2.4.26 first order ode separable

Table 2.1181: first order ode separable [1802]

#

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]

3.237

28

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

[_separable]

1.441

33

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

[_separable]

2.605

34

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

[_separable]

2.217

41

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

[_separable]

1.718

42

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

[_separable]

2.690

43

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

[_separable]

2.006

44

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

[_separable]

2.007

45

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

[_separable]

2.043

48

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

[_separable]

1.679

49

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

[_separable]

1.955

50

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

[_separable]

2.970

51

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

[_separable]

3.250

52

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

[_separable]

2.000

53

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

[_separable]

3.332

54

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

[_separable]

1.684

55

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

[_separable]

2.066

56

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

[_separable]

1.717

57

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

[_separable]

1.536

58

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

[_separable]

2.655

59

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

[_separable]

1.961

60

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

[_separable]

2.638

61

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

[_separable]

2.369

62

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

[_separable]

4.043

64

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

[_separable]

3.010

65

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

[_separable]

1.710

66

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

[_separable]

2.103

67

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

[_separable]

2.005

68

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

[_separable]

2.056

83

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

[_separable]

0.956

87

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

[_separable]

1.608

88

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

[_separable]

1.951

92

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

[_separable]

1.718

96

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

[_separable]

1.890

103

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

[_separable]

1.259

124

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

[_separable]

1.724

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]

2.601

180

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

[_separable]

2.066

183

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

[_separable]

2.177

184

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

[_separable]

2.174

188

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

[_separable]

2.498

191

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

[_separable]

2.342

197

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

[_separable]

2.073

202

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

[_separable]

2.522

209

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

[_separable]

2.657

210

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

[_separable]

3.694

213

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

[_separable]

1.790

214

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

[_separable]

4.585

669

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

[_separable]

4.059

670

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

[_separable]

1.695

673

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

[_separable]

4.004

674

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

[_separable]

2.484

677

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

[_separable]

1.941

678

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

[_separable]

3.345

679

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

[_separable]

2.115

680

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

[_separable]

2.211

681

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

[_separable]

2.312

684

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

[_separable]

1.637

685

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

[_separable]

2.068

686

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

[_separable]

2.873

687

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

[_separable]

3.974

688

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

[_separable]

2.283

689

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

[_separable]

2.245

690

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

[_separable]

2.289

691

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

[_separable]

1.963

692

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

[_separable]

1.892

693

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

[_separable]

2.802

694

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

[_separable]

3.324

695

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

[_separable]

2.659

696

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

[_separable]

2.609

697

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

[_separable]

2.264

699

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

[_separable]

4.154

700

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

[_separable]

2.987

701

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

[_separable]

2.315

702

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

[_separable]

2.375

703

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

[_separable]

2.417

714

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

[_separable]

1.270

718

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

[_separable]

1.882

719

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

[_separable]

2.254

723

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

[_separable]

2.191

727

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

[_separable]

2.310

748

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

[_separable]

2.210

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]

3.497

772

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

[_separable]

2.360

775

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

[_separable]

2.537

776

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

[_separable]

2.481

780

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

[_separable]

2.799

789

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

[_separable]

2.595

794

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

[_separable]

3.164

800

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

[_separable]

2.155

801

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

[_separable]

1.909

802

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

[_separable]

4.994

805

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

[_separable]

2.289

806

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

[_separable]

5.298

1129

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

[_separable]

4.489

1130

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

[_separable]

2.150

1131

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

[_separable]

2.923

1132

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

[_separable]

3.442

1133

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

[_separable]

2.884

1134

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

[_separable]

4.464

1136

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

[_separable]

1.648

1137

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

[_separable]

3.119

1139

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

[_separable]

2.300

1140

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

[_separable]

2.768

1141

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

[_separable]

2.075

1142

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

[_separable]

3.290

1145

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

[_separable]

4.575

1146

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

[_separable]

5.719

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]

25.141

1148

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

[_separable]

4.125

1150

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

[_separable]

2.420

1151

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

[_separable]

3.182

1154

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

[_separable]

3.674

1155

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

[_separable]

3.579

1156

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

[_separable]

4.562

1167

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

[_separable]

2.764

1172

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

[_separable]

1.894

1173

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

[_separable]

3.263

1174

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

[_separable]

5.226

1175

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

[_separable]

5.085

1177

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

[_separable]

2.302

1178

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

[_separable]

3.335

1193

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

[_separable]

5.744

1204

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

[_separable]

7.965

1207

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

[_separable]

2.280

1209

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

[_separable]

2.779

1219

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

[_separable]

3.133

1221

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

[_separable]

2.664

1224

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

[_separable]

2.207

1227

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

[_separable]

3.872

1230

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

[_separable]

3.654

1232

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

[_separable]

4.068

1237

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

[_separable]

2.069

1239

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

[_separable]

1.230

1241

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

[_separable]

3.318

1521

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

[_separable]

2.448

1522

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

[_separable]

3.672

1523

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

[_separable]

3.169

1532

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

[_separable]

3.741

1533

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

[_separable]

5.431

1538

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

[_separable]

2.800

1539

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

[_separable]

3.658

1540

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

[_separable]

3.730

1541

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

[_separable]

2.845

1542

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

[_separable]

3.444

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]

3.574

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]

4.081

1545

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

[_separable]

2.856

1546

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

[_separable]

3.362

1547

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

[_separable]

4.376

1569

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

[_separable]

2.682

1573

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

[_separable]

4.682

1578

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

[_separable]

3.895

1579

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

[_separable]

3.671

1580

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

[_separable]

4.832

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]

3.790

1582

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

[_separable]

8.437

1583

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

[_separable]

3.145

1584

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

[_separable]

2.568

1585

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

[_separable]

5.380

1586

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

[_separable]

2.973

1588

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

[_separable]

4.833

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]

4.393

1590

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

[_separable]

5.191

1591

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

[_separable]

2.908

1592

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

[_separable]

7.379

1593

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

[_separable]

4.349

1594

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

[_separable]

10.132

1598

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

[_separable]

5.532

1599

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

[_separable]

3.392

1600

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

[_separable]

3.515

1601

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

[_separable]

18.751

1602

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

[_separable]

3.047

1613

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

[_separable]

2.862

1617

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

[_separable]

3.189

1620

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

[_separable]

4.384

1622

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

[_separable]

12.188

1623

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

[_separable]

12.595

1624

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

[_separable]

13.401

1636

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

[_separable]

9.333

1690

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

[_separable]

4.238

1692

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

[_separable]

10.743

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]

4.384

1700

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

[_separable]

3.596

1711

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

[_separable]

7.569

1712

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

[_separable]

2.808

1713

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

[_separable]

4.435

1721

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

[_separable]

4.578

1722

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

[_separable]

3.832

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]

9.627

1726

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

[_separable]

6.056

1728

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

[_separable]

5.429

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]

5.424

2298

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

[_separable]

2.422

2299

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

[_separable]

3.161

2303

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

[_separable]

2.147

2305

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

[_separable]

3.431

2306

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

[_separable]

2.773

2307

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

[_separable]

2.269

2312

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

[_separable]

2.260

2317

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

[_separable]

2.819

2318

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

[_separable]

2.001

2319

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

[_separable]

3.286

2320

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

[_separable]

1.436

2321

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

[_separable]

3.452

2322

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

[_separable]

2.404

2323

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

[_separable]

2.038

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]

3.891

2325

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

[_separable]

2.770

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]

2.797

2328

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

[_separable]

3.958

2359

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

[_separable]

1.403

2360

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

[_separable]

33.914

2471

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

[_separable]

2.507

2472

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

[_separable]

2.585

2476

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

[_separable]

1.746

2478

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

[_separable]

2.503

2479

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

[_separable]

2.359

2480

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

[_separable]

2.352

2481

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

[_separable]

1.842

2486

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

[_separable]

1.730

2488

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

[_separable]

2.384

2489

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

[_separable]

1.727

2490

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

[_separable]

2.674

2491

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

[_separable]

1.267

2492

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

[_separable]

3.472

2493

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

[_separable]

2.129

2494

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

[_separable]

1.648

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]

3.534

2496

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

[_separable]

2.273

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]

2.173

2499

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

[_separable]

2.326

2518

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

[_separable]

3.740

2534

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

[_separable]

1.513

2535

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

[_separable]

7.899

2536

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

[_separable]

34.145

2840

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

[_separable]

2.094

2841

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

[_separable]

5.612

2842

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

[_separable]

2.838

2843

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

[_separable]

2.500

2844

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

[_separable]

2.149

2845

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

[_separable]

2.789

2846

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

[_separable]

3.846

2847

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

[_separable]

2.296

2848

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

[_separable]

2.690

2849

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

[_separable]

2.949

2850

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

[_separable]

5.786

2852

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

[_separable]

3.717

2853

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

[_separable]

3.833

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]

9.388

2855

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

[_separable]

2.901

2856

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

[_separable]

2.868

2857

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

[_separable]

2.721

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]

8.895

2859

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

[_separable]

7.296

2860

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

[_separable]

2.076

2861

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

[_separable]

4.155

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]

4.321

2863

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

[_separable]

5.845

2866

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

[_separable]

3.960

2868

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

[_separable]

6.891

2869

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

[_separable]

6.037

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]

2.956

2938

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

[_separable]

5.641

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]

2.869

2990

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

[_separable]

3.191

2992

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

[_separable]

