+y^{2} \\ \end{align*}

[_separable]

1.861

15118

\begin{align*} x \left ({\mathrm e}^{y}+4\right )&={\mathrm e}^{x +y} y^{\prime } \\ \end{align*}

[_separable]

2.569

15122

\begin{align*} y^{\prime }&=x \,{\mathrm e}^{y^{2}-x} \\ \end{align*}

[_separable]

1.451

15124

\begin{align*} x \left (1+y\right )^{2}&=\left (x^{2}+1\right ) y \,{\mathrm e}^{y} y^{\prime } \\ \end{align*}

[_separable]

2.447

15135

\begin{align*} 5 y^{\prime }-y x&=0 \\ \end{align*}

[_separable]

1.391

15335

\begin{align*} y-y^{\prime } x&=0 \\ \end{align*}

[_separable]

1.481

15336

\begin{align*} \left (1+u \right ) v+\left (1-v\right ) u v^{\prime }&=0 \\ \end{align*}

[_separable]

2.089

15337

\begin{align*} 1+y-\left (1-x \right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

1.710

15338

\begin{align*} \left (t^{2}+t^{2} x\right ) x^{\prime }+x^{2}+t x^{2}&=0 \\ \end{align*}

[_separable]

2.775

15339

\begin{align*} y-a +x^{2} y^{\prime }&=0 \\ \end{align*}

[_separable]

1.612

15340

\begin{align*} z-\left (-a^{2}+t^{2}\right ) z^{\prime }&=0 \\ \end{align*}

[_separable]

2.266

15341

\begin{align*} y^{\prime }&=\frac {1+y^{2}}{x^{2}+1} \\ \end{align*}

[_separable]

2.228

15342

\begin{align*} 1+s^{2}-\sqrt {t}\, s^{\prime }&=0 \\ \end{align*}

[_separable]

2.490

15343

\begin{align*} r^{\prime }+r \tan \left (t \right )&=0 \\ \end{align*}

[_separable]

1.547

15344

\begin{align*} \left (x^{2}+1\right ) y^{\prime }-\sqrt {1-y^{2}}&=0 \\ \end{align*}

[_separable]

2.706

15345

\begin{align*} y^{\prime } \sqrt {-x^{2}+1}-\sqrt {1-y^{2}}&=0 \\ \end{align*}

[_separable]

4.480

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]

2.953

15347

\begin{align*} x -x y^{2}+\left (y-x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

2.047

15374

\begin{align*} \left (-x^{2}+1\right ) y^{\prime }-y x +a x y^{2}&=0 \\ \end{align*}

[_separable]

4.086

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]

2.541

15394

\begin{align*} y&=y^{\prime } x +y^{\prime } \\ \end{align*}

[_separable]

1.759

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]

2.539

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]

2.946

15484

\begin{align*} -y+y^{\prime } x&=0 \\ \end{align*}

[_separable]

1.690

15491

\begin{align*} x^{2} y^{\prime }+2 y x&=0 \\ \end{align*}

[_separable]

2.278

15499

\begin{align*} 2 y^{\prime } x -y&=0 \\ \end{align*}

[_separable]

2.037

15506

\begin{align*} y^{\prime }-2 y x&=0 \\ \end{align*}

[_separable]

1.764

15509

\begin{align*} y^{\prime }&=x \sqrt {y} \\ \end{align*}

[_separable]

4.921

15512

\begin{align*} x \ln \left (x \right ) y^{\prime }-\left (1+\ln \left (x \right )\right ) y&=0 \\ \end{align*}

[_separable]

2.334

15530

\begin{align*} y^{\prime }&=y x \\ \end{align*}

[_separable]

1.800

15531

\begin{align*} y^{\prime }&=-y x \\ \end{align*}

[_separable]

1.743

15535

\begin{align*} y^{\prime }&=y x \\ \end{align*}

[_separable]

1.766

15536

\begin{align*} y^{\prime }&=\frac {x}{y} \\ \end{align*}

[_separable]

4.040

15537

\begin{align*} y^{\prime }&=\frac {y}{x} \\ \end{align*}

[_separable]

1.743

15542

\begin{align*} y^{\prime }&={\mathrm e}^{x -y} \\ \end{align*}

[_separable]

1.534

15548

\begin{align*} y^{\prime }&=\frac {1}{y x} \\ \end{align*}

[_separable]

2.217

15552

\begin{align*} y^{\prime }&=\frac {x}{y^{2}} \\ \end{align*}

[_separable]

2.434

15553

\begin{align*} y^{\prime }&=\frac {\sqrt {y}}{x} \\ \end{align*}

[_separable]

3.082

15554

\begin{align*} y^{\prime }&=\frac {x y}{1-y} \\ \end{align*}

[_separable]

2.211

15568

\begin{align*} y^{\prime }&=-x \sqrt {1-y^{2}} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

25.853

15583

\begin{align*} y^{\prime }&=x \,{\mathrm e}^{y-x^{2}} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

2.119

15584

\begin{align*} y^{\prime }&=\frac {y}{x} \\ y \left (-1\right ) &= 2 \\ \end{align*}

[_separable]

2.185

15585

\begin{align*} y^{\prime }&=\frac {2 x}{y} \\ y \left (0\right ) &= 2 \\ \end{align*}

[_separable]

5.723

15587

\begin{align*} y^{\prime }&=y x +x \\ y \left (1\right ) &= 2 \\ \end{align*}

[_separable]

1.994

15588

\begin{align*} x \,{\mathrm e}^{y}+y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

2.365

15589

\begin{align*} y-x^{2} y^{\prime }&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}

[_separable]

2.385

15591

\begin{align*} 2 x y^{\prime } y+y^{2}&=-1 \\ \end{align*}

[_separable]

2.059

15597

\begin{align*} y^{\prime }&=\frac {y}{x} \\ y \left (-1\right ) &= 2 \\ \end{align*}

[_separable]

2.940

15602

\begin{align*} x -y^{\prime } y&=0 \\ \end{align*}

[_separable]

4.090

15603

\begin{align*} y-y^{\prime } x&=0 \\ \end{align*}

[_separable]

1.769

15605

\begin{align*} x y \left (1-y\right )-2 y^{\prime }&=0 \\ \end{align*}

[_separable]

3.638

15606

\begin{align*} x \left (1-y^{3}\right )-3 y^{2} y^{\prime }&=0 \\ \end{align*}

[_separable]

1.934

15607

\begin{align*} \left (2 x -1\right ) y+x \left (x +1\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

1.970

15610

\begin{align*} y^{\prime }&=\frac {y}{x} \\ y \left (-1\right ) &= 1 \\ \end{align*}

[_separable]

2.070

15611

\begin{align*} y^{\prime }&=\frac {y}{x} \\ y \left (-1\right ) &= -1 \\ \end{align*}

[_separable]

2.103

15621

\begin{align*} y^{\prime }&=-\frac {3 x^{2}}{2 y} \\ y \left (-1\right ) &= 1 \\ \end{align*}

[_separable]

4.727

15622

\begin{align*} y^{\prime }&=-\frac {3 x^{2}}{2 y} \\ y \left (-1\right ) &= {\frac {1}{2}} \\ \end{align*}

[_separable]

2.789

15623

\begin{align*} y^{\prime }&=-\frac {3 x^{2}}{2 y} \\ y \left (-1\right ) &= 0 \\ \end{align*}

[_separable]

3.816

15624

\begin{align*} y^{\prime }&=-\frac {3 x^{2}}{2 y} \\ y \left (-1\right ) &= -1 \\ \end{align*}

[_separable]

4.953

15625

\begin{align*} y^{\prime }&=\frac {\sqrt {y}}{x} \\ y \left (-1\right ) &= 1 \\ \end{align*}

[_separable]

3.757

15626

\begin{align*} y^{\prime }&=\frac {\sqrt {y}}{x} \\ y \left (-1\right ) &= 0 \\ \end{align*}

[_separable]

3.527

15627

\begin{align*} y^{\prime }&=\frac {\sqrt {y}}{x} \\ y \left (-1\right ) &= -1 \\ \end{align*}

[_separable]

3.539

15628

\begin{align*} y^{\prime }&=\frac {\sqrt {y}}{x} \\ y \left (1\right ) &= 1 \\ \end{align*}

[_separable]

3.552

15629

\begin{align*} y^{\prime }&=3 x y^{{1}/{3}} \\ y \left (-1\right ) &= {\frac {3}{2}} \\ \end{align*}

[_separable]

32.006

15630

\begin{align*} y^{\prime }&=3 x y^{{1}/{3}} \\ y \left (-1\right ) &= 1 \\ \end{align*}

[_separable]

62.865

15631

\begin{align*} y^{\prime }&=3 x y^{{1}/{3}} \\ y \left (-1\right ) &= {\frac {1}{2}} \\ \end{align*}

[_separable]

25.158

15632

\begin{align*} y^{\prime }&=3 x y^{{1}/{3}} \\ y \left (-1\right ) &= 0 \\ \end{align*}

[_separable]

11.718

15633

\begin{align*} y^{\prime }&=3 x y^{{1}/{3}} \\ y \left (-1\right ) &= -1 \\ \end{align*}

[_separable]

32.981

15644

\begin{align*} y^{\prime }&=x \sqrt {1-y^{2}} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

26.237

15645

\begin{align*} y^{\prime }&=x \sqrt {1-y^{2}} \\ y \left (0\right ) &= {\frac {9}{10}} \\ \end{align*}

[_separable]

18.702

15646

\begin{align*} y^{\prime }&=x \sqrt {1-y^{2}} \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}

[_separable]

4.309

15647

\begin{align*} y^{\prime }&=x \sqrt {1-y^{2}} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

4.263

15774

\begin{align*} y^{\prime }&=\frac {1+y}{t +1} \\ \end{align*}

[_separable]

2.588

15775

\begin{align*} y^{\prime }&=t^{2} y^{2} \\ \end{align*}

[_separable]

4.385

15776

\begin{align*} y^{\prime }&=t^{4} y \\ \end{align*}

[_separable]

2.142

15781

\begin{align*} y^{\prime }&=2 t y^{2}+3 y^{2} \\ \end{align*}

[_separable]

3.200

15782

\begin{align*} y^{\prime }&=\frac {t}{y} \\ \end{align*}

[_separable]

5.184

15783

\begin{align*} y^{\prime }&=\frac {t}{y+t^{2} y} \\ \end{align*}

[_separable]

1.832

15784

\begin{align*} y^{\prime }&=t y^{{1}/{3}} \\ \end{align*}

[_separable]

12.329

15786

\begin{align*} y^{\prime }&=\frac {2 y+1}{t} \\ \end{align*}

[_separable]

3.221

15788

\begin{align*} y^{\prime }&=\frac {4 t}{1+3 y^{2}} \\ \end{align*}

[_separable]

1.822

15789

\begin{align*} v^{\prime }&=t^{2} v-2-2 v+t^{2} \\ \end{align*}

[_separable]

2.700

15790

\begin{align*} y^{\prime }&=\frac {1}{t y+t +y+1} \\ \end{align*}

[_separable]

2.450

15791

\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{t} y}{1+y^{2}} \\ \end{align*}

[_separable]

2.319

15793

\begin{align*} w^{\prime }&=\frac {w}{t} \\ \end{align*}

[_separable]

2.168

15795

\begin{align*} x^{\prime }&=-t x \\ x \left (0\right ) &= \frac {1}{\sqrt {\pi }} \\ \end{align*}

[_separable]

2.585

15796

\begin{align*} y^{\prime }&=t y \\ y \left (0\right ) &= 3 \\ \end{align*}

[_separable]

2.332

15798

\begin{align*} y^{\prime }&=t^{2} y^{3} \\ y \left (0\right ) &= -1 \\ \end{align*}

[_separable]

17.766

15800

\begin{align*} y^{\prime }&=\frac {t}{y-t^{2} y} \\ y \left (0\right ) &= 4 \\ \end{align*}

[_separable]

2.332

15802

\begin{align*} y^{\prime }&=t y^{2}+2 y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

3.634

15803

\begin{align*} x^{\prime }&=\frac {t^{2}}{x+t^{3} x} \\ x \left (0\right ) &= -2 \\ \end{align*}

[_separable]

2.706

15805

\begin{align*} y^{\prime }&=\left (1+y^{2}\right ) t \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

3.266

15807

\begin{align*} y^{\prime }&=2 t y^{2}+3 t^{2} y^{2} \\ y \left (1\right ) &= -1 \\ \end{align*}

[_separable]

2.955

15818

\begin{align*} y^{\prime }&=\left (t +1\right ) y \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}

[_separable]

2.618

15828

\begin{align*} y^{\prime }&=t y+t y^{2} \\ \end{align*}

[_separable]

4.054

15829

\begin{align*} y^{\prime }&=t^{2}+t^{2} y \\ \end{align*}

[_separable]

2.376

15830

\begin{align*} y^{\prime }&=t +t y \\ \end{align*}

[_separable]

2.235

15857

\begin{align*} y^{\prime }&=\frac {1}{\left (1+y\right ) \left (t -2\right )} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

2.447

15859

\begin{align*} y^{\prime }&=\frac {t}{y-2} \\ y \left (-1\right ) &= 0 \\ \end{align*}

[_separable]

3.095

15941

\begin{align*} y^{\prime }&=\frac {\left (t^{2}-4\right ) \left (1+y\right ) {\mathrm e}^{y}}{\left (-1+t \right ) \left (3-y\right )} \\ \end{align*}

[_separable]

4.450

15946

\begin{align*} y^{\prime }&=t y \\ \end{align*}

[_separable]

2.580

15948

\begin{align*} y^{\prime }&=\frac {t y}{t^{2}+1} \\ \end{align*}

[_separable]

2.445

15954

\begin{align*} x^{\prime }&=-t x \\ x \left (0\right ) &= {\mathrm e} \\ \end{align*}

[_separable]

2.796

15957

\begin{align*} y^{\prime }&=t^{2} y^{3}+y^{3} \\ y \left (0\right ) &= -{\frac {1}{2}} \\ \end{align*}

[_separable]

3.648

15960

\begin{align*} y^{\prime }&=\frac {\left (t +1\right )^{2}}{\left (1+y\right )^{2}} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

7.899

15961

\begin{align*} y^{\prime }&=2 t y^{2}+3 t^{2} y^{2} \\ y \left (1\right ) &= -1 \\ \end{align*}

[_separable]

4.309

15963

\begin{align*} y^{\prime }&=\frac {t^{2}}{y+t^{3} y} \\ y \left (0\right ) &= -2 \\ \end{align*}

[_separable]

2.920

15967

\begin{align*} y^{\prime }&=t^{2} y+1+y+t^{2} \\ \end{align*}

[_separable]

3.112

15968

\begin{align*} y^{\prime }&=\frac {2 y+1}{t} \\ \end{align*}

[_separable]

3.737

16156

\begin{align*} y^{\prime } y&=2 x \\ \end{align*}

[_separable]

3.454

16197

\begin{align*} y^{\prime }+3 y x&=6 x \\ \end{align*}

[_separable]

1.977

16200

\begin{align*} x^{2} y^{\prime }+x y^{2}&=x \\ \end{align*}

[_separable]

2.881

16203

\begin{align*} \left (x -2\right ) y^{\prime }&=3+y \\ \end{align*}

[_separable]

2.239

16204

\begin{align*} \left (y-2\right ) y^{\prime }&=x -3 \\ \end{align*}

[_separable]

3.777

16208

\begin{align*} y^{\prime }&=3 y^{2}-\sin \left (x \right ) y^{2} \\ \end{align*}

[_separable]

3.398

16213

\begin{align*} y^{\prime }+y x&=4 x \\ \end{align*}

[_separable]

1.779

16215

\begin{align*} y^{\prime }&=y x -3 x -2 y+6 \\ \end{align*}

[_separable]

2.042

16217

\begin{align*} y^{\prime } y&={\mathrm e}^{x -3 y^{2}} \\ \end{align*}

[_separable]

2.474

16218

\begin{align*} y^{\prime }&=\frac {x}{y} \\ \end{align*}

[_separable]

3.369

16220

\begin{align*} x y^{\prime } y&=y^{2}+9 \\ \end{align*}

[_separable]

3.635

16221

\begin{align*} y^{\prime }&=\frac {1+y^{2}}{x^{2}+1} \\ \end{align*}

[_separable]

3.051

16222

\begin{align*} y^{\prime } \cos \left (y\right )&=\sin \left (x \right ) \\ \end{align*}

[_separable]

2.642

16223

\begin{align*} y^{\prime }&={\mathrm e}^{2 x -3 y} \\ \end{align*}

[_separable]

1.641

16224

\begin{align*} y^{\prime }&=\frac {x}{y} \\ y \left (1\right ) &= 3 \\ \end{align*}

[_separable]

4.577

16225

\begin{align*} y^{\prime }&=2 x -1+2 y x -y \\ y \left (0\right ) &= 2 \\ \end{align*}

[_separable]

2.687

16226

\begin{align*} y^{\prime } y&=x y^{2}+x \\ y \left (0\right ) &= -2 \\ \end{align*}

[_separable]

2.660

16228

\begin{align*} y^{\prime }&=y x -4 x \\ \end{align*}

[_separable]

1.884

16230

\begin{align*} y^{\prime } y&=x y^{2}-9 x \\ \end{align*}

[_separable]

2.329

16232

\begin{align*} y^{\prime }&={\mathrm e}^{x +y^{2}} \\ \end{align*}

[_separable]

1.226

16234

\begin{align*} y^{\prime }&=y x -4 x \\ \end{align*}

[_separable]

1.928

16235

\begin{align*} y^{\prime }&=y x -3 x -2 y+6 \\ \end{align*}

[_separable]

2.178

16236

\begin{align*} y^{\prime }&=3 y^{2}-\sin \left (x \right ) y^{2} \\ \end{align*}

[_separable]

3.026

16238

\begin{align*} y^{\prime }&=\frac {y}{x} \\ \end{align*}

[_separable]

1.918

16239

\begin{align*} y^{\prime }&=\frac {6 x^{2}+4}{3 y^{2}-4 y} \\ \end{align*}

[_separable]

2.208

16240

\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=1+y^{2} \\ \end{align*}

[_separable]

2.786

16241

\begin{align*} \left (y^{2}-1\right ) y^{\prime }&=4 x y^{2} \\ \end{align*}

[_separable]

14.904

16244

\begin{align*} y^{\prime }&=3 x y^{3} \\ \end{align*}

[_separable]

3.744

16245

\begin{align*} y^{\prime }&=\frac {2+\sqrt {x}}{2+\sqrt {y}} \\ \end{align*}

[_separable]

2.701

16246

\begin{align*} y^{\prime }-3 y^{2} x^{2}&=-3 x^{2} \\ \end{align*}

[_separable]

3.448

16247

\begin{align*} y^{\prime }-3 y^{2} x^{2}&=3 x^{2} \\ \end{align*}

[_separable]

3.313

16250

\begin{align*} y^{\prime } y&=\sin \left (x \right ) \\ y \left (0\right ) &= -4 \\ \end{align*}

[_separable]

2.493

16251

\begin{align*} y^{\prime }&=2 x -1+2 y x -y \\ y \left (0\right ) &= -1 \\ \end{align*}

[_separable]

3.341

16252

\begin{align*} y^{\prime } x&=-y+y^{2} \\ y \left (2\right ) &= 1 \\ \end{align*}

[_separable]

3.201

16253

\begin{align*} y^{\prime } x&=-y+y^{2} \\ y \left (1\right ) &= 2 \\ \end{align*}

[_separable]

3.202

16254

\begin{align*} y^{\prime }&=\frac {y^{2}-1}{y x} \\ y \left (1\right ) &= -2 \\ \end{align*}

[_separable]

4.319

16255

\begin{align*} \left (y^{2}-1\right ) y^{\prime }&=4 y x \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

1.717

16263

\begin{align*} y^{\prime }&=y \sin \left (x \right ) \\ \end{align*}

[_separable]

1.843

16269

\begin{align*} y^{\prime }-2 y x&=x \\ \end{align*}

[_separable]

1.566

16317

\begin{align*} 2-2 x +3 y^{2} y^{\prime }&=0 \\ \end{align*}

[_separable]

1.861

16321

\begin{align*} 1+{\mathrm e}^{y}+x \,{\mathrm e}^{y} y^{\prime }&=0 \\ \end{align*}

[_separable]

2.367

16323

\begin{align*} 1+y^{4}+x y^{3} y^{\prime }&=0 \\ \end{align*}

[_separable]

2.714

16327

\begin{align*} 3 y+3 y^{2}+\left (2 x +4 y x \right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

4.245

16328

\begin{align*} 2 x \left (1+y\right )-y^{\prime }&=0 \\ \end{align*}

[_separable]

1.602

16333

\begin{align*} y^{\prime } x&=2 y^{2}-6 y \\ \end{align*}

[_separable]

3.467

16334

\begin{align*} 4 y^{2}-y^{2} x^{2}+y^{\prime }&=0 \\ \end{align*}

[_separable]

2.095

16348

\begin{align*} y^{\prime }&=\frac {1}{y x -3 x} \\ \end{align*}

[_separable]

1.964

16351

\begin{align*} \sin \left (y\right )+\left (x +1\right ) \cos \left (y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

4.796

16357

\begin{align*} y^{\prime }&=x y^{2}+3 y^{2}+x +3 \\ \end{align*}

[_separable]

2.694

16371

\begin{align*} y^{2}-y^{2} \cos \left (x \right )+y^{\prime }&=0 \\ \end{align*}

[_separable]

2.795

16374

\begin{align*} y^{\prime }&=y^{3}-y^{3} \cos \left (x \right ) \\ \end{align*}

[_separable]

4.967

16376

\begin{align*} y^{\prime }&={\mathrm e}^{4 x +3 y} \\ \end{align*}

[_separable]

1.516

16378

\begin{align*} y^{\prime }&={\mathrm e}^{4 x +3 y} \\ \end{align*}

[_separable]

1.205

16964

\begin{align*} y^{\prime }+y x&=0 \\ \end{align*}

[_separable]

1.609

16975

\begin{align*} y^{\prime }&=-\frac {x}{y} \\ \end{align*}

[_separable]

3.114

17005

\begin{align*} y^{\prime }&=\frac {\left (x -4\right ) y^{3}}{x^{3} \left (y-2\right )} \\ \end{align*}

[_separable]

6.742

17015

\begin{align*} y^{\prime }+y \cos \left (x \right )&=0 \\ \end{align*}

[_separable]

2.008

17038

\begin{align*} \frac {y^{\prime }}{t}&=\sqrt {y} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

10.939

17040

\begin{align*} y^{\prime }&=y \sqrt {t} \\ y \left (1\right ) &= 1 \\ \end{align*}

[_separable]

2.411

17042

\begin{align*} t y^{\prime }&=y \\ \end{align*}

[_separable]

1.714

17043

\begin{align*} y^{\prime }&=\tan \left (t \right ) y \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

2.155

17064

\begin{align*} y^{\prime }&=t y^{2} \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}

[_separable]

5.286

17065

\begin{align*} y^{\prime }&=-\frac {t}{y} \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}

[_separable]

6.007

17067

\begin{align*} y^{\prime }&=\frac {x}{y^{2}} \\ \end{align*}

[_separable]

2.744

17068

\begin{align*} \frac {1}{2 \sqrt {t}}+y^{2} y^{\prime }&=0 \\ \end{align*}

[_separable]

3.059

17069

\begin{align*} y^{\prime }&=\frac {\sqrt {y}}{x^{2}} \\ \end{align*}

[_separable]

5.461

17071

\begin{align*} 6+4 t^{3}+\left (5+\frac {9}{y^{8}}\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

2.504

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]

3.023

17073

\begin{align*} 4 \sinh \left (4 y\right ) y^{\prime }&=6 \cosh \left (3 x \right ) \\ \end{align*}

[_separable]

2.798

17074

\begin{align*} y^{\prime }&=\frac {1+y}{t +1} \\ \end{align*}

[_separable]

2.115

17075

\begin{align*} y^{\prime }&=\frac {2+y}{2 t +1} \\ \end{align*}

[_separable]

3.580

17076

\begin{align*} \frac {3}{t^{2}}&=\left (\frac {1}{\sqrt {y}}+\sqrt {y}\right ) y^{\prime } \\ \end{align*}

[_separable]

3.383

17077

\begin{align*} 3 \sin \left (x \right )-4 y^{\prime } \cos \left (y\right )&=0 \\ \end{align*}

[_separable]

2.183

17078

\begin{align*} \cos \left (y\right ) y^{\prime }&=8 \sin \left (8 t \right ) \\ \end{align*}

[_separable]

3.087

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]

4.840

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]

7.320

17082

\begin{align*} y^{\prime }&={\mathrm e}^{2 y+10 t} \\ \end{align*}

[_separable]

1.685

17083

\begin{align*} y^{\prime }&={\mathrm e}^{3 y+2 t} \\ \end{align*}

[_separable]

1.709

17084

\begin{align*} \sin \left (t \right )^{2}&=\cos \left (y\right )^{2} y^{\prime } \\ \end{align*}

[_separable]

2.729

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]

28.892

17086

\begin{align*} x^{\prime }&=\frac {\sec \left (t \right )^{2}}{\sec \left (x\right ) \tan \left (x\right )} \\ \end{align*}

[_separable]

27.240

17087

\begin{align*} \left (2-\frac {5}{y^{2}}\right ) y^{\prime }+4 \cos \left (x \right )^{2}&=0 \\ \end{align*}

[_separable]

2.927

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]

3.690

17090

\begin{align*} y^{\prime }&=\frac {\left (1+2 \,{\mathrm e}^{y}\right ) {\mathrm e}^{-y}}{t \ln \left (t \right )} \\ \end{align*}