3.978

2995

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

[_separable]

27.260

3003

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

[_separable]

2.855

3010

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

[_separable]

6.701

3014

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

[_separable]

5.056

3015

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

[_separable]

4.029

3019

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

[_separable]

2.864

3023

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

[_separable]

3.072

3027

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

[_separable]

2.832

3030

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

[_separable]

9.247

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]

3.774

3039

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

[_separable]

5.524

3041

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

[_separable]

2.787

3051

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

[_separable]

3.738

3295

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

[_separable]

6.484

3408

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

[_separable]

3.165

3409

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

[_separable]

6.724

3410

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

[_separable]

3.354

3411

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

[_separable]

2.487

3412

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

[_separable]

6.459

3426

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

[_separable]

3.076

3430

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

[_separable]

2.665

3431

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

[_separable]

8.188

3437

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

[_separable]

3.450

3450

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

[_separable]

4.969

3452

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

[_separable]

4.859

3456

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

[_separable]

8.338

3457

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

[_separable]

5.451

3458

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

[_separable]

3.445

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]

4.550

3472

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

[_separable]

3.526

3514

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

[_separable]

3.276

3515

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

[_separable]

2.970

3516

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

[_separable]

4.277

3517

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

[_separable]

3.134

3518

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

[_separable]

3.306

3519

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

[_separable]

3.211

3520

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

[_separable]

3.222

3521

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

[_separable]

3.503

3522

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

[_separable]

5.969

3524

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

[_separable]

5.948

3525

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

[_separable]

4.401

3526

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

[_separable]

8.939

3527

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

[_separable]

5.098

3528

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

[_separable]

4.927

3561

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

[_separable]

4.011

3592

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

[_separable]

3.557

3593

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

[_separable]

3.082

3594

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

[_separable]

4.746

3595

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

[_separable]

3.013

3596

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

[_separable]

3.422

3597

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

[_separable]

3.332

3598

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

[_separable]

3.252

3599

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

[_separable]

3.439

3600

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

[_separable]

6.945

3601

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

[_separable]

3.885

3602

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

[_separable]

5.848

3603

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

[_separable]

4.434

3604

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

[_separable]

9.401

3605

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

[_separable]

5.112

3606

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

[_separable]

4.540

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]

14.033

3682

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

[_separable]

35.815

4093

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

[_separable]

4.461

4094

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

[_separable]

3.069

4095

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

[_separable]

3.655

4101

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

[_separable]

7.671

4104

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

[_separable]

3.464

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]

6.845

4110

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

[_separable]

5.946

4189

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

[_separable]

3.854

4212

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

[_separable]

1.741

4213

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

[_separable]

2.687

4214

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

[_separable]

1.793

4215

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

[_separable]

1.212

4216

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

[_separable]

1.483

4218

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

[_separable]

1.624

4219

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

[_separable]

1.641

4220

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

[_separable]

1.808

4221

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

[_separable]

1.842

4222

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

[_separable]

4.918

4223

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

[_separable]

1.863

4224

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

[_separable]

3.292

4225

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

[_separable]

2.084

4226

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

[_separable]

2.907

4227

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

[_separable]

1.418

4229

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

[_separable]

3.558

4230

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

[_separable]

4.415

4231

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

[_separable]

3.857

4232

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

[_separable]

1.970

4233

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

[_separable]

2.326

4234

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

[_separable]

2.707

4235

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

[_separable]

1.782

4236

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

[_separable]

2.055

4237

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

[_separable]

3.943

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]

1.780

4257

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

[_separable]

1.750

4264

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

[_separable]

2.482

4294

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

[_separable]

2.149

4300

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

[_separable]

1.943

4301

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

[_separable]

2.628

4302

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

[_separable]

2.715

4303

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

[_separable]

4.515

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]

4.920

4306

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

[_separable]

3.260

4307

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

[_separable]

2.341

4308

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

[_separable]

8.576

4309

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

[_separable]

2.740

4310

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

[_separable]

3.153

4311

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

[_separable]

22.901

4312

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

[_separable]

3.523

4360

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

[_separable]

2.138

4397

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

[_separable]

2.009

4411

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

[_separable]

2.173

4428

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

[_separable]

2.192

4618

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

[_separable]

2.346

4625

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

[_separable]

2.379

4628

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

[_separable]

4.641

4636

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

[_separable]

2.593

4638

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

[_separable]

2.402

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]

2.788

4676

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

[_separable]

3.069

4680

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

[_separable]

3.905

4681

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

[_separable]

3.700

4687

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

[_separable]

4.742

4689

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

[_separable]

5.115

4695

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

[_separable]

4.933

4701

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

[_separable]

4.621

4714

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

[_separable]

2.852

4715

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

[_separable]

3.022

4719

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

[_separable]

2.561

4720

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

[_separable]

2.616

4721

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

[_separable]

2.901

4722

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

[_separable]

3.388

4723

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

[_separable]

2.816

4724

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

[_separable]

2.499

4725

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

[_separable]

3.213

4727

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

[_separable]

2.063

4728

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

[_separable]

2.397

4732

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

[_separable]

3.835

4735

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

[_separable]

1.710

4736

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

[_separable]

2.810

4737

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

[_separable]

2.433

4741

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

[_separable]

1.528

4760

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

[_separable]

2.569

4761

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

[_separable]

2.522

4768

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

[_separable]

1.772

4771

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

[_separable]

2.548

4775

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

[_separable]

3.739

4796

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

[_separable]

5.993

4803

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

[_separable]

6.947

4804

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

[_separable]

6.184

4805

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

[_separable]

6.148

4815

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

[_separable]

3.000

4822

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

[_separable]

3.684

4828

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

[_separable]

3.746

4845

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

[_separable]

3.252

4846

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

[_separable]

3.019

4848

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

[_separable]

3.753

4852

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

[_separable]

3.664

4853

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

[_separable]

9.440

4855

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

[_separable]

6.906

4856

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

[_separable]

7.861

4858

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

[_separable]

4.053

4864

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

[_separable]

2.317

4869

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

[_separable]

2.585

4874

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

[_separable]

3.438

4902

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

[_separable]

4.712

4907

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

[_separable]

2.698

4913

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

[_separable]

3.559

4914

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

[_separable]

3.362

4915

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

[_separable]

3.371

4916

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

[_separable]

4.017

4917

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

[_separable]

3.960

4920

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

[_separable]

7.685

4921

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

[_separable]

6.019

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]

7.043

4931

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

[_separable]

7.974

4932

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

[_separable]

7.105

4936

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

[_separable]

2.768

4942

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

[_separable]

7.471

4943

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

[_separable]

3.413

4945

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

[_separable]

7.496

4947

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

[_separable]

5.109

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]

9.216

4950

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

[_separable]

2.810

4962

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

[_separable]

4.921

4963

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

[_separable]

4.556

4964

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

[_separable]

3.851

4965

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

[_separable]

2.773

4972

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

[_separable]

2.786

4980

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

[_separable]

2.582

4981

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

[_separable]

3.080

4995

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

[_separable]

4.854

4999

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

[_separable]

3.429

5011

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

[_separable]

5.452

5012

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

[_separable]

4.611

5014

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

[_separable]

41.334

5015

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

[_separable]

41.101

5016

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

[_separable]

10.830

5017

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

[_separable]

18.648

5019

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

[_separable]

5.053

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]

7.661

5021

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

[_separable]

4.588

5022

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

[_separable]

5.698

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]

6.030

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]

8.757

5026

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

[_separable]

4.018

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]

4.898

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]

13.477

5030

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

[_separable]

5.276

5031

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

[_separable]

5.601

5035

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

[_separable]

7.092

5036

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

[_separable]

2.342

5039

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

[_separable]

6.685

5045

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

[_separable]

4.822

5051

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

[_separable]

3.613

5094

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

[_separable]

10.326

5095

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

[_separable]

3.787

5123

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

[_separable]

6.406

5130

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

[_separable]

7.292

5132

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

[_separable]

4.619

5136

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

[_separable]

4.099

5137

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

[_separable]

4.353

5138

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

[_separable]

4.198

5143

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

[_separable]

4.288

5155

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

[_separable]

4.465

5156

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

[_separable]

6.376

5158

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

[_separable]

4.981

5178

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

[_separable]

9.096

5186

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

[_separable]

7.170

5187

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

[_separable]

6.554

5188

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

[_separable]

8.392

5195

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

[_separable]

7.348

5203

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

[_separable]

11.984

5206

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

[_separable]

5.645

5207

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

[_separable]

9.731

5208

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

[_separable]

2.898

5209

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

[_separable]

2.745

5223

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

[_separable]

3.079

5251

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

[_separable]

5.372

5258

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

[_separable]

6.322

5275

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

[_separable]

3.533

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]

3.705

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]

9.628

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]

4.357

5285

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

[_separable]

7.516

5297

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

[_separable]

3.612

5303

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

[_separable]

5.477

5333

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

[_separable]

7.219

5334

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

[_separable]

7.969

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]

6.755

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]

6.178

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]

8.682

5544

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

[[_1st_order, _with_linear_symmetries]]

43.747

5684

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

[_separable]

50.361

5706

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

[_separable]

17.365

6824

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

[_separable]

4.945

6825

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

[_separable]

6.996

6826

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

[_separable]

9.728

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]

6.385

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]

4.592

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]

24.740

6842

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

[_separable]

9.694

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]

10.956

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]