[_separable]

3.566

17091

\begin{align*} x \sin \left (x^{2}\right )&=\frac {\cos \left (\sqrt {y}\right ) y^{\prime }}{\sqrt {y}} \\ \end{align*}

[_separable]

9.737

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]

3.257

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]

10.355

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]

13.269

17095

\begin{align*} \frac {\sqrt {\ln \left (x \right )}}{x}&=\frac {{\mathrm e}^{\frac {3}{y}} y^{\prime }}{y} \\ \end{align*}

[_separable]

2.375

17096

\begin{align*} y^{\prime }&=\frac {5^{-t}}{y^{2}} \\ \end{align*}

[_separable]

1.822

17097

\begin{align*} y^{\prime }&=t^{2} y^{2}+y^{2}-t^{2}-1 \\ \end{align*}

[_separable]

3.358

17099

\begin{align*} 4 \left (x -1\right )^{2} y^{\prime }-3 \left (3+y\right )^{2}&=0 \\ \end{align*}

[_separable]

4.398

17100

\begin{align*} y^{\prime }&=\sin \left (t -y\right )+\sin \left (t +y\right ) \\ \end{align*}

[_separable]

4.799

17111

\begin{align*} y^{\prime }&=\frac {\sqrt {t}}{y} \\ y \left (0\right ) &= 2 \\ \end{align*}

[_separable]

7.215

17113

\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{t}}{1+y} \\ y \left (0\right ) &= -2 \\ \end{align*}

[_separable]

2.310

17114

\begin{align*} y^{\prime }&={\mathrm e}^{t -y} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

5.777

17118

\begin{align*} y^{\prime }&=\frac {\sin \left (x \right )}{\cos \left (y\right )+1} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

3.258

17119

\begin{align*} y^{\prime }&=\frac {3+y}{1+3 x} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

2.731

17120

\begin{align*} y^{\prime }&={\mathrm e}^{x -y} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

2.434

17121

\begin{align*} y^{\prime }&={\mathrm e}^{2 x -y} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

2.753

17122

\begin{align*} y^{\prime }&=\frac {3 y+1}{x +3} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

2.862

17123

\begin{align*} y^{\prime }&=y \cos \left (t \right ) \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

2.661

17124

\begin{align*} y^{\prime }&=y^{2} \cos \left (t \right ) \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

3.060

17125

\begin{align*} y^{\prime }&=\sqrt {y}\, \cos \left (t \right ) \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

4.303

17126

\begin{align*} y^{\prime }+y f \left (t \right )&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

2.043

17127

\begin{align*} y^{\prime }&=-\frac {y-2}{x -2} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

2.592

17137

\begin{align*} y^{\prime }&=y f \left (t \right ) \\ y \left (1\right ) &= 1 \\ \end{align*}

[_separable]

2.370

17156

\begin{align*} y^{\prime }-y x&=x \\ \end{align*}

[_separable]

1.964

17160

\begin{align*} x^{\prime }&=\frac {3 x t^{2}}{-t^{3}+1} \\ \end{align*}

[_separable]

1.705

17166

\begin{align*} 2 t y+y^{\prime }&=2 t \\ y \left (0\right ) &= -1 \\ \end{align*}

[_separable]

2.131

17170

\begin{align*} \left (t^{2}+4\right ) y^{\prime }+2 t y&=2 t \\ y \left (0\right ) &= -4 \\ \end{align*}

[_separable]

2.445

17198

\begin{align*} \frac {t}{\sqrt {t^{2}+y^{2}}}+\frac {y y^{\prime }}{\sqrt {t^{2}+y^{2}}}&=0 \\ \end{align*}

[_separable]

4.652

17205

\begin{align*} {\mathrm e}^{t y}+\frac {t \,{\mathrm e}^{t y} y^{\prime }}{y}&=0 \\ \end{align*}

[_separable]

3.166

17209

\begin{align*} \frac {3 t^{2}}{y}-\frac {t^{3} y^{\prime }}{y^{2}}&=0 \\ \end{align*}

[_separable]

3.073

17214

\begin{align*} \sin \left (y\right )^{2}+t \sin \left (2 y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

8.587

17238

\begin{align*} t^{2} y+t^{3} y^{\prime }&=0 \\ \end{align*}

[_separable]

2.400

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]

3.238

17259

\begin{align*} y^{\prime }-\frac {y}{t}&=\frac {y^{2}}{t} \\ \end{align*}

[_separable]

2.254

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]

11.415

17266

\begin{align*} \sqrt {t^{2}+1}+y y^{\prime }&=0 \\ \end{align*}

[_separable]

2.155

17296

\begin{align*} y^{\prime }-\frac {2 y}{x}&=-x^{2} y \\ \end{align*}

[_separable]

2.767

17310

\begin{align*} y^{\prime }&=\frac {2 t^{5}}{5 y^{2}} \\ \end{align*}

[_separable]

3.283

17311

\begin{align*} \cos \left (4 x \right )-8 y^{\prime } \sin \left (y\right )&=0 \\ \end{align*}

[_separable]

3.286

17312

\begin{align*} y^{\prime }-\frac {y}{t}&=\frac {y^{2}}{t} \\ \end{align*}

[_separable]

2.492

17313

\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{8 y}}{t} \\ \end{align*}

[_separable]

2.441

17314

\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{5 t}}{y^{4}} \\ \end{align*}

[_separable]

3.085

17315

\begin{align*} -\frac {1}{x^{5}}+\frac {1}{x^{3}}&=\left (2 y^{4}-6 y^{9}\right ) y^{\prime } \\ \end{align*}

[_separable]

2.839

17316

\begin{align*} y^{\prime }&=\frac {y \,{\mathrm e}^{-2 t}}{\ln \left (y\right )} \\ \end{align*}

[_separable]

2.562

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]

3.441

17330

\begin{align*} t y+y^{\prime }&=t \\ \end{align*}

[_separable]

2.267

17347

\begin{align*} y^{\prime }&=t y^{3} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

7.587

17348

\begin{align*} y^{\prime }&=\frac {t}{y^{3}} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

9.886

17349

\begin{align*} y^{\prime }&=-\frac {y}{t -2} \\ y \left (2\right ) &= 0 \\ \end{align*}

[_separable]

2.456

17838

\begin{align*} y^{\prime }&=\frac {x}{y} \\ \end{align*}

[_separable]

6.083

17850

\begin{align*} \left (-x^{2}+1\right ) y^{\prime }+y x&=2 x \\ \end{align*}

[_separable]

2.634

17856

\begin{align*} y^{\prime }&=\left (y-1\right ) x \\ \end{align*}

[_separable]

2.473

17861

\begin{align*} y^{\prime }&=\frac {1+y}{x -1} \\ \end{align*}

[_separable]

2.644

17866

\begin{align*} y^{\prime }&=-\frac {y}{x} \\ \end{align*}

[_separable]

3.033

17876

\begin{align*} 1+y^{2}+\left (x^{2}+1\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

3.691

17877

\begin{align*} x y^{\prime } y+1+y^{2}&=0 \\ \end{align*}

[_separable]

4.978

17878

\begin{align*} \sin \left (x \right ) y^{\prime }-y \cos \left (x \right )&=0 \\ y \left (\frac {\pi }{2}\right ) &= 1 \\ \end{align*}

[_separable]

3.645

17879

\begin{align*} 1+y^{2}&=y^{\prime } x \\ \end{align*}

[_separable]

3.924

17880

\begin{align*} y y^{\prime } \sqrt {x^{2}+1}+x \sqrt {1+y^{2}}&=0 \\ \end{align*}

[_separable]

4.747

17881

\begin{align*} x \sqrt {1-y^{2}}+y \sqrt {-x^{2}+1}\, y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

10.059

17883

\begin{align*} y \ln \left (y\right )+y^{\prime } x&=1 \\ y \left (1\right ) &= 1 \\ \end{align*}

[_separable]

7.550

17884

\begin{align*} y^{\prime }&=a^{x +y} \\ \end{align*}

[_separable]

3.168

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]

6.132

17886

\begin{align*} 2 x \sqrt {1-y^{2}}&=\left (x^{2}+1\right ) y^{\prime } \\ \end{align*}

[_separable]

5.039

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]

5.646

17888

\begin{align*} \sin \left (x \right ) y^{2}+\cos \left (x \right )^{2} \ln \left (y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

6.369

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]

10.022

17894

\begin{align*} y^{\prime }&=\frac {y}{x} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

5.754

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]

4.464

17907

\begin{align*} \left (x +1\right ) y^{\prime }&=y-1 \\ \end{align*}

[_separable]

2.874

17908

\begin{align*} y^{\prime }&=2 x \left (\pi +y\right ) \\ \end{align*}

[_separable]

2.658

17909

\begin{align*} x^{2} y^{\prime }+\sin \left (2 y\right )&=1 \\ y \left (\infty \right ) &= \frac {11 \pi }{4} \\ \end{align*}

[_separable]

13.454

17939

\begin{align*} y^{\prime }+y \cos \left (x \right )&=\cos \left (x \right ) \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

2.931

17953

\begin{align*} y^{\prime }+2 y x&=2 x y^{2} \\ \end{align*}

[_separable]

4.627

17956

\begin{align*} y^{\prime }+3 y x&=y \,{\mathrm e}^{x^{2}} \\ \end{align*}

[_separable]

3.823

17961

\begin{align*} y^{\prime }-y \cos \left (x \right )&=y^{2} \cos \left (x \right ) \\ \end{align*}

[_separable]

5.424

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]

34.829

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]

4.688

18055

\begin{align*} y^{\prime } \left (3 x^{2}-2 x \right )-y \left (6 x -2\right )&=0 \\ \end{align*}

[_separable]

1.724

18062

\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]

3.516

18071

\begin{align*} \sin \left (\ln \left (x \right )\right )-\cos \left (\ln \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

2.931

18098

\begin{align*} y x&=y^{\prime } \ln \left (\frac {y^{\prime }}{x}\right ) \\ \end{align*}

[_separable]

15.637

18473

\begin{align*} y^{\prime }&=\frac {x^{4}}{y} \\ \end{align*}

[_separable]

2.487

18474

\begin{align*} y^{\prime }&=\frac {x^{2} \left (x^{3}+1\right )}{y} \\ \end{align*}

[_separable]

1.706

18475

\begin{align*} y^{\prime }+y^{3} \sin \left (x \right )&=0 \\ \end{align*}

[_separable]

3.500

18476

\begin{align*} y^{\prime }&=\frac {7 x^{2}-1}{7+5 y} \\ \end{align*}

[_separable]

1.954

18477

\begin{align*} y^{\prime }&=\sin \left (2 x \right )^{2} \cos \left (y\right )^{2} \\ \end{align*}

[_separable]

3.108

18478

\begin{align*} y^{\prime } x&=\sqrt {1-y^{2}} \\ \end{align*}

[_separable]

3.562

18479

\begin{align*} y^{\prime } y&=\left (x y^{2}+x \right ) {\mathrm e}^{x^{2}} \\ \end{align*}

[_separable]

2.740

18480

\begin{align*} y^{\prime }&=\frac {x^{2}+{\mathrm e}^{-x}}{y^{2}-{\mathrm e}^{y}} \\ \end{align*}

[_separable]

2.647

18481

\begin{align*} y^{\prime }&=\frac {x^{2}}{1+y^{2}} \\ \end{align*}

[_separable]

1.510

18482

\begin{align*} y^{\prime }&=\frac {\sec \left (x \right )^{2}}{y^{3}+1} \\ \end{align*}

[_separable]

2.264

18484

\begin{align*} y^{\prime }&=x \left (y-y^{2}\right ) \\ \end{align*}

[_separable]

2.920

18485

\begin{align*} y^{\prime }&=\left (1-12 x \right ) y^{2} \\ y \left (0\right ) &= -{\frac {1}{8}} \\ \end{align*}

[_separable]

3.728

18486

\begin{align*} y^{\prime }&=\frac {3-2 x}{y} \\ y \left (1\right ) &= -6 \\ \end{align*}

[_separable]

2.753

18487

\begin{align*} x +y y^{\prime } {\mathrm e}^{-x}&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

2.305

18488

\begin{align*} r^{\prime }&=\frac {r^{2}}{\theta } \\ r \left (1\right ) &= 2 \\ \end{align*}

[_separable]

2.612

18489

\begin{align*} y^{\prime }&=\frac {3 x}{y+x^{2} y} \\ y \left (0\right ) &= -7 \\ \end{align*}

[_separable]

1.984

18490

\begin{align*} y^{\prime }&=\frac {2 x}{1+2 y} \\ y \left (2\right ) &= 0 \\ \end{align*}

[_separable]

3.500

18491

\begin{align*} y^{\prime }&=2 x y^{2}+4 x^{3} y^{2} \\ y \left (1\right ) &= -2 \\ \end{align*}

[_separable]

3.707

18492

\begin{align*} y^{\prime }&=x^{2} {\mathrm e}^{-3 y} \\ y \left (2\right ) &= 0 \\ \end{align*}

[_separable]

3.505

18493

\begin{align*} y^{\prime }&=\left (1+y^{2}\right ) \tan \left (2 x \right ) \\ y \left (0\right ) &= -\sqrt {3} \\ \end{align*}

[_separable]

5.576

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]

2.843

18495

\begin{align*} y^{\prime }&=\frac {-{\mathrm e}^{x}+3 x^{2}}{2 y-11} \\ y \left (0\right ) &= 11 \\ \end{align*}

[_separable]

2.634

18496

\begin{align*} x^{2} y^{\prime }&=y-y x \\ y \left (1\right ) &= 2 \\ \end{align*}

[_separable]

2.801

18497

\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{-x}-{\mathrm e}^{x}}{3+4 y} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

2.501

18498

\begin{align*} 2 y^{\prime } y&=\frac {x}{\sqrt {x^{2}-4}} \\ y \left (3\right ) &= -1 \\ \end{align*}

[_separable]

3.024

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]

25.050

18500

\begin{align*} \sqrt {-x^{2}+1}\, y^{2} y^{\prime }&=\arcsin \left (x \right ) \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

3.484

18501

\begin{align*} y^{\prime }&=\frac {3 x^{2}+1}{12 y^{2}-12 y} \\ y \left (0\right ) &= 2 \\ \end{align*}

[_separable]

5.763

18502

\begin{align*} y^{\prime }&=\frac {2 x^{2}}{2 y^{2}-6} \\ y \left (1\right ) &= 0 \\ \end{align*}

[_separable]

1.601

18503

\begin{align*} y^{\prime }&=2 y^{2}+x y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

3.441

18504

\begin{align*} y^{\prime }&=\frac {6-{\mathrm e}^{x}}{3+2 y} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

2.116

18505

\begin{align*} y^{\prime }&=\frac {2 \cos \left (2 x \right )}{10+2 y} \\ y \left (0\right ) &= -1 \\ \end{align*}

[_separable]

2.174

18506

\begin{align*} y^{\prime }&=2 \left (x +1\right ) \left (1+y^{2}\right ) \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

2.936

18507

\begin{align*} y^{\prime }&=\frac {t \left (4-y\right ) y}{3} \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}

[_separable]

4.058

18508

\begin{align*} y^{\prime }&=\frac {t y \left (4-y\right )}{t +1} \\ y \left (0\right ) &= 2 \\ \end{align*}

[_separable]

4.056

18546

\begin{align*} y+\left (t -4\right ) t y^{\prime }&=0 \\ y \left (2\right ) &= 1 \\ \end{align*}

[_separable]

2.122

18555

\begin{align*} y^{\prime }&=\frac {t^{2}+1}{3 y-y^{2}} \\ \end{align*}

[_separable]

1.724

18556

\begin{align*} y^{\prime }&=\frac {\cot \left (t \right ) y}{1+y} \\ \end{align*}

[_separable]

2.556

18559

\begin{align*} y^{\prime }&=-\frac {4 t}{y} \\ y \left (0\right ) &= y_{0} \\ \end{align*}

[_separable]

5.091

18560

\begin{align*} y^{\prime }&=2 t y^{2} \\ y \left (0\right ) &= y_{0} \\ \end{align*}

[_separable]

4.147

18562

\begin{align*} y^{\prime }&=\frac {t^{2}}{\left (t^{3}+1\right ) y} \\ y \left (0\right ) &= y_{0} \\ \end{align*}

[_separable]

1.833

18563

\begin{align*} y^{\prime }&=t \left (3-y\right ) y \\ \end{align*}

[_separable]

2.909

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]

1.374

18568

\begin{align*} 3+2 x +\left (-2+2 y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

3.611

18578

\begin{align*} \ln \left (y\right ) x +y x +\left (y \ln \left (x \right )+y x \right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

2.716

18579

\begin{align*} \frac {x}{\left (y^{2}+x^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (y^{2}+x^{2}\right )^{{3}/{2}}}&=0 \\ \end{align*}

[_separable]

4.012

18582

\begin{align*} x^{2} y^{3}+x \left (1+y^{2}\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

1.783

18585

\begin{align*} \left (2+x \right ) \sin \left (y\right )+x \cos \left (y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

2.342

18594

\begin{align*} y^{\prime } y&=x +1 \\ \end{align*}

[_separable]

1.920

18595

\begin{align*} \left (1+y^{4}\right ) y^{\prime }&=x^{4}+1 \\ \end{align*}

[_separable]

1.661

18597

\begin{align*} x \left (x -1\right ) y^{\prime }&=y \left (1+y\right ) \\ \end{align*}

[_separable]

3.491

18610

\begin{align*} 5 \left (t^{2}+1\right ) y^{\prime }&=4 t y \left (y^{3}-1\right ) \\ \end{align*}

[_separable]

31.163

18621

\begin{align*} \frac {\sqrt {x}\, y^{\prime }}{y}&=1 \\ \end{align*}

[_separable]

2.159

19066

\begin{align*} y y^{\prime } \sqrt {x^{2}+1}+x \sqrt {1+y^{2}}&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

3.550

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]

27.748

19068

\begin{align*} y^{\prime } \sqrt {-x^{2}+1}+\sqrt {1-y^{2}}&=0 \\ \end{align*}

[_separable]

5.407

19228

\begin{align*} y^{\prime } x&=2 y \\ \end{align*}

[_separable]

6.066

19229

\begin{align*} y^{\prime } y&={\mathrm e}^{2 x} \\ \end{align*}

[_separable]

6.472

19249

\begin{align*} x y^{\prime } y&=y-1 \\ \end{align*}

[_separable]

9.033

19250

\begin{align*} x^{5} y^{\prime }+y^{5}&=0 \\ \end{align*}

[_separable]

13.608

19251

\begin{align*} y^{\prime } x&=\left (-2 x^{2}+1\right ) \tan \left (y\right ) \\ \end{align*}

[_separable]

4.463

19252

\begin{align*} y^{\prime }&=2 y x \\ \end{align*}

[_separable]

4.697

19253

\begin{align*} y^{\prime } \sin \left (y\right )&=x^{2} \\ \end{align*}

[_separable]

3.497

19255

\begin{align*} y^{\prime }+\tan \left (x \right ) y&=0 \\ \end{align*}

[_separable]

3.931

19256

\begin{align*} y^{\prime }-\tan \left (x \right ) y&=0 \\ \end{align*}

[_separable]

4.187

19257

\begin{align*} 1+y^{2}+\left (x^{2}+1\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

5.800

19258

\begin{align*} y \ln \left (y\right )-y^{\prime } x&=0 \\ \end{align*}

[_separable]

8.182

19265

\begin{align*} y^{\prime }&={\mathrm e}^{3 x -2 y} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

6.729

19267

\begin{align*} {\mathrm e}^{-y}+\left (x^{2}+1\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

4.392

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]

6.380

19270

\begin{align*} x y^{\prime } y&=\left (x +1\right ) \left (1+y\right ) \\ y \left (1\right ) &= 0 \\ \end{align*}

[_separable]

5.613

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]

7.001

19302

\begin{align*} 1+y+\left (1-x \right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

4.591

19308

\begin{align*} \ln \left (y\right ) x +y x +\left (y \ln \left (x \right )+y x \right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

7.629

19311

\begin{align*} \frac {x}{\left (y^{2}+x^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (y^{2}+x^{2}\right )^{{3}/{2}}}&=0 \\ \end{align*}

[_separable]

21.329

19319

\begin{align*} \left (2+x \right ) \sin \left (y\right )+x \cos \left (y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

4.712

19327

\begin{align*} y-y^{\prime } x&=x y^{3} y^{\prime } \\ \end{align*}

[_separable]

8.619

19331

\begin{align*} y^{\prime } x -y+y^{2}&=0 \\ \end{align*}

[_separable]

5.751

19377

\begin{align*} y^{\prime } x +y&=x^{2} y^{\prime }+y^{2} \\ \end{align*}

[_separable]

9.693

19400

\begin{align*} 3 x^{2} \ln \left (y\right )+\frac {x^{3} y^{\prime }}{y}&=0 \\ \end{align*}

[_separable]

9.212

19672

\begin{align*} 1+2 x+\left (-t^{2}+4\right ) x^{\prime }&=0 \\ \end{align*}

[_separable]

13.168

19678

\begin{align*} x^{\prime }+x \tan \left (t \right )&=0 \\ \end{align*}

[_separable]

4.384

19681

\begin{align*} x^{\prime }+2 t x+t x^{4}&=0 \\ \end{align*}

[_separable]

5.359

19706

\begin{align*} y^{\prime }&=\frac {\sqrt {1-y^{2}}\, \arcsin \left (y\right )}{x} \\ \end{align*}

[_separable]

28.064

19711

\begin{align*} \sin \left (x \right ) \cos \left (y\right )^{2}+\cos \left (x \right )^{2} y^{\prime }&=0 \\ \end{align*}

[_separable]

5.824

19713

\begin{align*} y-y^{\prime } x&=b \left (1+x^{2} y^{\prime }\right ) \\ \end{align*}

[_separable]

6.546

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]

5.861

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]

37.374

19723

\begin{align*} y^{\prime }+y x&=x \\ \end{align*}

[_separable]

5.132

19740

\begin{align*} y^{\prime }&=x \left (a y^{2}+b \right ) \\ \end{align*}

[_separable]

9.432

19741

\begin{align*} n^{\prime }&=\left (n^{2}+1\right ) x \\ \end{align*}

[_separable]

5.446

19742

\begin{align*} v^{\prime }+\frac {2 v}{u}&=3 v \\ \end{align*}

[_separable]

4.406

19743

\begin{align*} \sqrt {-u^{2}+1}\, v^{\prime }&=2 u \sqrt {1-v^{2}} \\ \end{align*}

[_separable]

8.866

19745

\begin{align*} \frac {y^{\prime }}{x}&=y \sin \left (x^{2}-1\right )-\frac {2 y}{\sqrt {x}} \\ \end{align*}

[_separable]

23.713

19747

\begin{align*} v^{\prime }+2 u v&=2 u \\ \end{align*}

[_separable]

5.012

19748

\begin{align*} 1+v^{2}+\left (u^{2}+1\right ) v v^{\prime }&=0 \\ \end{align*}

[_separable]

10.169

19749

\begin{align*} u \ln \left (u \right ) v^{\prime }+\sin \left (v\right )^{2}&=1 \\ \end{align*}

[_separable]

5.728

19797

\begin{align*} y^{\prime }+y \sin \left (x \right )&=\sin \left (x \right ) y^{2} \\ \end{align*}

[_separable]

12.092

19798

\begin{align*} \left (-x^{2}+1\right ) y^{\prime }-y x&=a x y^{2} \\ \end{align*}

[_separable]

21.419

19802

\begin{align*} y \sqrt {x^{2}-1}+x \sqrt {y^{2}-1}\, y^{\prime }&=0 \\ \end{align*}

[_separable]

123.590

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]

4.888

19804

\begin{align*} \sqrt {2 a y-y^{2}}\, \csc \left (x \right )+y \tan \left (x \right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

37.123

19805

\begin{align*} y \left (3+y\right ) y^{\prime }&=x \left (3+2 y\right ) \\ \end{align*}

[_separable]

6.112

19808

\begin{align*} \cos \left (y\right ) \sin \left (x \right )+\cos \left (x \right ) \sin \left (y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

4.889

19896

\begin{align*} \left (1-x \right ) y^{\prime }-1-y&=0 \\ \end{align*}

[_separable]

6.725

19898

\begin{align*} y-y^{\prime } x&=a \left (y^{\prime }+y^{2}\right ) \\ \end{align*}

[_separable]

12.187

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]

9.266

19913

\begin{align*} a \left (y^{\prime } x +2 y\right )&=x y^{\prime } y \\ \end{align*}

[_separable]

26.100

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]

35.825

19939

\begin{align*} y^{2}+x y^{2}+\left (x^{2}-x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

11.337

19952

\begin{align*} \left (x +1\right ) y^{\prime }+1&=2 \,{\mathrm e}^{y} \\ \end{align*}

[_separable]

9.941

19958

\begin{align*} y^{\prime } y&=a x \\ \end{align*}

[_separable]

22.668

19963

\begin{align*} y-y^{\prime } x&=b \left (1+x^{2} y^{\prime }\right ) \\ \end{align*}

[_separable]

6.992

19990

\begin{align*} x y \left (y-y^{\prime } x \right )&=y^{\prime } y+x \\ \end{align*}

[_separable]

13.646

20019

\begin{align*} \sqrt {x}\, y^{\prime }&=\sqrt {y} \\ \end{align*}

[_separable]

3.949

20226

\begin{align*} x \cos \left (y\right )^{2}&=y \cos \left (x \right )^{2} y^{\prime } \\ \end{align*}