1.737

6915

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

[_separable]

5.547

6983

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

[_separable]

9.309

6994

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

[_separable]

26.364

7004

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

[_separable]

6.436

7010

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

[_separable]

7.362

7023

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

[_separable]

17.087

7024

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

[_separable]

8.013

7038

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

[_separable]

3.431

7039

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

[_separable]

4.632

7149

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

[_separable]

4.013

7155

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

[_separable]

5.375

7156

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

[_separable]

9.675

7157

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

[_separable]

7.796

7158

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

[_separable]

11.000

7159

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

[_separable]

4.138

7161

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

[_separable]

5.106

7162

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

[_separable]

4.686

7163

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

[_separable]

12.119

7217

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

[_separable]

4.075

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]

21.715

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]

7.432

7220

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

[_separable]

8.409

7222

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

[_separable]

5.567

7223

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

[_separable]

6.026

7224

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

[_separable]

12.518

7226

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

[_separable]

4.778

7228

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

[_separable]

13.095

7245

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

[_separable]

8.081

7333

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

[_separable]

6.089

7341

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

[_separable]

9.921

7352

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

[_separable]

6.274

7356

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

[_separable]

6.735

7361

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

[_separable]

2.741

7363

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

[_separable]

4.687

7365

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

[_separable]

3.580

7383

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

[_separable]

3.546

7384

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

[_separable]

3.859

7386

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

[_separable]

4.747

7387

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

[_separable]

4.964

7388

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

[_separable]

4.337

7389

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

[_separable]

3.879

7390

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

[_separable]

19.851

7391

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

[_separable]

4.449

7392

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

[_separable]

16.765

7394

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

[_separable]

6.905

7395

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

[_separable]

5.776

7396

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

[_separable]

10.049

7397

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

[_separable]

6.042

7398

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

[_separable]

6.787

7400

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

[_separable]

7.692

7402

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

[_separable]

3.600

7403

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

[_separable]

6.087

7404

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

[_separable]

5.477

7405

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

[_separable]

14.073

7407

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

[_separable]

5.934

7408

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

[_separable]

29.683

7409

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

[_separable]

6.003

7412

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

[_separable]

10.180

7413

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

[_separable]

13.049

7414

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

[_separable]

11.566

7415

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

[_separable]

9.682

7416

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

[_separable]

9.503

7420

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

[_separable]

5.722

7432

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

[_separable]

3.716

7448

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

[_separable]

10.150

7467

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

[_separable]

8.437

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]

11.848

7525

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

[_separable]

6.214

7529

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

[_separable]

7.639

7530

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

[_separable]

5.242

7549

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

[_separable]

5.280

7561

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

[_separable]

13.269

7682

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

[_separable]

8.546

7696

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

[_separable]

6.980

7700

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

[_separable]

17.185

7702

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

[_separable]

5.273

7707

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

[_separable]

16.451

7708

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

[_separable]

6.651

7709

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

[_separable]

5.274

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]

6.736

7711

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

[_separable]

4.131

7733

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

[_separable]

5.350

7735

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

[_separable]

4.553

7738

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

[_separable]

3.892

7741

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

[_separable]

7.085

7748

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

[_separable]

6.187

7751

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

[_separable]

13.835

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]

8.575

7845

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

[_separable]

7.621

7846

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

[_separable]

13.936

7855

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

[_separable]

7.106

7856

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

[_separable]

12.077

7857

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

[_separable]

10.361

7858

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

[_separable]

4.671

7864

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

[_separable]

6.352

7865

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

[_separable]

4.404

7869

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

[_separable]

7.010

7872

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

[_separable]

6.816

7875

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

[_separable]

8.531

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]

6.274

7908

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

[_separable]

6.829

7918

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

[_separable]

5.823

7927

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

[_separable]

8.087

8160

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

[_separable]

3.063

8167

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

[_separable]

3.157

8168

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

[_separable]

3.598

8179

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

[_separable]

2.888

8180

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

[_separable]

4.018

8189

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

[_separable]

2.977

8210

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

[_separable]

3.901

8211

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

[_separable]

3.154

8212

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

[_separable]

3.449

8213

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

[_separable]

3.929

8223

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

[_separable]

3.205

8226

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

[_separable]

2.134

8228

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

[_separable]

1.770

8229

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

[_separable]

1.709

8236

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

[_separable]

2.389

8243

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

[_separable]

6.835

8245

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

[_separable]

5.759

8256

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

[_separable]

9.310

8260

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

[_separable]

3.342

8265

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

[_separable]

4.864

8266

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

[_separable]

9.334

8279

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

[_separable]

6.784

8301

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

[_separable]

6.413

8302

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

[_separable]

2.487

8303

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

[_separable]

3.317

8304

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

[_separable]

6.561

8309

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

[_separable]

7.704

8310

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

[_separable]

8.092

8315

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

[_separable]

4.612

8316

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

[_separable]

5.022

8342

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

[_separable]

3.007

8343

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

[_separable]

3.389

8344

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

[_separable]

1.625

8345

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

[_separable]

2.842

8346

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

[_separable]

3.115

8347

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

[_separable]

4.296

8348

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

[_separable]

2.376

8349

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

[_separable]

4.794

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]

4.208

8351

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

[_separable]

2.974

8355

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

[_separable]

2.546

8356

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

[_separable]

4.043

8357

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

[_separable]

2.886

8358

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

[_separable]

0.312

8359

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

[_separable]

3.068

8361

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

[_separable]

4.451

8362

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

[_separable]

2.767

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]

10.670

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]

3.679

8367

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

[_separable]

3.473

8368

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

[_separable]

2.518

8369

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

[_separable]

4.197

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]

11.806

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]

3.323

8373

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

[_separable]

2.487

8374

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

[_separable]

2.179

8375

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

[_separable]

3.406

8379

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

[_separable]

4.197

8380

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

[_separable]

4.251

8381

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

[_separable]

4.234

8382

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

[_separable]

4.230

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]

3.810

8397

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

[_separable]

3.224

8398

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

[_separable]

4.786

8400

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

[_separable]

2.994

8401

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

[_separable]

3.800

8402

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

[_separable]

5.105

8403

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

[_separable]

8.294

8406

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

[_separable]

3.494

8413

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

[_separable]

0.605

8414

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

[_separable]

0.809

8415

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

[_separable]

0.741

8416

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

[_separable]

0.460

8417

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

[_separable]

3.813

8424

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

[_separable]

2.262

8429

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

[_separable]

3.003

8441

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

[_separable]

2.315

8454

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

[_separable]

2.823

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]

2.491

8467

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

[_separable]

7.170

8475

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

[_separable]

6.049

8657

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

[_separable]

4.373

8658

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

[_separable]

3.097

8659

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

[_separable]

2.326

8660

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

[_separable]

4.423

8661

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

[_separable]

1.651

8662

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

[_separable]

5.678

8663

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

[_separable]

4.063

8665

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

[_separable]

6.126

8666

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

[_separable]

3.745

8667

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

[_separable]

3.395

8669

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

[_separable]

2.990

8670

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

[_separable]

4.909

8671

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

[_separable]

5.142

8672

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

[_separable]

2.314

8673

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

[_separable]

14.004

8674

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

[_separable]

19.803

8675

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

[_separable]

3.182

8676

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

[_separable]

2.533

8677

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

[_separable]

2.180

8678

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

[_separable]

13.091

8679

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

[_separable]

4.357

8680

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

[_separable]

2.403

8690

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

[_separable]

4.642

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]

3.577

8693

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

[_separable]

3.007

8751

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

[_separable]

8.102

8777

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

[_separable]

3.220

8778

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

[_separable]

2.013

8779

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

[_separable]

4.267

8787

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

[_separable]

8.305

8858

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

[_separable]

2.753

8876

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

[_separable]

2.490

8878

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

[_separable]

2.566

9006

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

[_separable]

3.024

9007

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

[_separable]

8.332

9008

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

[_separable]

2.319

9009

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

[_separable]

2.017

9010

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

[_separable]

4.465

9049

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

[_separable]

3.776

9050

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

[_separable]

2.837

9082

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

[_separable]

9.471

9083

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

[_separable]

2.825

9084

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

[_separable]

2.816

9085

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

[_separable]

4.596

9086

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

[_separable]

4.897

9087

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

[_separable]

2.802

9088

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

[_separable]

2.286

9089

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

[_separable]

2.987

9090

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

[_separable]

5.312

9091

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

[_separable]

2.914

9092

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

[_separable]

3.494

9093

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

[_separable]

2.385

9094

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

[_separable]

2.474

9095

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

[_separable]

3.418

9096

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

[_separable]

6.276

9097

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

[_separable]

3.148

9119

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

[_separable]

4.328

9123

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

[_separable]

4.540

9133

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

[_separable]

3.223

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]

4.177

9194

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

[_separable]

3.532

9195

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

[_separable]

2.629

9198

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

[_separable]

4.276

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]

3.658

9202

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

[_separable]

6.867

9203

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

[_separable]

3.547

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]

15.576

9207

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

[_separable]

2.916

9348

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

[_separable]

3.260

9360

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

[_separable]

2.750

9362

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

[_separable]

3.290

9971

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

[_separable]

3.770

9972

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

[_separable]

6.081

9987

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

[_separable]

5.448

9988

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

[_separable]

2.418

9989

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

[_separable]

4.317

9990

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

[_separable]