[_separable]

4.209

20227

\begin{align*} y^{\prime }&={\mathrm e}^{x -y}+x^{2} {\mathrm e}^{-y} \\ \end{align*}

[_separable]

1.777

20228

\begin{align*} x^{2} y^{\prime }+y&=1 \\ \end{align*}

[_separable]

1.458

20229

\begin{align*} 2 y+\left (x^{2}+1\right ) \arctan \left (x \right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

1.811

20230

\begin{align*} x y^{2}+x +\left (y+x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

1.870

20231

\begin{align*} y^{\prime }&={\mathrm e}^{x +y}+x^{2} {\mathrm e}^{y} \\ \end{align*}

[_separable]

1.638

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]

9.128

20233

\begin{align*} \frac {\cos \left (y\right )^{2} y^{\prime }}{x}+\frac {\cos \left (x \right )^{2}}{y}&=0 \\ \end{align*}

[_separable]

3.937

20234

\begin{align*} \left ({\mathrm e}^{x}+1\right ) y y^{\prime }&=\left (1+y\right ) {\mathrm e}^{x} \\ \end{align*}

[_separable]

2.439

20235

\begin{align*} \csc \left (x \right ) \ln \left (y\right ) y^{\prime }+y^{2} x^{2}&=0 \\ \end{align*}

[_separable]

5.870

20236

\begin{align*} y^{\prime }&=\frac {\sin \left (x \right )+\cos \left (x \right ) x}{y \left (2 \ln \left (y\right )+1\right )} \\ \end{align*}

[_separable]

0.695

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]

24.509

20238

\begin{align*} y^{2}+x y^{2}+\left (x^{2}-x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

2.622

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]

25.508

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]

2.932

20241

\begin{align*} y-y^{\prime } x&=a \left (y^{\prime }+y^{2}\right ) \\ \end{align*}

[_separable]

2.572

20282

\begin{align*} x +y^{\prime }&=x \,{\mathrm e}^{\left (n -1\right ) y} \\ \end{align*}

[_separable]

2.717

20311

\begin{align*} y^{\prime }&={\mathrm e}^{3 x -2 y}+x^{2} {\mathrm e}^{-2 y} \\ \end{align*}

[_separable]

1.938

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]

24.884

20317

\begin{align*} s^{\prime }+x^{2}&=x^{2} {\mathrm e}^{3 s} \\ \end{align*}

[_separable]

2.311

20481

\begin{align*} y-y^{\prime } x&=a \left (y^{\prime }+y^{2}\right ) \\ \end{align*}

[_separable]

3.696

20482

\begin{align*} y-y^{\prime } x&=b \left (1+x^{2} y^{\prime }\right ) \\ \end{align*}

[_separable]

2.224

20677

\begin{align*} y-y^{\prime } x&=0 \\ \end{align*}

[_separable]

2.169

20678

\begin{align*} \cot \left (y\right )-\tan \left (x \right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

3.023

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]

29.906

20682

\begin{align*} 1+y^{2}-x y^{\prime } y&=0 \\ \end{align*}

[_separable]

5.233

20728

\begin{align*} x y \left (y-y^{\prime } x \right )&=y^{\prime } y+x \\ \end{align*}

[_separable]

6.373

20811

\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{x}}{2 y} \\ \end{align*}

[_separable]

3.700

20812

\begin{align*} y^{\prime }&=y^{2} \left (t^{2}+1\right ) \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

4.276

20813

\begin{align*} y^{\prime }&=\frac {\sqrt {1-y^{2}}}{x} \\ \end{align*}

[_separable]

134.348

20814

\begin{align*} y^{\prime } x&=y \left (1-2 y\right ) \\ y \left (1\right ) &= 2 \\ \end{align*}

[_separable]

10.683

20815

\begin{align*} y^{\prime }-y \sin \left (x \right )&=\sin \left (x \right ) \\ \end{align*}

[_separable]

3.550

20817

\begin{align*} s^{\prime }+2 s&=s t^{2} \\ s \left (0\right ) &= 1 \\ \end{align*}

[_separable]

3.554

20826

\begin{align*} y^{\prime }&=\frac {x}{y}-\frac {x}{1+y} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

8.279

20829

\begin{align*} y^{\prime }+2 y x&=2 x y^{2} \\ \end{align*}

[_separable]

6.310

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]

17.857

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]

3.147

20973

\begin{align*} y^{\prime }&=\frac {2 y \left (y-1\right )}{x \left (2-y\right )} \\ \end{align*}

[_separable]

75.521

20975

\begin{align*} y^{\prime }&=f \left (x \right ) y \ln \left (\frac {1}{y}\right ) \\ \end{align*}

[_separable]

14.245

20983

\begin{align*} y&=y^{\prime } x +a y^{\prime }+b \\ \end{align*}

[_separable]

8.400

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]

26.614

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]

3.915

21009

\begin{align*} x^{\prime }+\frac {x}{t^{2}-1}&=0 \\ x \left (-2\right ) &= 1 \\ \end{align*}

[_separable]

3.198

21013

\begin{align*} x^{\prime }&=2 t x \\ x \left (0\right ) &= 4 \\ \end{align*}

[_separable]

3.105

21014

\begin{align*} x^{\prime }&=-t^{2} x \\ \end{align*}

[_separable]

2.833

21024

\begin{align*} x^{\prime }&=\frac {x}{t^{2}+1} \\ x \left (0\right ) &= 1 \\ \end{align*}

[_separable]

3.370

21031

\begin{align*} x^{\prime }+\frac {\sin \left (t \right ) x}{1+{\mathrm e}^{t}}&=0 \\ \end{align*}

[_separable]

4.612

21054

\begin{align*} x^{\prime }&=4 t^{3} x^{4} \\ \end{align*}

[_separable]

8.076

21055

\begin{align*} x^{\prime }&=-t x^{2} \\ \end{align*}

[_separable]

19.829

21056

\begin{align*} x^{\prime }&={\mathrm e}^{t} \left (1+x^{2}\right ) \\ x \left (0\right ) &= 0 \\ \end{align*}

[_separable]

4.720

21057

\begin{align*} x^{\prime }&=\frac {t}{x} \\ x \left (\sqrt {2}\right ) &= 1 \\ \end{align*}

[_separable]

8.734

21058

\begin{align*} x^{\prime }&=-\frac {t}{4 x^{3}} \\ x \left (1\right ) &= 1 \\ \end{align*}

[_separable]

5.061

21059

\begin{align*} x^{\prime }&=-t^{2} x^{2} \\ x \left (1\right ) &= 2 \\ \end{align*}

[_separable]

9.409

21060

\begin{align*} x^{\prime }&=5 t \sqrt {x} \\ x \left (0\right ) &= 1 \\ \end{align*}

[_separable]

41.820

21061

\begin{align*} x^{\prime }&=4 t^{3} \sqrt {x} \\ x \left (0\right ) &= 1 \\ \end{align*}

[_separable]

30.706

21062

\begin{align*} x^{\prime }&=2 t \sqrt {x} \\ x \left (a \right ) &= 0 \\ \end{align*}

[_separable]

26.037

21063

\begin{align*} x^{\prime }&=-\left (1+p \right ) t^{p} x^{2} \\ \end{align*}

[_separable]

7.174

21065

\begin{align*} 2 x^{2}+1&=\left (y^{5}-1\right ) y^{\prime } \\ \end{align*}

[_separable]

10.493

21075

\begin{align*} x -2 y^{3} y^{\prime }&=0 \\ \end{align*}

[_separable]

10.944

21083

\begin{align*} x y^{\prime } y+1+y^{2}&=0 \\ \end{align*}

[_separable]

7.831

21092

\begin{align*} x^{\prime }+2 t x&=-4 t x^{3} \\ \end{align*}

[_separable]

12.078

21333

\begin{align*} y^{\prime }&=f \left (x \right ) g \left (y\right ) \\ \end{align*}

[_separable]

2.189

21334

\begin{align*} -y+y^{\prime } x&=0 \\ \end{align*}

[_separable]

3.757

21336

\begin{align*} y^{\prime } y+x&=0 \\ \end{align*}

[_separable]

11.799

21337

\begin{align*} y^{\prime } x +y&=0 \\ \end{align*}

[_separable]

4.728

21338

\begin{align*} y^{\prime } x -2 y&=0 \\ \end{align*}

[_separable]

5.937

21340

\begin{align*} 2 x \left (1+y\right )-y^{\prime } y&=0 \\ y \left (0\right ) &= -2 \\ \end{align*}

[_separable]

11.856

21341

\begin{align*} y^{\prime }&=-\frac {x}{y} \\ \end{align*}

[_separable]

7.417

21342

\begin{align*} y^{\prime }&=\frac {2 y}{x} \\ \end{align*}

[_separable]

4.666

21343

\begin{align*} -2+2 y+x^{2} \sin \left (y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

12.782

21344

\begin{align*} y^{\prime }&=\frac {x +1}{1+y^{2}} \\ \end{align*}

[_separable]

8.927

21345

\begin{align*} y^{\prime }&=\frac {a x +b}{y^{n}+d} \\ \end{align*}

[_separable]

18.682

21346

\begin{align*} y^{\prime }&=-\frac {x}{y} \\ y \left (0\right ) &= a_{0} \\ \end{align*}

[_separable]

14.425

21347

\begin{align*} y^{\prime }&=x^{2} y \\ \end{align*}

[_separable]

4.184

21348

\begin{align*} y^{\prime }&=\frac {1+y^{2}}{x^{2}+1} \\ \end{align*}

[_separable]

8.797

21349

\begin{align*} \cos \left (x \right ) x +\left (1-6 y^{5}\right ) y^{\prime }&=0 \\ y \left (\pi \right ) &= 0 \\ \end{align*}

[_separable]

9.846

21350

\begin{align*} y^{\prime }&=\frac {x}{y^{3}} \\ \end{align*}

[_separable]

7.668

21351

\begin{align*} y^{\prime }&=\frac {x}{y^{2} \sqrt {x^{2}+1}} \\ \end{align*}

[_separable]

5.988

21352

\begin{align*} y^{\prime }&=2 y x \\ y \left (0\right ) &= 5 \\ \end{align*}

[_separable]

4.249

21353

\begin{align*} x y^{2}-x +\left (y+x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

11.713

21354

\begin{align*} y^{\prime }&=x^{2} y^{3} \\ \end{align*}

[_separable]

11.528

21355

\begin{align*} y^{\prime }&=\frac {y \ln \left (x \right )}{x} \\ \end{align*}

[_separable]

8.936

21356

\begin{align*} y^{\prime }&=x^{2} y \\ \end{align*}

[_separable]

3.956

21357

\begin{align*} {\mathrm e}^{x}-y^{\prime } y&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

4.518

21371

\begin{align*} \left (x -4\right ) y^{4}-x^{3} \left (y^{2}-3\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

15.300

21372

\begin{align*} 1+y^{2}+\left (x^{2}+1\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

10.889

21373

\begin{align*} x \sin \left (y\right )+\left (x^{2}+1\right ) \cos \left (y\right ) y^{\prime }&=0 \\ y \left (1\right ) &= \frac {\pi }{2} \\ \end{align*}

[_separable]

10.140

21401

\begin{align*} y^{\prime }+2 y x&=0 \\ \end{align*}

[_separable]

4.196

21406

\begin{align*} y^{\prime }&=2 y x -x \\ \end{align*}

[_separable]

3.771

21411

\begin{align*} y-y^{\prime } x&=0 \\ \end{align*}

[_separable]

3.924

21412

\begin{align*} y^{\prime } x -y+y^{2}&=0 \\ \end{align*}

[_separable]

8.585

21427

\begin{align*} \frac {y^{\prime }}{x}-\frac {y}{x^{2}}&=0 \\ \end{align*}

[_separable]

4.036

21432

\begin{align*} y^{\prime }+q \left (x \right ) y&=0 \\ y \left (\textit {x\_0} \right ) &= y_{0} \\ \end{align*}

[_separable]

7.226

21439

\begin{align*} \left (x^{2}+1\right ) y^{\prime }+4 y x&=x \\ y \left (2\right ) &= 1 \\ \end{align*}

[_separable]

12.412

21442

\begin{align*} y^{\prime }-2 y x&=x \\ \end{align*}

[_separable]

3.759

21458

\begin{align*} y^{\prime }+y x&=x y^{2} \\ \end{align*}

[_separable]

8.828

21791

\begin{align*} y^{\prime } y+x&=0 \\ \end{align*}

[_separable]

22.436

21795

\begin{align*} y^{\prime }&=-\frac {x}{4 y} \\ \end{align*}

[_separable]

9.153

21796

\begin{align*} y^{\prime }&=\frac {x}{y} \\ \end{align*}

[_separable]

26.850

21797

\begin{align*} 3 x^{2}-2 y^{3} y^{\prime }&=0 \\ \end{align*}

[_separable]

11.879

21798

\begin{align*} 1+y+y^{2}+x \left (x^{2}-4\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

38.114

21799

\begin{align*} r^{\prime } \sin \left (t \right )+r \cos \left (t \right )&=0 \\ \end{align*}

[_separable]

5.425

21801

\begin{align*} y^{\prime } y+x&=0 \\ y \left (1\right ) &= 2 \\ \end{align*}

[_separable]

10.701

21802

\begin{align*} r^{\prime }&=r \tan \left (t \right ) \\ r \left (0\right ) &= 1 \\ \end{align*}

[_separable]

5.134

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]

25.327

21821

\begin{align*} x^{3} y^{\prime }-x^{2} y&=x^{5} y \\ \end{align*}

[_separable]

24.636

21842

\begin{align*} -y+y^{\prime } x&=y^{3} \\ \end{align*}

[_separable]

26.202

21843

\begin{align*} y^{\prime }+3 x^{2} y&=3 x^{2} \\ \end{align*}

[_separable]

4.454

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]

53.454

21926

\begin{align*} x^{2} y^{\prime }+y^{2}&=x^{2} y y^{\prime }-x y^{2} \\ \end{align*}

[_separable]

39.975

21965

\begin{align*} y^{\prime }+2 x y^{2}&=0 \\ \end{align*}

[_separable]

1.785

21977

\begin{align*} y^{\prime }&=\frac {y^{2}}{x} \\ \end{align*}

[_separable]

1.662

21980

\begin{align*} \sin \left (x \right )+y^{2} y^{\prime }&=0 \\ \end{align*}

[_separable]

1.869

21986

\begin{align*} y^{\prime }&=y x \\ \end{align*}

[_separable]

1.482

21988

\begin{align*} y^{\prime }&=\frac {x^{2}}{y^{2}} \\ \end{align*}

[_separable]

2.782

21989

\begin{align*} y^{\prime }&=-\frac {2 y}{x} \\ \end{align*}

[_separable]

1.798

21991

\begin{align*} x -y^{2} y^{\prime }&=0 \\ \end{align*}

[_separable]

1.880

21992

\begin{align*} y^{\prime }&=x^{3} y^{2} \\ \end{align*}

[_separable]

2.403

21994

\begin{align*} y^{\prime }&=\frac {x +1}{1+y^{4}} \\ \end{align*}

[_separable]

1.528

21995

\begin{align*} {\mathrm e}^{x}-y^{\prime } y&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

1.342

21996

\begin{align*} \cos \left (x \right ) x +\left (1-6 y^{5}\right ) y^{\prime }&=0 \\ y \left (\pi \right ) &= 0 \\ \end{align*}

[_separable]

3.112

21997

\begin{align*} y^{\prime } y+x&=0 \\ \end{align*}

[_separable]

3.002

21998

\begin{align*} \frac {1}{x}-\frac {y^{\prime }}{y}&=0 \\ \end{align*}

[_separable]

1.598

22000

\begin{align*} x +\frac {y^{\prime }}{y}&=0 \\ \end{align*}

[_separable]

1.550

22001

\begin{align*} x^{2}+1+\left (y^{2}+y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

1.709

22002

\begin{align*} \sin \left (x \right )+y^{\prime } y&=0 \\ y \left (0\right ) &= -2 \\ \end{align*}

[_separable]

2.180

22003

\begin{align*} x^{2}+1+\frac {y^{\prime }}{y}&=0 \\ y \left (-1\right ) &= 1 \\ \end{align*}

[_separable]

1.873

22004

\begin{align*} x \,{\mathrm e}^{x}+\left (y^{5}-1\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

2.137

22005

\begin{align*} y^{\prime }&=\frac {y}{x} \\ \end{align*}

[_separable]

1.537

22006

\begin{align*} y^{\prime }&=\frac {x \,{\mathrm e}^{x}}{2 y} \\ \end{align*}

[_separable]

1.701

22007

\begin{align*} y^{\prime }&=\frac {x^{2} y-y}{1+y} \\ y \left (3\right ) &= -1 \\ \end{align*}

[_separable]

2.517

22011

\begin{align*} y^{\prime }&=y x \\ y \left (1\right ) &= -2 \\ \end{align*}

[_separable]

2.615

22022

\begin{align*} \left (x^{2}+1\right ) y^{\prime }+2 y x&=0 \\ \end{align*}

[_separable]

0.970

22026

\begin{align*} y^{\prime }&=-\frac {2 x y}{x^{2}+1} \\ y \left (2\right ) &= -5 \\ \end{align*}

[_separable]

1.313

22032

\begin{align*} y^{\prime } x +y&=0 \\ \end{align*}

[_separable]

1.562

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]

16.170

22035

\begin{align*} y-y^{\prime } x&=0 \\ \end{align*}

[_separable]

1.357

22036

\begin{align*} y^{\prime } x -y+y^{2}&=0 \\ \end{align*}

[_separable]

1.396

22039

\begin{align*} y^{\prime }&=2 y x -x \\ \end{align*}

[_separable]

1.516

22042

\begin{align*} y+1-y^{\prime } x&=0 \\ \end{align*}

[_separable]

1.666

22043

\begin{align*} \left (1-x \right ) y^{\prime }+y&=0 \\ \end{align*}

[_separable]

1.474

22047

\begin{align*} 3 x^{2} y-x^{2}+y^{\prime }&=0 \\ \end{align*}

[_separable]

1.554

22048

\begin{align*} 1-2 x y^{\prime } y&=0 \\ \end{align*}

[_separable]

1.677

22050

\begin{align*} y+3 y^{\prime } x&=0 \\ \end{align*}

[_separable]

1.736

22051

\begin{align*} 2 x y^{2}+\frac {x}{y^{2}}+4 x^{2} y y^{\prime }&=0 \\ \end{align*}

[_separable]

2.542

22058

\begin{align*} y^{\prime }-2 y x&=x \\ \end{align*}

[_separable]

1.421

22063

\begin{align*} y^{\prime }+y x&=x y^{2} \\ \end{align*}

[_separable]

2.315

22068

\begin{align*} y^{\prime }+x^{2} y&=x^{2} \\ \end{align*}

[_separable]

1.531

22070

\begin{align*} y^{\prime }+6 y x&=0 \\ y \left (\pi \right ) &= 5 \\ \end{align*}

[_separable]

1.664

22071

\begin{align*} y^{\prime }-\frac {3 y}{x^{2}}&=\frac {1}{x^{2}} \\ \end{align*}

[_separable]

1.539

22075

\begin{align*} y^{\prime }+y x&=6 x \sqrt {y} \\ \end{align*}

[_separable]

2.320

22087

\begin{align*} y^{\prime }-2 y&=y x \\ \end{align*}

[_separable]

1.561

22090

\begin{align*} y^{\prime }-\frac {2 y}{x}&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

2.725

22091

\begin{align*} y^{\prime }-\frac {2 y}{x}&=0 \\ y \left (1\right ) &= 3 \\ \end{align*}

[_separable]

2.034

22319

\begin{align*} y^{\prime }&=\frac {-x +3}{y+5} \\ \end{align*}

[_separable]

2.837

22326

\begin{align*} y^{\prime }+\tan \left (x \right ) y&=0 \\ y \left (\pi \right ) &= 4 \\ \end{align*}

[_separable]

1.734

22352

\begin{align*} y^{\prime }&=\frac {y}{x} \\ \end{align*}

[_separable]

1.541

22359

\begin{align*} y^{\prime }&=-\frac {x}{y} \\ y \left (1\right ) &= 2 \\ \end{align*}

[_separable]

3.315

22360

\begin{align*} y^{\prime }&=-\frac {y}{x} \\ y \left (1\right ) &= 3 \\ \end{align*}

[_separable]

2.105

22361

\begin{align*} 3 x \left (1+y^{2}\right )+y \left (x^{2}+2\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

2.500

22362

\begin{align*} 2 y+{\mathrm e}^{-3 x} y^{\prime }&=0 \\ \end{align*}

[_separable]

1.944

22363

\begin{align*} y^{\prime }&=\frac {x y^{2}+x}{4 y} \\ y \left (1\right ) &= 0 \\ \end{align*}

[_separable]

2.087

22364

\begin{align*} y^{\prime } x&=1+y^{2} \\ \end{align*}

[_separable]

2.413

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]

2.917

22366

\begin{align*} x \sqrt {1+y^{2}}&=y y^{\prime } \sqrt {x^{2}+1} \\ \end{align*}

[_separable]

3.510

22367

\begin{align*} 2 y \cos \left (x \right )+3 \sin \left (x \right ) y^{\prime }&=0 \\ y \left (\frac {\pi }{2}\right ) &= 2 \\ \end{align*}

[_separable]

2.579

22368

\begin{align*} y^{\prime }&=8 y x +3 y \\ \end{align*}

[_separable]

1.752

22370

\begin{align*} y+\left (x^{3}+x^{3} y^{2}\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

2.930

22371

\begin{align*} y^{\prime }&=-\frac {3 x +x y^{2}}{x^{2} y+2 y} \\ \end{align*}

[_separable]

2.266

22372

\begin{align*} y^{\prime }&=\frac {\left (y-1\right ) \left (3+y\right )}{\left (y-2\right ) \left (x +3\right )} \\ \end{align*}

[_separable]

5.806

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]

5.828

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]

4.910

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]

3.270

22410

\begin{align*} 3 x +4 y^{\prime } y&=0 \\ \end{align*}

[_separable]

3.484

22421

\begin{align*} \left (x^{2}+1\right ) y^{\prime }+2 y x&=0 \\ y \left (1\right ) &= -3 \\ \end{align*}

[_separable]

1.484

22439

\begin{align*} i^{\prime }&=\frac {t -i t}{t^{2}+1} \\ i \left (0\right ) &= 0 \\ \end{align*}

[_separable]

2.084

22508

\begin{align*} \left (x^{2}+1\right ) \left (y^{3}-1\right )&=x^{2} y^{2} y^{\prime } \\ \end{align*}

[_separable]

2.227

22512

\begin{align*} 3-y+2 y^{\prime } x&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}

[_separable]

2.412

22514

\begin{align*} s^{2} t s^{\prime }+t^{2}+4&=0 \\ \end{align*}

[_separable]

1.657

22538

\begin{align*} \cos \left (y\right ) \sin \left (x \right )+\cos \left (x \right ) \sin \left (y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

2.957

22543

\begin{align*} \left (1+y\right ) y^{\prime }&=x \sqrt {y} \\ \end{align*}

[_separable]

2.116

22544

\begin{align*} \tan \left (x \right ) \sin \left (y\right )+3 y^{\prime }&=0 \\ \end{align*}

[_separable]

3.249

22548

\begin{align*} x^{2} y+\left (x^{3}+1\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

2.187

22555

\begin{align*} q^{\prime }&=\frac {p \,{\mathrm e}^{p^{2}-q^{2}}}{q} \\ \end{align*}

[_separable]

2.587

22557

\begin{align*} \left (x +x \cos \left (y\right )\right ) y^{\prime }-\sin \left (y\right )-y&=0 \\ \end{align*}

[_separable]

4.297

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]

1.729

22562

\begin{align*} u v-2 v+\left (-u^{2}+u \right ) v^{\prime }&=0 \\ \end{align*}

[_separable]

1.566

22566

\begin{align*} x \sqrt {1-y^{2}}+y \sqrt {-x^{2}+1}\, y^{\prime }&=0 \\ \end{align*}

[_separable]

2.570

22568

\begin{align*} y^{\prime }&=\frac {\left (3+y\right )^{2}}{4 x^{2}} \\ \end{align*}

[_separable]

2.558

22582

\begin{align*} {\mathrm e}^{2 x -y}+{\mathrm e}^{y-2 x} y^{\prime }&=0 \\ \end{align*}

[_separable]

1.003

22586

\begin{align*} y^{\prime } \sqrt {x^{3}+1}&=x^{2} y+x^{2} \\ \end{align*}

[_separable]

2.766

22592

\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{x -y}}{y} \\ \end{align*}

[_separable]

2.507

22594

\begin{align*} y^{\prime } \sqrt {-x^{2}+1}+\sqrt {1-y^{2}}&=0 \\ \end{align*}

[_separable]

13.725

22595

\begin{align*} 1+y^{2}+\left (x^{2}+1\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

2.491

22608

\begin{align*} y^{\prime }&=\frac {y}{x} \\ \end{align*}

[_separable]

1.344

22947

\begin{align*} y^{\prime } y&=x^{2} \\ \end{align*}

[_separable]

1.829

22948

\begin{align*} \left (x +1\right ) y^{\prime }&=1+y \\ \end{align*}

[_separable]

1.504

22949

\begin{align*} 1+y^{2}&=\left (x^{2}+1\right ) y^{\prime } \\ \end{align*}

[_separable]

2.084

22950

\begin{align*} y^{\prime } \sin \left (y\right )&=\sec \left (x \right )^{2} \\ \end{align*}

[_separable]