12.608

9998

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

[_separable]

9.758

9999

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

[_separable]

4.320

10000

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

[_separable]

3.786

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]

118.432

10256

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

[_separable]

2.075

10264

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

[_separable]

1.519

10324

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

[_separable]

1.441

11311

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

[_separable]

2.968

11331

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

[_separable]

3.242

11333

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

[_separable]

3.137

11337

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

[_separable]

4.426

11361

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

[_separable]

19.283

11362

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

[_separable]

3.570

11364

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

[_separable]

9.633

11367

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

[_separable]

30.419

11368

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

[_separable]

4.237

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]

3.365

11376

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

[_separable]

2.790

11396

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

[_separable]

3.809

11417

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

[_separable]

3.574

11430

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

[_separable]

3.560

11434

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

[_separable]

2.465

11457

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

[_separable]

5.592

11458

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

[_separable]

4.401

11473

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

[_separable]

2.125

11482

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

[_separable]

3.056

11489

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

[_separable]

9.088

11490

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

[_separable]

14.380

11498

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

[_separable]

17.056

11508

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

[_separable]

3.106

11539

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

[_separable]

5.330

11552

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

[_separable]

5.952

11603

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

[_separable]

3.280

11628

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

[_separable]

5.859

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]

7.023

11646

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

[_separable]

11.003

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]

4.048

11652

\begin{align*} 3 \sin \left (x \right ) \sin \left (y\right ) y^{\prime }+5 \cos \left (x \right )^{4} y&=0 \\ \end{align*}

[_separable]

7.986

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]

26.135

11851

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

[_separable]

13.500

13203

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

[_separable]

2.798

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]

7.518

13972

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

[_separable]

2.821

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]

4.573

13974

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

[_separable]

4.559

13979

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

[_separable]

7.010

13993

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

[_separable]

3.402

13994

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

[_separable]

26.216

14015

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

[_separable]

4.714

14016

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

[_separable]

17.497

14020

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

[_separable]

4.555

14027

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

[_separable]

7.632

14033

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

[_separable]

2.483

14034

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

[_separable]

3.306

14192

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

[_separable]

2.814

14193

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

[_separable]

4.590

14198

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

[_separable]

2.536

14219

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

[_separable]

2.358

14220

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

[_separable]

2.272

14221

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

[_separable]

4.993

14222

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

[_separable]

3.030

14224

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

[_separable]

1.925

14227

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

[_separable]

6.240

14228

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

[_separable]

2.816

14230

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

[_separable]

3.941

14231

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

[_separable]

6.053

14232

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

[_separable]

2.709

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]

2.734

14234

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

[_separable]

2.286

14235

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

[_separable]

3.524

14236

\begin{align*} x^{\prime }&=6 t \left (x-1\right )^{{2}/{3}} \\ \end{align*}

[_separable]

5.770

14241

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

[_separable]

2.859

14243

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

[_separable]

2.935

14253

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

[_separable]

2.419

14255

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

[_separable]

2.005

14258

\begin{align*} \cos \left (\theta \right ) v^{\prime }+v&=3 \\ \end{align*}

[_separable]

3.204

14261

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

[_separable]

2.198

14266

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

[_separable]

2.043

14269

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

[_separable]

5.724

14277

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

[_separable]

3.708

14278

\begin{align*} t \cot \left (x\right ) x^{\prime }&=-2 \\ \end{align*}

[_separable]

4.227

14420

\begin{align*} y^{\prime }+4 y x&=8 x \\ \end{align*}

[_separable]

2.165

14436

\begin{align*} y^{\prime }&=x^{2} \sin \left (y\right ) \\ y \left (1\right ) &= -2 \\ \end{align*}

[_separable]

2.901

14437

\begin{align*} y^{\prime }&=\frac {y^{2}}{x -2} \\ y \left (1\right ) &= 0 \\ \end{align*}

[_separable]

1.859

14446

\begin{align*} \frac {\left (2 s-1\right ) s^{\prime }}{t}+\frac {s-s^{2}}{t^{2}}&=0 \\ \end{align*}

[_separable]

15.793

14457

\begin{align*} \left (x^{2}+1\right ) y^{\prime }+4 y x&=0 \\ \end{align*}

[_separable]

2.316

14458

\begin{align*} y x +2 x +y+2+\left (x^{2}+2 x \right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

2.611

14459

\begin{align*} 2 r \left (s^{2}+1\right )+\left (r^{4}+1\right ) s^{\prime }&=0 \\ \end{align*}

[_separable]

3.493

14460

\begin{align*} \csc \left (y\right )+\sec \left (x \right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

2.493

14461

\begin{align*} \tan \left (\theta \right )+2 r \theta ^{\prime }&=0 \\ \end{align*}

[_separable]

4.784

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]

3.043

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]

3.688

14471

\begin{align*} y+2+y \left (x +4\right ) y^{\prime }&=0 \\ y \left (-3\right ) &= -1 \\ \end{align*}

[_separable]

4.769

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]

3.141

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]

4.046

14484

\begin{align*} y^{\prime }+4 y x&=8 x \\ \end{align*}

[_separable]

2.264

14485

\begin{align*} x^{\prime }+\frac {x}{t^{2}}&=\frac {1}{t^{2}} \\ \end{align*}

[_separable]

2.324

14486

\begin{align*} \left (u^{2}+1\right ) v^{\prime }+4 u v&=3 u \\ \end{align*}

[_separable]

2.694

14495

\begin{align*} y^{\prime }-\frac {y}{x}&=-\frac {y^{2}}{x} \\ \end{align*}

[_separable]

2.924

14497

\begin{align*} y^{\prime }+\left (4 y-\frac {8}{y^{3}}\right ) x&=0 \\ \end{align*}

[_separable]

2.727

14498

\begin{align*} x^{\prime }+\frac {\left (1+t \right ) x}{2 t}&=\frac {1+t}{t x} \\ \end{align*}

[_separable]

3.290

14500

\begin{align*} y^{\prime }+3 x^{2} y&=x^{2} \\ y \left (0\right ) &= 2 \\ \end{align*}

[_separable]

2.750

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]

3.724

14514

\begin{align*} \left (1+y\right ) y^{\prime }+x \left (y^{2}+2 y\right )&=x \\ \end{align*}

[_separable]

4.937

14518

\begin{align*} 6 x^{2} y-\left (x^{3}+1\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

2.579

14520

\begin{align*} y-1+x \left (x +1\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

2.315

14524

\begin{align*} 8 x^{3} y-12 x^{3}+\left (x^{4}+1\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

2.783

14529

\begin{align*} y x +x^{2} y^{\prime }&=x y^{3} \\ \end{align*}

[_separable]

11.452

14530

\begin{align*} \left (x^{3}+1\right ) y^{\prime }+6 x^{2} y&=6 x^{2} \\ \end{align*}

[_separable]

2.820

14533

\begin{align*} 8+2 y^{2}+\left (-x^{2}+1\right ) y y^{\prime }&=0 \\ y \left (3\right ) &= 0 \\ \end{align*}

[_separable]

4.319

14538

\begin{align*} y^{\prime }&=\frac {x y}{x^{2}+1} \\ y \left (\sqrt {15}\right ) &= 2 \\ \end{align*}

[_separable]

2.457

14886

\begin{align*} x^{\prime }&=t^{3} \left (1-x\right ) \\ x \left (0\right ) &= 3 \\ \end{align*}

[_separable]

3.023

14887

\begin{align*} y^{\prime }&=\left (1+y^{2}\right ) \tan \left (x \right ) \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

5.893

14888

\begin{align*} x^{\prime }&=t^{2} x \\ \end{align*}

[_separable]

2.749

14890

\begin{align*} y^{\prime }&=y^{2} {\mathrm e}^{-t^{2}} \\ \end{align*}

[_separable]

3.195

14892

\begin{align*} y^{\prime } x&=k y \\ \end{align*}

[_separable]

3.460

14893

\begin{align*} i^{\prime }&=p \left (t \right ) i \\ \end{align*}

[_separable]

2.630

14899

\begin{align*} x^{\prime }+t x&=4 t \\ x \left (0\right ) &= 2 \\ \end{align*}

[_separable]

3.023

14912

\begin{align*} V^{\prime }\left (x \right )+2 y y^{\prime }&=0 \\ \end{align*}

[_separable]

0.826

14913

\begin{align*} \left (\frac {1}{y}-a \right ) y^{\prime }+\frac {2}{x}-b&=0 \\ \end{align*}

[_separable]

4.464

15015

\begin{align*} \tan \left (y\right )-\cot \left (x \right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

2.562

15022

\begin{align*} y^{\prime }&={\mathrm e}^{x -y} \\ \end{align*}

[_separable]

2.423

15029

\begin{align*} y&=y^{\prime } x +\frac {1}{y} \\ \end{align*}

[_separable]

16.246

15115

\begin{align*} y^{\prime }&=y \,{\mathrm e}^{x +y} \left (x^{2}+1\right ) \\ \end{align*}

[_separable]

2.407

15116

\begin{align*} x^{2} y^{\prime }&=1+y^{2} \\ \end{align*}

[_separable]

3.127

15118

\begin{align*} x \left ({\mathrm e}^{y}+4\right )&={\mathrm e}^{x +y} y^{\prime } \\ \end{align*}

[_separable]

4.635

15122

\begin{align*} y^{\prime }&=x \,{\mathrm e}^{y^{2}-x} \\ \end{align*}

[_separable]