1.743

22951

\begin{align*} x^{\prime }&=\frac {x}{t} \\ \end{align*}

[_separable]

1.298

22952

\begin{align*} \left (-x^{2}+1\right ) y^{\prime }&=1-y^{2} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

2.397

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]

3.743

22954

\begin{align*} y^{\prime } x&=\left (x +1\right ) y^{2} \\ y \left (1\right ) &= 1 \\ \end{align*}

[_separable]

2.040

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]

2.381

22956

\begin{align*} \left (x^{2}-1\right ) y^{\prime }&=\left (y-1\right ) x \\ \end{align*}

[_separable]

1.474

22957

\begin{align*} \left (y+2\right ) x +y \left (2+x \right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

2.788

22958

\begin{align*} x y \left (x^{2}+1\right ) y^{\prime }-y^{2}&=1 \\ \end{align*}

[_separable]

3.275

22959

\begin{align*} y^{\prime } x +y&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}

[_separable]

1.855

22960

\begin{align*} y^{\prime } x +y-1&=0 \\ y \left (1\right ) &= 2 \\ \end{align*}

[_separable]

1.390

22962

\begin{align*} x^{2} y^{\prime }+2 y x&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}

[_separable]

1.980

22963

\begin{align*} x \cos \left (y\right ) y^{\prime }+\sin \left (y\right )&=5 \\ \end{align*}

[_separable]

3.770

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]

2.270

22965

\begin{align*} x \sec \left (y\right )^{2} y^{\prime }+1+\tan \left (y\right )&=0 \\ \end{align*}

[_separable]

17.115

22966

\begin{align*} {\mathrm e}^{y} \left (y^{\prime } x +1\right )&=5 \\ \end{align*}

[_separable]

2.154

22977

\begin{align*} y^{\prime }+2 y x&=x \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

1.499

22978

\begin{align*} y^{\prime }-2 y x&=3 x \\ y \left (1\right ) &= 1 \\ \end{align*}

[_separable]

1.601

22986

\begin{align*} y^{\prime }-y \sin \left (x \right )&=\sin \left (x \right ) \\ y \left (0\right ) &= 2 \\ \end{align*}

[_separable]

1.947

22988

\begin{align*} \left ({\mathrm e}^{x}+1\right ) y^{\prime }+{\mathrm e}^{x} y&={\mathrm e}^{x} \\ y \left (0\right ) &= 2 \\ \end{align*}

[_separable]

2.046

23056

\begin{align*} \frac {r^{\prime }}{r}&=\tan \left (\theta \right ) \\ \end{align*}

[_separable]

1.621

23057

\begin{align*} \left (1+\cos \left (\theta \right )\right ) r^{\prime }&=-r \sin \left (\theta \right ) \\ \end{align*}

[_separable]

2.355

23058

\begin{align*} \cot \left (\theta \right ) r^{\prime }&=r+b \\ \end{align*}

[_separable]

1.805

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]

3.199

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]

3.673

23127

\begin{align*} x^{\prime }&=\frac {a x^{{5}/{6}}}{\left (-B t +b \right )^{{3}/{2}}} \\ \end{align*}

[_separable]

31.041

23128

\begin{align*} -y+y^{\prime } x&=1 \\ y \left (2\right ) &= 3 \\ \end{align*}

[_separable]

2.053

23130

\begin{align*} y^{\prime } x +y^{2}&=1 \\ y \left (-2\right ) &= 1 \\ \end{align*}

[_separable]

2.692

23132

\begin{align*} y^{\prime }&=y x \\ y \left (1\right ) &= 2 \\ \end{align*}

[_separable]

1.647

23134

\begin{align*} y^{\prime } x +\left (x +1\right ) y&=0 \\ \end{align*}

[_separable]

0.993

23137

\begin{align*} y^{\prime } x +y&=3 \\ \end{align*}

[_separable]

1.201

23142

\begin{align*} y^{\prime }&=x -y x -y+1 \\ \end{align*}

[_separable]

1.713

23143

\begin{align*} \left (x^{2}+4\right ) y^{\prime }+3 y x&=0 \\ \end{align*}

[_separable]

1.635

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]

8.767

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]

2.537

23150

\begin{align*} y^{\prime }&=\frac {\left (a -x \right ) y}{d \,x^{2}+c x +b} \\ \end{align*}

[_separable]

4.010

23151

\begin{align*} y^{\prime } x +y&=3 \\ \end{align*}

[_separable]

1.222

23154

\begin{align*} y^{\prime } x +\left (x +1\right ) y&=0 \\ \end{align*}

[_separable]

0.968

23162

\begin{align*} y^{\prime }-\frac {x}{x^{2}+1}&=-\frac {x y}{x^{2}+1} \\ \end{align*}

[_separable]

1.649

23167

\begin{align*} y^{\prime }-2 y x&=4 x \sqrt {y} \\ \end{align*}

[_separable]

2.321

23171

\begin{align*} y^{\prime } x -\frac {y}{\ln \left (x \right )}&=0 \\ y \left ({\mathrm e}\right ) &= -1 \\ \end{align*}

[_separable]

1.949

23172

\begin{align*} \left (x^{2}+1\right ) y^{\prime }+2 y x&=-2 x \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

1.884

23185

\begin{align*} \cos \left (y\right )+\sin \left (x \right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

2.264

23194

\begin{align*} y-y^{\prime } x&=0 \\ \end{align*}

[_separable]

1.583

23203

\begin{align*} y^{\prime } x +y&=3 \\ \end{align*}

[_separable]

1.370

23256

\begin{align*} 7 y^{\prime }-y x&=0 \\ \end{align*}

[_separable]

1.779

23269

\begin{align*} y^{\prime } x +y&=0 \\ \end{align*}

[_separable]

1.955

23849

\begin{align*} 2 y^{\prime } x +y&=0 \\ \end{align*}

[_separable]

2.374

23850

\begin{align*} \left (x^{2}+1\right ) y y^{\prime }+4&=0 \\ \end{align*}

[_separable]

2.569

23851

\begin{align*} x^{2} y+\left (x +1\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}

[_separable]

2.809

23852

\begin{align*} y x +{\mathrm e}^{x} y^{\prime }&=0 \\ \end{align*}

[_separable]

2.636

23853

\begin{align*} y^{3}+y^{\prime } \sqrt {-x^{2}+1}&=0 \\ \end{align*}

[_separable]

5.404

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]

7.068

23855

\begin{align*} \left (x^{2}-1\right ) y+\left (1+y^{2}\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

2.124

23856

\begin{align*} y x +\ln \left (y\right ) y^{\prime }&=0 \\ y \left (2\right ) &= 1 \\ \end{align*}

[_separable]

1.916

23857

\begin{align*} \left (x^{3}+1\right ) y^{\prime }+x y^{2}&=0 \\ \end{align*}

[_separable]

2.526

23858

\begin{align*} y^{2} \sec \left (x \right )^{2} y^{\prime }+x&=0 \\ \end{align*}

[_separable]

3.159

23919

\begin{align*} y^{\prime }+y x&=x y^{5} \\ \end{align*}

[_separable]

4.291

23941

\begin{align*} y^{\prime }&=x^{2} y \\ \end{align*}

[_separable]

3.945

23946

\begin{align*} y^{5} x^{2}+{\mathrm e}^{x^{3}} y^{\prime }&=0 \\ y \left (0\right ) &= 2 \\ \end{align*}

[_separable]

3.794

23948

\begin{align*} x \sqrt {a^{2}+x^{2}}&=y \sqrt {y^{2}-a^{2}}\, y^{\prime } \\ \end{align*}

[_separable]

5.933

23956

\begin{align*} y^{\prime }&=\sin \left (y\right )^{3} \cos \left (x \right )^{2} \\ \end{align*}

[_separable]

7.239

23957

\begin{align*} y x -x&=\left (x y^{2}+x -y^{2}-1\right ) y^{\prime } \\ \end{align*}

[_separable]

3.297

23963

\begin{align*} {\mathrm e}^{2 x +3 y}+{\mathrm e}^{4 x -5 y} y^{\prime }&=0 \\ \end{align*}

[_separable]

2.288

23971

\begin{align*} y^{\prime }-y x&=x \\ \end{align*}

[_separable]

3.910

24120

\begin{align*} \left (1-x \right ) y^{\prime }&=y^{2} \\ \end{align*}

[_separable]

4.156

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]

4.259

24122

\begin{align*} x y^{3}+{\mathrm e}^{x^{2}} y^{\prime }&=0 \\ \end{align*}

[_separable]

6.872

24123

\begin{align*} 2 y-3 y^{\prime } x&=0 \\ \end{align*}

[_separable]

5.424

24124

\begin{align*} m y-n x y^{\prime }&=0 \\ \end{align*}

[_separable]

5.554

24125

\begin{align*} y^{\prime }&=x y^{2} \\ \end{align*}

[_separable]

6.047

24126

\begin{align*} v^{\prime }&=-\frac {v}{p} \\ \end{align*}

[_separable]

4.536

24127

\begin{align*} y \,{\mathrm e}^{2 x}-\left (4+{\mathrm e}^{2 x}\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

6.222

24128

\begin{align*} 1&=b \left (\cos \left (y\right )+x \sin \left (y\right ) y^{\prime }\right ) \\ \end{align*}

[_separable]

7.310

24129

\begin{align*} y x -\left (2+x \right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

4.502

24130

\begin{align*} x^{2}+y \left (x -1\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

3.403

24131

\begin{align*} y x +x -\left (1+x^{2}+y^{2}+y^{2} x^{2}\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

3.749

24132

\begin{align*} x \cos \left (y\right )^{2}+\tan \left (y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

33.050

24133

\begin{align*} x y^{3}+\left (1+y\right ) {\mathrm e}^{-x} y^{\prime }&=0 \\ \end{align*}

[_separable]

8.148

24134

\begin{align*} \theta ^{\prime }&=z \left (-z^{2}+1\right ) \sec \left (\theta \right )^{2} \\ \end{align*}

[_separable]

3.969

24135

\begin{align*} x^{\prime }&=\sin \left (x\right )^{2} \cos \left (t \right )^{3} \\ \end{align*}

[_separable]

6.602

24136

\begin{align*} y^{\prime } x +y+x y \left (1+y^{\prime }\right )&=0 \\ \end{align*}

[_separable]

5.138

24137

\begin{align*} \cos \left (y\right )&=y^{\prime } x \\ \end{align*}

[_separable]

5.408

24142

\begin{align*} y-\left ({\mathrm e}^{3 x}+1\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

6.920

24143

\begin{align*} y \ln \left (x \right ) \ln \left (y\right )+y^{\prime }&=0 \\ \end{align*}

[_separable]

5.094

24144

\begin{align*} x y^{\prime } y-y^{2}&=1 \\ y \left (2\right ) &= 1 \\ \end{align*}

[_separable]

7.194

24145

\begin{align*} r^{\prime }&=-2 r t \\ r \left (0\right ) &= r_{0} \\ \end{align*}

[_separable]

4.975

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]

8.532

24148

\begin{align*} y^{\prime }&=x \,{\mathrm e}^{-y-x^{2}} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

3.960

24187

\begin{align*} 2 y x -y+\left (x^{2}+x \right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

2.043

24190

\begin{align*} 1+y^{2}+\left (y+x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

5.587

24212

\begin{align*} y \left (1+y^{2}\right )+x \left (y^{2}-1\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

6.738

24243

\begin{align*} y^{\prime }&=-2 y x +x \\ \end{align*}

[_separable]

2.058

24268

\begin{align*} y^{\prime }&={\mathrm e}^{x +y} \\ \end{align*}

[_separable]

1.829

24271

\begin{align*} x^{2}+1+x^{2} y^{2} y^{\prime }&=0 \\ \end{align*}

[_separable]

2.569

24274

\begin{align*} y^{\prime }-\cos \left (x \right )&=\tan \left (y\right )^{2} \cos \left (x \right ) \\ \end{align*}

[_separable]

2.215

24278

\begin{align*} y^{\prime }&=\sec \left (x \right )^{2} \sec \left (y\right )^{3} \\ \end{align*}

[_separable]

2.409

24281

\begin{align*} y x +\sqrt {x^{2}+1}\, y^{\prime }&=0 \\ \end{align*}

[_separable]

2.896

24286

\begin{align*} x^{\prime }&=\cos \left (x\right ) \cos \left (t \right )^{2} \\ \end{align*}

[_separable]

2.729

24292

\begin{align*} a^{2} \left (y^{\prime }-1\right )&=x^{2} y^{\prime }+y^{2} \\ \end{align*}

[_separable]

4.073

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]

17.085

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]

15.712

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]

8.968

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]

8.558

24337

\begin{align*} -y+y^{\prime } x&=x^{k} y \\ \end{align*}

[_separable]

7.938

24338

\begin{align*} -y+y^{\prime } x&=y \\ \end{align*}

[_separable]

3.416

24909

\begin{align*} t y^{\prime }&=y \\ \end{align*}

[_separable]

1.353

24918

\begin{align*} y^{\prime }&=2 t y \\ \end{align*}

[_separable]

1.366

24920

\begin{align*} \left (t +1\right ) y^{\prime }+y&=0 \\ \end{align*}

[_separable]

1.190

24931

\begin{align*} \left (t +1\right ) y^{\prime }+y&=0 \\ y \left (1\right ) &= -9 \\ \end{align*}

[_separable]

1.477

24940

\begin{align*} y^{\prime }&=-t y \\ \end{align*}

[_separable]

1.334

24942

\begin{align*} y^{\prime }&=t y^{2} \\ \end{align*}

[_separable]

2.211

24943

\begin{align*} y^{\prime }&=\frac {t y}{1+y} \\ \end{align*}

[_separable]

1.604

24952

\begin{align*} t y^{\prime }&=y-2 t y \\ \end{align*}

[_separable]

0.806

24953

\begin{align*} y^{\prime }&=t y^{2}-y^{2}+t -1 \\ \end{align*}

[_separable]

2.387

24956

\begin{align*} {\mathrm e}^{t} y^{\prime }&=y^{3}-y \\ \end{align*}

[_separable]

3.723

24957

\begin{align*} y y^{\prime }&=t \\ y \left (2\right ) &= -1 \\ \end{align*}

[_separable]

3.358

24958

\begin{align*} 1-y^{2}-t y y^{\prime }&=0 \\ \end{align*}

[_separable]

3.992

24959

\begin{align*} y^{3} y^{\prime }&=t \\ \end{align*}

[_separable]

1.874

24960

\begin{align*} y^{4} y^{\prime }&=t +2 \\ \end{align*}

[_separable]

1.559

24961

\begin{align*} y^{\prime }&=t y^{2} \\ \end{align*}

[_separable]

2.098

24962

\begin{align*} \tan \left (t \right ) y+y^{\prime }&=\tan \left (t \right ) \\ \end{align*}

[_separable]

1.711

24963

\begin{align*} y^{\prime }&=t^{m} y^{n} \\ \end{align*}

[_separable]

3.385

24967

\begin{align*} t y y^{\prime }+t^{2}+1&=0 \\ \end{align*}

[_separable]

1.418

24968

\begin{align*} y+1+\left (y-1\right ) \left (t^{2}+1\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

2.696

24969

\begin{align*} 2 y y^{\prime }&={\mathrm e}^{t} \\ \end{align*}

[_separable]

1.285

24970

\begin{align*} \left (1-t \right ) y^{\prime }&=y^{2} \\ \end{align*}

[_separable]

1.507

24972

\begin{align*} y^{\prime }&=4 t y^{2} \\ y \left (1\right ) &= 0 \\ \end{align*}

[_separable]

2.992

24973

\begin{align*} y^{\prime }&=\frac {y x +2 y}{x} \\ y \left (1\right ) &= {\mathrm e} \\ \end{align*}

[_separable]

1.320

24974

\begin{align*} 2 t y+y^{\prime }&=0 \\ y \left (0\right ) &= 4 \\ \end{align*}

[_separable]

1.642

24975

\begin{align*} y^{\prime }&=\frac {\cot \left (y\right )}{t} \\ y \left (1\right ) &= \frac {\pi }{4} \\ \end{align*}

[_separable]

3.584

24976

\begin{align*} \frac {\left (u^{2}+1\right ) y^{\prime }}{y}&=u \\ y \left (0\right ) &= 2 \\ \end{align*}

[_separable]

1.813

24977

\begin{align*} t y-\left (t +2\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

1.727

24978

\begin{align*} y^{\prime }&=\frac {1+y^{2}}{t} \\ y \left (1\right ) &= \sqrt {3} \\ \end{align*}

[_separable]

2.496

24987

\begin{align*} t \left (t +1\right ) y^{\prime }&=2+y \\ \end{align*}

[_separable]

1.599

24990

\begin{align*} y \cos \left (t \right )+y^{\prime }&=\cos \left (t \right ) \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

2.116

24997

\begin{align*} t y^{\prime }+2 y \ln \left (t \right )&=4 \ln \left (t \right ) \\ \end{align*}

[_separable]

2.246

25013

\begin{align*} t y+y^{\prime }&=t y^{3} \\ \end{align*}

[_separable]

3.640

25015

\begin{align*} \left (-t^{2}+1\right ) y^{\prime }-t y&=5 t y^{2} \\ \end{align*}

[_separable]

3.399

25017

\begin{align*} y y^{\prime }+t y^{2}&=t \\ y \left (0\right ) &= -2 \\ \end{align*}

[_separable]

1.911

25038

\begin{align*} y^{\prime }&=t y \\ y \left (1\right ) &= 1 \\ \end{align*}

[_separable]

1.718

25042

\begin{align*} y^{\prime }&=t y \\ y \left (1\right ) &= 1 \\ \end{align*}

[_separable]

1.634

25398

\begin{align*} y^{\prime }&=a \left (t \right ) y \\ \end{align*}

[_separable]

2.082

25430

\begin{align*} y^{\prime }-a \left (t \right ) y&=0 \\ \end{align*}

[_separable]

1.857

25465

\begin{align*} y^{\prime }&=\sin \left (t \right ) y+Q \sin \left (t \right ) \\ \end{align*}

[_separable]

2.329

25466

\begin{align*} y^{\prime }&=\sin \left (t \right ) y \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

2.441

25468

\begin{align*} y^{\prime }&=\frac {y}{t +1} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

2.036

25490

\begin{align*} y^{\prime }&=a \left (t \right ) y \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

2.132

25491

\begin{align*} y^{\prime }&=t y \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

1.886

25492

\begin{align*} y^{\prime }&=t^{m} y^{n} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

113.811

25493

\begin{align*} y^{\prime }&=a \left (t \right ) y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

2.929

25495

\begin{align*} y^{\prime }&=\frac {y}{t} \\ \end{align*}

[_separable]

1.835

25497

\begin{align*} y^{\prime }&=\frac {y^{2}}{t^{2}} \\ \end{align*}

[_separable]

3.409

25498

\begin{align*} y^{\prime }&={\mathrm e}^{t +y} \\ \end{align*}

[_separable]

1.850

25499

\begin{align*} y^{\prime }&=t y+t +y+1 \\ \end{align*}

[_separable]

2.207

25500

\begin{align*} y^{\prime }&=\left (y+4\right ) \cos \left (t \right ) \\ \end{align*}

[_separable]

2.375

25501

\begin{align*} y^{\prime }&=y \,{\mathrm e}^{t} \\ \end{align*}

[_separable]

2.143

25502

\begin{align*} y^{\prime }&=-4 t y \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

2.113

25503

\begin{align*} y^{\prime }&=t y^{3} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

5.298

25504

\begin{align*} \left (t +1\right ) y^{\prime }&=4 y \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

2.559

25656

\begin{align*} y^{2}-1+y^{\prime } x&=0 \\ \end{align*}

[_separable]

2.868

25663

\begin{align*} y^{\prime }&=2 x y^{2} \\ \end{align*}

[_separable]

2.488

25664

\begin{align*} 2 y^{\prime }&=y^{3} \cos \left (x \right ) \\ \end{align*}

[_separable]

3.517

25675

\begin{align*} y^{\prime } x -2 y&=0 \\ \end{align*}

[_separable]

2.199

25676

\begin{align*} y^{\prime }&=-\frac {x}{y} \\ \end{align*}

[_separable]

3.147

25683

\begin{align*} 3 y^{\prime } x +5 y&=10 \\ \end{align*}

[_separable]

2.439

25693

\begin{align*} y^{\prime }+2 x y^{2}&=0 \\ y \left (2\right ) &= {\frac {1}{3}} \\ \end{align*}

[_separable]

2.822

25694

\begin{align*} y^{\prime }+2 x y^{2}&=0 \\ y \left (-2\right ) &= {\frac {1}{2}} \\ \end{align*}

[_separable]

2.811

25695

\begin{align*} y^{\prime }+2 x y^{2}&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

3.648

25696

\begin{align*} y^{\prime }+2 x y^{2}&=0 \\ y \left (\frac {1}{2}\right ) &= -4 \\ \end{align*}

[_separable]

2.874

25706

\begin{align*} y^{\prime } x&=2 y \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

3.293

25709

\begin{align*} y^{\prime } x&=y \\ \end{align*}

[_separable]

1.820

25711

\begin{align*} \left (4-y^{2}\right ) y^{\prime }&=x^{2} \\ \end{align*}

[_separable]

1.422

25712

\begin{align*} \left (y^{3}+1\right ) y^{\prime }&=x^{2} \\ \end{align*}

[_separable]

1.420

25719

\begin{align*} y^{\prime } x&=y \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

3.013

25722

\begin{align*} y^{\prime } y&=3 x \\ y \left (-2\right ) &= 3 \\ \end{align*}

[_separable]

5.149

25723

\begin{align*} y^{\prime } y&=3 x \\ y \left (2\right ) &= -4 \\ \end{align*}

[_separable]

4.790

25732

\begin{align*} y^{\prime }&=x \sqrt {y} \\ y \left (2\right ) &= 1 \\ \end{align*}

[_separable]

12.730

25735

\begin{align*} y^{\prime } x&=2 y \\ \end{align*}

[_separable]

2.963

25736

\begin{align*} y^{\prime } x&=2 y \\ \end{align*}

[_separable]

3.027

25738

\begin{align*} y^{\prime } x&=y \\ \end{align*}

[_separable]

2.528

25743

\begin{align*} 3 y^{\prime } x -2 y&=0 \\ \end{align*}

[_separable]

2.985

25744

\begin{align*} \left (-2+2 y\right ) y^{\prime }&=2 x -1 \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

5.294

25757

\begin{align*} y^{\prime } x +y&=\frac {1}{y^{2}} \\ \end{align*}

[_separable]

4.709

25779

\begin{align*} y^{\prime }&=\cos \left (y\right ) \sin \left (x \right ) \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

4.494

25780

\begin{align*} y^{\prime }&=\cos \left (y\right ) \sin \left (x \right ) \\ y \left (1\right ) &= 0 \\ \end{align*}

[_separable]

3.323

25781

\begin{align*} y^{\prime }&=\cos \left (y\right ) \sin \left (x \right ) \\ y \left (3\right ) &= 3 \\ \end{align*}

[_separable]

5.020

25782

\begin{align*} y^{\prime }&=\cos \left (y\right ) \sin \left (x \right ) \\ y \left (0\right ) &= -{\frac {5}{2}} \\ \end{align*}

[_separable]

4.196

25787

\begin{align*} y^{\prime } y&=-x \\ y \left (1\right ) &= 1 \\ \end{align*}

[_separable]

5.944

25788

\begin{align*} y^{\prime } y&=-x \\ y \left (0\right ) &= 4 \\ \end{align*}

[_separable]

7.671

25793

\begin{align*} y^{\prime }&=x \,{\mathrm e}^{y} \\ y \left (0\right ) &= -2 \\ \end{align*}

[_separable]

3.469

25794

\begin{align*} y^{\prime }&=x \,{\mathrm e}^{y} \\ y \left (1\right ) &= {\frac {5}{2}} \\ \end{align*}

[_separable]

3.524

25819

\begin{align*} y^{\prime } x&=4 y \\ \end{align*}

[_separable]

2.026

25820

\begin{align*} y^{\prime }+2 x y^{2}&=0 \\ \end{align*}

[_separable]

2.486

25821

\begin{align*} y^{\prime }&={\mathrm e}^{2 y+3 x} \\ \end{align*}

[_separable]

1.455

25822

\begin{align*} y \,{\mathrm e}^{x} y^{\prime }&={\mathrm e}^{-y}+{\mathrm e}^{-2 x -y} \\ \end{align*}

[_separable]

2.675

25823

\begin{align*} y^{\prime }&=\frac {y \ln \left (x \right ) x^{2}}{\left (1+y\right )^{2}} \\ \end{align*}

[_separable]

2.014

25824

\begin{align*} y^{\prime }&=\frac {\left (3+2 y\right )^{2}}{\left (5+4 x \right )^{2}} \\ \end{align*}

[_separable]

3.658

25825

\begin{align*} \csc \left (y\right )+\sec \left (x \right )^{2} y^{\prime }&=0 \\ \end{align*}

[_separable]

2.283

25826

\begin{align*} \sin \left (3 x \right )+2 y \cos \left (3 x \right )^{3} y^{\prime }&=0 \\ \end{align*}

[_separable]

4.296

25827

\begin{align*} \left (1+{\mathrm e}^{y}\right )^{2} {\mathrm e}^{-y}+\left ({\mathrm e}^{x}+1\right )^{3} {\mathrm e}^{-x} y^{\prime }&=0 \\ \end{align*}

[_separable]

3.845

25828

\begin{align*} x \sqrt {1+y^{2}}&=y y^{\prime } \sqrt {x^{2}+1} \\ \end{align*}

[_separable]

2.909