2.493

15124

\begin{align*} x \left (1+y\right )^{2}&=\left (x^{2}+1\right ) y \,{\mathrm e}^{y} y^{\prime } \\ \end{align*}

[_separable]

3.855

15135

\begin{align*} 5 y^{\prime }-y x&=0 \\ \end{align*}

[_separable]

2.786

15335

\begin{align*} y-y^{\prime } x&=0 \\ \end{align*}

[_separable]

2.603

15336

\begin{align*} \left (1+u \right ) v+\left (1-v\right ) u v^{\prime }&=0 \\ \end{align*}

[_separable]

4.070

15337

\begin{align*} 1+y-\left (1-x \right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

3.156

15338

\begin{align*} \left (t^{2}+t^{2} x\right ) x^{\prime }+x^{2}+t x^{2}&=0 \\ \end{align*}

[_separable]

6.013

15339

\begin{align*} y-a +x^{2} y^{\prime }&=0 \\ \end{align*}

[_separable]

2.642

15340

\begin{align*} z-\left (-a^{2}+t^{2}\right ) z^{\prime }&=0 \\ \end{align*}

[_separable]

3.716

15341

\begin{align*} y^{\prime }&=\frac {1+y^{2}}{x^{2}+1} \\ \end{align*}

[_separable]

3.513

15342

\begin{align*} 1+s^{2}-\sqrt {t}\, s^{\prime }&=0 \\ \end{align*}

[_separable]

3.983

15343

\begin{align*} r^{\prime }+r \tan \left (t \right )&=0 \\ \end{align*}

[_separable]

3.081

15344

\begin{align*} \left (x^{2}+1\right ) y^{\prime }-\sqrt {1-y^{2}}&=0 \\ \end{align*}

[_separable]

4.368

15345

\begin{align*} y^{\prime } \sqrt {-x^{2}+1}-\sqrt {1-y^{2}}&=0 \\ \end{align*}

[_separable]

9.546

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]

4.035

15347

\begin{align*} x -x y^{2}+\left (y-x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

3.693

15374

\begin{align*} \left (-x^{2}+1\right ) y^{\prime }-y x +a x y^{2}&=0 \\ \end{align*}

[_separable]

7.760

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]

5.474

15394

\begin{align*} y&=y^{\prime } x +y^{\prime } \\ \end{align*}

[_separable]

3.070

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]

5.969

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]

4.091

15484

\begin{align*} -y+y^{\prime } x&=0 \\ \end{align*}

[_separable]

2.834

15491

\begin{align*} x^{2} y^{\prime }+2 y x&=0 \\ \end{align*}

[_separable]

4.724

15499

\begin{align*} 2 y^{\prime } x -y&=0 \\ \end{align*}

[_separable]

3.887

15506

\begin{align*} y^{\prime }-2 y x&=0 \\ \end{align*}

[_separable]

3.269

15509

\begin{align*} y^{\prime }&=x \sqrt {y} \\ \end{align*}

[_separable]

12.220

15512

\begin{align*} x \ln \left (x \right ) y^{\prime }-\left (1+\ln \left (x \right )\right ) y&=0 \\ \end{align*}

[_separable]

4.373

15530

\begin{align*} y^{\prime }&=y x \\ \end{align*}

[_separable]

3.313

15531

\begin{align*} y^{\prime }&=-y x \\ \end{align*}

[_separable]

3.175

15535

\begin{align*} y^{\prime }&=y x \\ \end{align*}

[_separable]

3.240

15536

\begin{align*} y^{\prime }&=\frac {x}{y} \\ \end{align*}

[_separable]

9.147

15537

\begin{align*} y^{\prime }&=\frac {y}{x} \\ \end{align*}

[_separable]

3.214

15542

\begin{align*} y^{\prime }&={\mathrm e}^{x -y} \\ \end{align*}

[_separable]

2.763

15548

\begin{align*} y^{\prime }&=\frac {1}{y x} \\ \end{align*}

[_separable]

3.879

15552

\begin{align*} y^{\prime }&=\frac {x}{y^{2}} \\ \end{align*}

[_separable]

4.231

15553

\begin{align*} y^{\prime }&=\frac {\sqrt {y}}{x} \\ \end{align*}

[_separable]

5.912

15554

\begin{align*} y^{\prime }&=\frac {x y}{1-y} \\ \end{align*}

[_separable]

4.084

15568

\begin{align*} y^{\prime }&=-x \sqrt {1-y^{2}} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

6.759

15583

\begin{align*} y^{\prime }&=x \,{\mathrm e}^{-x^{2}+y} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

2.881

15584

\begin{align*} y^{\prime }&=\frac {y}{x} \\ y \left (-1\right ) &= 2 \\ \end{align*}

[_separable]

3.142

15585

\begin{align*} y^{\prime }&=\frac {2 x}{y} \\ y \left (0\right ) &= 2 \\ \end{align*}

[_separable]

9.876

15587

\begin{align*} y^{\prime }&=y x +x \\ y \left (1\right ) &= 2 \\ \end{align*}

[_separable]

3.053

15588

\begin{align*} x \,{\mathrm e}^{y}+y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

9.427

15589

\begin{align*} y-x^{2} y^{\prime }&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}

[_separable]

3.608

15591

\begin{align*} 2 y y^{\prime } x +y^{2}&=-1 \\ \end{align*}

[_separable]

4.524

15597

\begin{align*} y^{\prime }&=\frac {y}{x} \\ y \left (-1\right ) &= 2 \\ \end{align*}

[_separable]

4.174

15602

\begin{align*} x -y y^{\prime }&=0 \\ \end{align*}

[_separable]

9.728

15603

\begin{align*} y-y^{\prime } x&=0 \\ \end{align*}

[_separable]

2.924

15605

\begin{align*} x y \left (1-y\right )-2 y^{\prime }&=0 \\ \end{align*}

[_separable]

6.397

15606

\begin{align*} x \left (1-y^{3}\right )-3 y^{2} y^{\prime }&=0 \\ \end{align*}

[_separable]

3.329

15607

\begin{align*} \left (2 x -1\right ) y+x \left (x +1\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

3.316

15610

\begin{align*} y^{\prime }&=\frac {y}{x} \\ y \left (-1\right ) &= 1 \\ \end{align*}

[_separable]

3.151

15611

\begin{align*} y^{\prime }&=\frac {y}{x} \\ y \left (-1\right ) &= -1 \\ \end{align*}

[_separable]

3.063

15621

\begin{align*} y^{\prime }&=-\frac {3 x^{2}}{2 y} \\ y \left (-1\right ) &= 1 \\ \end{align*}

[_separable]

5.125

15622

\begin{align*} y^{\prime }&=-\frac {3 x^{2}}{2 y} \\ y \left (-1\right ) &= {\frac {1}{2}} \\ \end{align*}

[_separable]

5.280

15623

\begin{align*} y^{\prime }&=-\frac {3 x^{2}}{2 y} \\ y \left (-1\right ) &= 0 \\ \end{align*}

[_separable]

5.457

15625

\begin{align*} y^{\prime }&=\frac {\sqrt {y}}{x} \\ y \left (-1\right ) &= 1 \\ \end{align*}

[_separable]

7.805

15626

\begin{align*} y^{\prime }&=\frac {\sqrt {y}}{x} \\ y \left (-1\right ) &= 0 \\ \end{align*}

[_separable]

6.303

15627

\begin{align*} y^{\prime }&=\frac {\sqrt {y}}{x} \\ y \left (-1\right ) &= -1 \\ \end{align*}

[_separable]

6.269

15628

\begin{align*} y^{\prime }&=\frac {\sqrt {y}}{x} \\ y \left (1\right ) &= 1 \\ \end{align*}

[_separable]

6.908

15629

\begin{align*} y^{\prime }&=3 x y^{{1}/{3}} \\ y \left (-1\right ) &= {\frac {3}{2}} \\ \end{align*}

[_separable]

65.826

15630

\begin{align*} y^{\prime }&=3 x y^{{1}/{3}} \\ y \left (-1\right ) &= 1 \\ \end{align*}

[_separable]

50.734

15631

\begin{align*} y^{\prime }&=3 x y^{{1}/{3}} \\ y \left (-1\right ) &= {\frac {1}{2}} \\ \end{align*}

[_separable]

66.683

15632

\begin{align*} y^{\prime }&=3 x y^{{1}/{3}} \\ y \left (-1\right ) &= 0 \\ \end{align*}

[_separable]

54.527

15633

\begin{align*} y^{\prime }&=3 x y^{{1}/{3}} \\ y \left (-1\right ) &= -1 \\ \end{align*}

[_separable]

65.299

15644

\begin{align*} y^{\prime }&=x \sqrt {1-y^{2}} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

34.640

15645

\begin{align*} y^{\prime }&=x \sqrt {1-y^{2}} \\ y \left (0\right ) &= {\frac {9}{10}} \\ \end{align*}

[_separable]

51.974

15646

\begin{align*} y^{\prime }&=x \sqrt {1-y^{2}} \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}

[_separable]

54.097

15647

\begin{align*} y^{\prime }&=x \sqrt {1-y^{2}} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

34.234

15774

\begin{align*} y^{\prime }&=\frac {1+y}{1+t} \\ \end{align*}

[_separable]

3.575

15775

\begin{align*} y^{\prime }&=t^{2} y^{2} \\ \end{align*}

[_separable]

8.806

15776

\begin{align*} y^{\prime }&=t^{4} y \\ \end{align*}

[_separable]

3.934

15781

\begin{align*} y^{\prime }&=2 t y^{2}+3 y^{2} \\ \end{align*}

[_separable]

5.488

15782

\begin{align*} y^{\prime }&=\frac {t}{y} \\ \end{align*}

[_separable]

11.205

15783

\begin{align*} y^{\prime }&=\frac {t}{y+t^{2} y} \\ \end{align*}

[_separable]

2.854

15784

\begin{align*} y^{\prime }&=t y^{{1}/{3}} \\ \end{align*}

[_separable]

19.419

15786

\begin{align*} y^{\prime }&=\frac {2 y+1}{t} \\ \end{align*}

[_separable]

5.582

15788

\begin{align*} y^{\prime }&=\frac {4 t}{1+3 y^{2}} \\ \end{align*}

[_separable]

2.683

15789

\begin{align*} v^{\prime }&=t^{2} v-2-2 v+t^{2} \\ \end{align*}

[_separable]

3.977

15790

\begin{align*} y^{\prime }&=\frac {1}{t y+t +y+1} \\ \end{align*}

[_separable]

5.619

15791

\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{t} y}{1+y^{2}} \\ \end{align*}

[_separable]

3.457

15793

\begin{align*} w^{\prime }&=\frac {w}{t} \\ \end{align*}

[_separable]

3.270

15795

\begin{align*} x^{\prime }&=-t x \\ x \left (0\right ) &= \frac {1}{\sqrt {\pi }} \\ \end{align*}

[_separable]

4.527

15796

\begin{align*} y^{\prime }&=t y \\ y \left (0\right ) &= 3 \\ \end{align*}

[_separable]

4.294

15798

\begin{align*} y^{\prime }&=t^{2} y^{3} \\ y \left (0\right ) &= -1 \\ \end{align*}

[_separable]

19.967

15800

\begin{align*} y^{\prime }&=\frac {t}{y-t^{2} y} \\ y \left (0\right ) &= 4 \\ \end{align*}

[_separable]

3.772

15802

\begin{align*} y^{\prime }&=t y^{2}+2 y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

6.171

15803

\begin{align*} x^{\prime }&=\frac {t^{2}}{x+t^{3} x} \\ x \left (0\right ) &= -2 \\ \end{align*}

[_separable]

3.949

15805

\begin{align*} y^{\prime }&=\left (1+y^{2}\right ) t \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

4.684

15807

\begin{align*} y^{\prime }&=2 t y^{2}+3 t^{2} y^{2} \\ y \left (1\right ) &= -1 \\ \end{align*}

[_separable]

3.883

15818

\begin{align*} y^{\prime }&=\left (1+t \right ) y \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}

[_separable]

4.896

15828

\begin{align*} y^{\prime }&=t y+t y^{2} \\ \end{align*}

[_separable]

6.308

15829

\begin{align*} y^{\prime }&=t^{2}+t^{2} y \\ \end{align*}

[_separable]

3.625

15830

\begin{align*} y^{\prime }&=t +t y \\ \end{align*}

[_separable]

3.501

15859

\begin{align*} y^{\prime }&=\frac {t}{y-2} \\ y \left (-1\right ) &= 0 \\ \end{align*}

[_separable]

6.759

15941

\begin{align*} y^{\prime }&=\frac {\left (t^{2}-4\right ) \left (1+y\right ) {\mathrm e}^{y}}{\left (t -1\right ) \left (3-y\right )} \\ \end{align*}

[_separable]

5.592

15946

\begin{align*} y^{\prime }&=t y \\ \end{align*}

[_separable]

4.224

15948

\begin{align*} y^{\prime }&=\frac {t y}{t^{2}+1} \\ \end{align*}

[_separable]

3.698

15954

\begin{align*} x^{\prime }&=-t x \\ x \left (0\right ) &= {\mathrm e} \\ \end{align*}

[_separable]

5.095

15957

\begin{align*} y^{\prime }&=t^{2} y^{3}+y^{3} \\ y \left (0\right ) &= -{\frac {1}{2}} \\ \end{align*}

[_separable]

4.931

15960

\begin{align*} y^{\prime }&=\frac {\left (1+t \right )^{2}}{\left (1+y\right )^{2}} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

9.244

15961

\begin{align*} y^{\prime }&=2 t y^{2}+3 t^{2} y^{2} \\ y \left (1\right ) &= -1 \\ \end{align*}

[_separable]

4.278

15963

\begin{align*} y^{\prime }&=\frac {t^{2}}{y+y t^{3}} \\ y \left (0\right ) &= -2 \\ \end{align*}

[_separable]

4.344

15967

\begin{align*} y^{\prime }&=t^{2} y+1+y+t^{2} \\ \end{align*}

[_separable]

4.353

15968

\begin{align*} y^{\prime }&=\frac {2 y+1}{t} \\ \end{align*}

[_separable]

6.447

16156

\begin{align*} y y^{\prime }&=2 x \\ \end{align*}

[_separable]

11.580

16197

\begin{align*} y^{\prime }+3 y x&=6 x \\ \end{align*}

[_separable]

3.946

16200

\begin{align*} x^{2} y^{\prime }+x y^{2}&=x \\ \end{align*}

[_separable]

7.059

16203

\begin{align*} \left (x -2\right ) y^{\prime }&=3+y \\ \end{align*}

[_separable]

4.672

16204

\begin{align*} \left (-2+y\right ) y^{\prime }&=x -3 \\ \end{align*}

[_separable]

19.897

16208

\begin{align*} y^{\prime }&=3 y^{2}-\sin \left (x \right ) y^{2} \\ \end{align*}

[_separable]

4.882

16213

\begin{align*} y^{\prime }+y x&=4 x \\ \end{align*}

[_separable]

3.993

16215

\begin{align*} y^{\prime }&=y x -3 x -2 y+6 \\ \end{align*}

[_separable]

4.454

16217

\begin{align*} y y^{\prime }&={\mathrm e}^{-3 y^{2}+x} \\ \end{align*}

[_separable]

4.642

16218

\begin{align*} y^{\prime }&=\frac {x}{y} \\ \end{align*}

[_separable]

13.441

16220

\begin{align*} y y^{\prime } x&=y^{2}+9 \\ \end{align*}

[_separable]

9.737

16221

\begin{align*} y^{\prime }&=\frac {1+y^{2}}{x^{2}+1} \\ \end{align*}

[_separable]

4.565

16222

\begin{align*} y^{\prime } \cos \left (y\right )&=\sin \left (x \right ) \\ \end{align*}

[_separable]

3.056

16223

\begin{align*} y^{\prime }&={\mathrm e}^{2 x -3 y} \\ \end{align*}

[_separable]

4.006

16224

\begin{align*} y^{\prime }&=\frac {x}{y} \\ y \left (1\right ) &= 3 \\ \end{align*}

[_separable]

22.768

16225

\begin{align*} y^{\prime }&=2 x -1+2 y x -y \\ y \left (0\right ) &= 2 \\ \end{align*}

[_separable]

4.794

16228

\begin{align*} y^{\prime }&=y x -4 x \\ \end{align*}

[_separable]

3.736

16230

\begin{align*} y y^{\prime }&=x y^{2}-9 x \\ \end{align*}

[_separable]

4.786

16232

\begin{align*} y^{\prime }&={\mathrm e}^{x +y^{2}} \\ \end{align*}

[_separable]

2.119

16234

\begin{align*} y^{\prime }&=y x -4 x \\ \end{align*}

[_separable]

3.698

16235

\begin{align*} y^{\prime }&=y x -3 x -2 y+6 \\ \end{align*}

[_separable]

4.258

16236

\begin{align*} y^{\prime }&=3 y^{2}-\sin \left (x \right ) y^{2} \\ \end{align*}

[_separable]

4.614

16238

\begin{align*} y^{\prime }&=\frac {y}{x} \\ \end{align*}

[_separable]

3.625

16239

\begin{align*} y^{\prime }&=\frac {6 x^{2}+4}{3 y^{2}-4 y} \\ \end{align*}

[_separable]

4.356

16240

\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=1+y^{2} \\ \end{align*}

[_separable]

4.697

16241

\begin{align*} \left (-1+y^{2}\right ) y^{\prime }&=4 x y^{2} \\ \end{align*}

[_separable]

45.531

16244

\begin{align*} y^{\prime }&=3 x y^{3} \\ \end{align*}

[_separable]

12.708

16245

\begin{align*} y^{\prime }&=\frac {2+\sqrt {x}}{2+\sqrt {y}} \\ \end{align*}

[_separable]

5.747

16246

\begin{align*} y^{\prime }-3 y^{2} x^{2}&=-3 x^{2} \\ \end{align*}

[_separable]

5.706

16247

\begin{align*} y^{\prime }-3 y^{2} x^{2}&=3 x^{2} \\ \end{align*}

[_separable]

4.606

16250

\begin{align*} y y^{\prime }&=\sin \left (x \right ) \\ y \left (0\right ) &= -4 \\ \end{align*}

[_separable]

2.918

16251

\begin{align*} y^{\prime }&=2 x -1+2 y x -y \\ y \left (0\right ) &= -1 \\ \end{align*}

[_separable]

4.053

16252

\begin{align*} y^{\prime } x&=y^{2}-y \\ y \left (2\right ) &= 1 \\ \end{align*}

[_separable]

9.958

16253

\begin{align*} y^{\prime } x&=y^{2}-y \\ y \left (1\right ) &= 2 \\ \end{align*}

[_separable]

10.474

16255

\begin{align*} \left (-1+y^{2}\right ) y^{\prime }&=4 y x \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

4.697

16263

\begin{align*} y^{\prime }&=\sin \left (x \right ) y \\ \end{align*}

[_separable]

4.546

16269

\begin{align*} y^{\prime }-2 y x&=x \\ \end{align*}

[_separable]

3.762

16317

\begin{align*} 2-2 x +3 y^{2} y^{\prime }&=0 \\ \end{align*}

[_separable]

4.373

16321

\begin{align*} 1+{\mathrm e}^{y}+x \,{\mathrm e}^{y} y^{\prime }&=0 \\ \end{align*}

[_separable]

6.570

16323

\begin{align*} 1+y^{4}+x y^{3} y^{\prime }&=0 \\ \end{align*}

[_separable]

7.083

16327

\begin{align*} 3 y+3 y^{2}+\left (2 x +4 y x \right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

32.188

16328

\begin{align*} 2 x \left (1+y\right )-y^{\prime }&=0 \\ \end{align*}

[_separable]

3.931

16333

\begin{align*} y^{\prime } x&=2 y^{2}-6 y \\ \end{align*}

[_separable]

13.988

16334

\begin{align*} 4 y^{2}-y^{2} x^{2}+y^{\prime }&=0 \\ \end{align*}

[_separable]

4.169

16348

\begin{align*} y^{\prime }&=\frac {1}{y x -3 x} \\ \end{align*}

[_separable]

20.022

16351

\begin{align*} \sin \left (y\right )+\left (x +1\right ) \cos \left (y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

14.733

16357

\begin{align*} y^{\prime }&=x y^{2}+3 y^{2}+x +3 \\ \end{align*}

[_separable]

5.386

16371

\begin{align*} y^{2}-y^{2} \cos \left (x \right )+y^{\prime }&=0 \\ \end{align*}

[_separable]

4.926

16374

\begin{align*} y^{\prime }&=y^{3}-y^{3} \cos \left (x \right ) \\ \end{align*}

[_separable]

6.931

16376

\begin{align*} y^{\prime }&={\mathrm e}^{4 x +3 y} \\ \end{align*}

[_separable]

4.286

16378

\begin{align*} y^{\prime }&={\mathrm e}^{4 x +3 y} \\ \end{align*}

[_separable]

2.382

16964

\begin{align*} y^{\prime }+y x&=0 \\ \end{align*}

[_separable]

4.566

16975

\begin{align*} y^{\prime }&=-\frac {x}{y} \\ \end{align*}

[_separable]

11.323

17005

\begin{align*} y^{\prime }&=\frac {\left (x -4\right ) y^{3}}{x^{3} \left (-2+y\right )} \\ \end{align*}

[_separable]

15.300

17015

\begin{align*} y^{\prime }+\cos \left (x \right ) y&=0 \\ \end{align*}

[_separable]

4.986

17038

\begin{align*} \frac {y^{\prime }}{t}&=\sqrt {y} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

23.814

17040

\begin{align*} y^{\prime }&=y \sqrt {t} \\ y \left (1\right ) &= 1 \\ \end{align*}

[_separable]

6.230

17042

\begin{align*} y^{\prime } t&=y \\ \end{align*}

[_separable]

3.996

17043

\begin{align*} y^{\prime }&=\tan \left (t \right ) y \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

7.223

17064

\begin{align*} y^{\prime }&=t y^{2} \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}

[_separable]

21.352

17065

\begin{align*} y^{\prime }&=-\frac {t}{y} \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}

[_separable]

20.773

17067

\begin{align*} y^{\prime }&=\frac {x}{y^{2}} \\ \end{align*}

[_separable]

7.815

17068

\begin{align*} \frac {1}{2 \sqrt {t}}+y^{2} y^{\prime }&=0 \\ \end{align*}

[_separable]

9.418

17069

\begin{align*} y^{\prime }&=\frac {\sqrt {y}}{x^{2}} \\ \end{align*}

[_separable]

25.052

17071

\begin{align*} 6+4 t^{3}+\left (5+\frac {9}{y^{8}}\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

5.414

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]

6.240

17073

\begin{align*} 4 \sinh \left (4 y\right ) y^{\prime }&=6 \cosh \left (3 x \right ) \\ \end{align*}

[_separable]

5.145

17074

\begin{align*} y^{\prime }&=\frac {1+y}{1+t} \\ \end{align*}

[_separable]

4.981

17075

\begin{align*} y^{\prime }&=\frac {2+y}{2 t +1} \\ \end{align*}

[_separable]

10.855

17076

\begin{align*} \frac {3}{t^{2}}&=\left (\frac {1}{\sqrt {y}}+\sqrt {y}\right ) y^{\prime } \\ \end{align*}

[_separable]

8.497

17077

\begin{align*} 3 \sin \left (x \right )-4 y^{\prime } \cos \left (y\right )&=0 \\ \end{align*}

[_separable]

3.827

17078

\begin{align*} \cos \left (y\right ) y^{\prime }&=8 \sin \left (8 t \right ) \\ \end{align*}

[_separable]

5.618

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]

8.734

17081

\begin{align*} \cosh \left (6 t \right )+5 \sinh \left (4 t \right )+20 \sinh \left (y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

8.726

17082

\begin{align*} y^{\prime }&={\mathrm e}^{2 y+10 t} \\ \end{align*}

[_separable]

5.010

17083

\begin{align*} y^{\prime }&={\mathrm e}^{3 y+2 t} \\ \end{align*}

[_separable]

5.047

17084

\begin{align*} \sin \left (t \right )^{2}&=\cos \left (y\right )^{2} y^{\prime } \\ \end{align*}

[_separable]

4.654

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]

25.717

17086

\begin{align*} x^{\prime }&=\frac {\sec \left (t \right )^{2}}{\sec \left (x\right ) \tan \left (x\right )} \\ \end{align*}

[_separable]

28.076

17087

\begin{align*} \left (2-\frac {5}{y^{2}}\right ) y^{\prime }+4 \cos \left (x \right )^{2}&=0 \\ \end{align*}

[_separable]

6.552

17088

\begin{align*} y^{\prime }&=\frac {t^{3}}{y \sqrt {\left (1-y^{2}\right ) \left (t^{4}+9\right )}} \\ \end{align*}

[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]

10.163

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]

6.713

17090

\begin{align*} y^{\prime }&=\frac {\left (1+2 \,{\mathrm e}^{y}\right ) {\mathrm e}^{-y}}{t \ln \left (t \right )} \\ \end{align*}

[_separable]

10.185

17091

\begin{align*} x \sin \left (x^{2}\right )&=\frac {\cos \left (\sqrt {y}\right ) y^{\prime }}{\sqrt {y}} \\ \end{align*}

[_separable]

24.657

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]

6.445

17093

\begin{align*} \frac {\cos \left (y\right ) y^{\prime }}{\left (1-\sin \left (y\right )\right )^{2}}&=\sin \left (x \right )^{3} \cos \left (x \right ) \\ \end{align*}

[_separable]

11.181

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]

13.139

17095

\begin{align*} \frac {\sqrt {\ln \left (x \right )}}{x}&=\frac {{\mathrm e}^{\frac {3}{y}} y^{\prime }}{y} \\ \end{align*}

[_separable]

5.299

17096

\begin{align*} y^{\prime }&=\frac {5^{-t}}{y^{2}} \\ \end{align*}

[_separable]

5.216

17097

\begin{align*} y^{\prime }&=t^{2} y^{2}+y^{2}-t^{2}-1 \\ \end{align*}

[_separable]

8.323

17099

\begin{align*} 4 \left (x -1\right )^{2} y^{\prime }-3 \left (3+y\right )^{2}&=0 \\ \end{align*}

[_separable]

12.115

17100

\begin{align*} y^{\prime }&=\sin \left (t -y\right )+\sin \left (y+t \right ) \\ \end{align*}

[_separable]

11.197

17113

\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{t}}{1+y} \\ y \left (0\right ) &= -2 \\ \end{align*}

[_separable]

8.651

17114

\begin{align*} y^{\prime }&={\mathrm e}^{t -y} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

7.943

17118

\begin{align*} y^{\prime }&=\frac {\sin \left (x \right )}{\cos \left (y\right )+1} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

4.982

17119

\begin{align*} y^{\prime }&=\frac {3+y}{1+3 x} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

6.813

17120

\begin{align*} y^{\prime }&={\mathrm e}^{x -y} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

8.171

17121

\begin{align*} y^{\prime }&={\mathrm e}^{2 x -y} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

10.612

17122

\begin{align*} y^{\prime }&=\frac {3 y+1}{x +3} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

8.946

17123

\begin{align*} y^{\prime }&=y \cos \left (t \right ) \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

7.642

17124

\begin{align*} y^{\prime }&=y^{2} \cos \left (t \right ) \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

6.058

17125

\begin{align*} y^{\prime }&=\sqrt {y}\, \cos \left (t \right ) \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

11.587

17126

\begin{align*} y^{\prime }+y f \left (t \right )&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

6.167

17127

\begin{align*} y^{\prime }&=-\frac {-2+y}{x -2} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

6.425

17137

\begin{align*} y^{\prime }&=y f \left (t \right ) \\ y \left (1\right ) &= 1 \\ \end{align*}

[_separable]

8.642

17156

\begin{align*} y^{\prime }-y x&=x \\ \end{align*}

[_separable]

4.498

17160

\begin{align*} x^{\prime }&=\frac {3 x t^{2}}{-t^{3}+1} \\ \end{align*}

[_separable]

3.802

17166

\begin{align*} 2 t y+y^{\prime }&=2 t \\ y \left (0\right ) &= -1 \\ \end{align*}

[_separable]

6.685

17170

\begin{align*} \left (t^{2}+4\right ) y^{\prime }+2 t y&=2 t \\ y \left (0\right ) &= -4 \\ \end{align*}

[_separable]

6.162

17198

\begin{align*} \frac {t}{\sqrt {t^{2}+y^{2}}}+\frac {y y^{\prime }}{\sqrt {t^{2}+y^{2}}}&=0 \\ \end{align*}

[_separable]

19.727

17205

\begin{align*} {\mathrm e}^{t y}+\frac {t \,{\mathrm e}^{t y} y^{\prime }}{y}&=0 \\ \end{align*}

[_separable]

8.477

17209

\begin{align*} \frac {3 t^{2}}{y}-\frac {t^{3} y^{\prime }}{y^{2}}&=0 \\ \end{align*}

[_separable]

8.419

17214

\begin{align*} \sin \left (y\right )^{2}+t \sin \left (2 y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

29.203

17238

\begin{align*} t^{2} y+t^{3} y^{\prime }&=0 \\ \end{align*}

[_separable]

5.950

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]

6.178

17259

\begin{align*} y^{\prime }-\frac {y}{t}&=\frac {y^{2}}{t} \\ \end{align*}

[_separable]

6.628

17263

\begin{align*} 2 \ln \left (t \right )-\ln \left (4 y^{2}\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

13.567

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]

17.460

17266

\begin{align*} \sqrt {t^{2}+1}+y y^{\prime }&=0 \\ \end{align*}

[_separable]

5.342

17296

\begin{align*} y^{\prime }-\frac {2 y}{x}&=-x^{2} y \\ \end{align*}

[_separable]

6.971

17310

\begin{align*} y^{\prime }&=\frac {2 t^{5}}{5 y^{2}} \\ \end{align*}

[_separable]

9.007

17311

\begin{align*} \cos \left (4 x \right )-8 y^{\prime } \sin \left (y\right )&=0 \\ \end{align*}

[_separable]

5.237

17312

\begin{align*} y^{\prime }-\frac {y}{t}&=\frac {y^{2}}{t} \\ \end{align*}

[_separable]

6.960

17313

\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{8 y}}{t} \\ \end{align*}

[_separable]

4.497

17314

\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{5 t}}{y^{4}} \\ \end{align*}

[_separable]

5.166

17315

\begin{align*} -\frac {1}{x^{5}}+\frac {1}{x^{3}}&=\left (2 y^{4}-6 y^{9}\right ) y^{\prime } \\ \end{align*}

[_separable]

4.733

17316

\begin{align*} y^{\prime }&=\frac {y \,{\mathrm e}^{-2 t}}{\ln \left (y\right )} \\ \end{align*}

[_separable]

6.200

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]

7.388

17330

\begin{align*} t y+y^{\prime }&=t \\ \end{align*}

[_separable]

5.441

17347

\begin{align*} y^{\prime }&=t y^{3} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

12.566

17348

\begin{align*} y^{\prime }&=\frac {t}{y^{3}} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

10.533

17349

\begin{align*} y^{\prime }&=-\frac {y}{-2+t} \\ y \left (2\right ) &= 0 \\ \end{align*}

[_separable]

4.878

17838

\begin{align*} y^{\prime }&=\frac {x}{y} \\ \end{align*}

[_separable]

3.700

17850

\begin{align*} \left (-x^{2}+1\right ) y^{\prime }+y x&=2 x \\ \end{align*}

[_separable]

3.065

17856

\begin{align*} y^{\prime }&=\left (-1+y\right ) x \\ \end{align*}

[_separable]

1.730

17861

\begin{align*} y^{\prime }&=\frac {1+y}{x -1} \\ \end{align*}

[_separable]

1.930

17866

\begin{align*} y^{\prime }&=-\frac {y}{x} \\ \end{align*}

[_separable]

2.240

17876

\begin{align*} 1+y^{2}+\left (x^{2}+1\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

2.762

17877

\begin{align*} y y^{\prime } x +1+y^{2}&=0 \\ \end{align*}

[_separable]

3.284

17878

\begin{align*} \sin \left (x \right ) y^{\prime }-\cos \left (x \right ) y&=0 \\ y \left (\frac {\pi }{2}\right ) &= 1 \\ \end{align*}

[_separable]

3.351

17879

\begin{align*} 1+y^{2}&=y^{\prime } x \\ \end{align*}

[_separable]

2.852

17880

\begin{align*} y y^{\prime } \sqrt {x^{2}+1}+x \sqrt {1+y^{2}}&=0 \\ \end{align*}

[_separable]

2.651

17881

\begin{align*} x \sqrt {1-y^{2}}+y \sqrt {-x^{2}+1}\, y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

3.569

17884

\begin{align*} y^{\prime }&=a^{x +y} \\ \end{align*}

[_separable]

1.193

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]

4.323

17886

\begin{align*} 2 x \sqrt {1-y^{2}}&=\left (x^{2}+1\right ) y^{\prime } \\ \end{align*}

[_separable]

3.217

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]

4.547

17888

\begin{align*} \sin \left (x \right ) y^{2}+\cos \left (x \right )^{2} \ln \left (y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

4.063

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]

5.268

17894

\begin{align*} y^{\prime }&=\frac {y}{x} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

2.116

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]

3.386

17907

\begin{align*} \left (x +1\right ) y^{\prime }&=-1+y \\ \end{align*}

[_separable]

2.348

17908

\begin{align*} y^{\prime }&=2 x \left (\pi +y\right ) \\ \end{align*}

[_separable]

2.193

17939

\begin{align*} y^{\prime }+\cos \left (x \right ) y&=\cos \left (x \right ) \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

2.589

17953

\begin{align*} y^{\prime }+2 y x&=2 x y^{2} \\ \end{align*}

[_separable]

3.675

17956

\begin{align*} y^{\prime }+3 y x&=y \,{\mathrm e}^{x^{2}} \\ \end{align*}

[_separable]

3.503

17961

\begin{align*} y^{\prime }-\cos \left (x \right ) y&=y^{2} \cos \left (x \right ) \\ \end{align*}

[_separable]

4.512

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]

28.332

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]

5.382

18055

\begin{align*} y^{\prime } \left (3 x^{2}-2 x \right )-y \left (6 x -2\right )&=0 \\ \end{align*}

[_separable]

2.137

18062

\begin{align*} \left (x -1\right ) \left (y^{2}-y+1\right )&=\left (-1+y\right ) \left (x^{2}+x +1\right ) y^{\prime } \\ \end{align*}

[_separable]

3.941

18071

\begin{align*} \sin \left (\ln \left (x \right )\right )-\cos \left (\ln \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

3.273

18072

\begin{align*} y^{\prime }&=\sqrt {\frac {9 y^{2}-6 y+2}{x^{2}-2 x +5}} \\ \end{align*}

[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]

3.329

18098

\begin{align*} y x&=y^{\prime } \ln \left (\frac {y^{\prime }}{x}\right ) \\ \end{align*}

[_separable]

2.950

18473

\begin{align*} y^{\prime }&=\frac {x^{4}}{y} \\ \end{align*}

[_separable]

3.746

18474

\begin{align*} y^{\prime }&=\frac {x^{2} \left (x^{3}+1\right )}{y} \\ \end{align*}

[_separable]

1.884

18475

\begin{align*} y^{\prime }+y^{3} \sin \left (x \right )&=0 \\ \end{align*}

[_separable]

3.645

18476

\begin{align*} y^{\prime }&=\frac {7 x^{2}-1}{7+5 y} \\ \end{align*}

[_separable]

2.914

18477

\begin{align*} y^{\prime }&=\sin \left (2 x \right )^{2} \cos \left (y\right )^{2} \\ \end{align*}

[_separable]

2.622

18478

\begin{align*} y^{\prime } x&=\sqrt {1-y^{2}} \\ \end{align*}

[_separable]

4.222

18479

\begin{align*} y y^{\prime }&=\left (x y^{2}+x \right ) {\mathrm e}^{x^{2}} \\ \end{align*}

[_separable]

2.947

18480

\begin{align*} y^{\prime }&=\frac {x^{2}+{\mathrm e}^{-x}}{y^{2}-{\mathrm e}^{y}} \\ \end{align*}

[_separable]

2.687

18481

\begin{align*} y^{\prime }&=\frac {x^{2}}{1+y^{2}} \\ \end{align*}

[_separable]

1.560

18482

\begin{align*} y^{\prime }&=\frac {\sec \left (x \right )^{2}}{y^{3}+1} \\ \end{align*}

[_separable]

2.386

18484

\begin{align*} y^{\prime }&=x \left (y-y^{2}\right ) \\ \end{align*}

[_separable]

3.609

18485

\begin{align*} y^{\prime }&=\left (1-12 x \right ) y^{2} \\ y \left (0\right ) &= -{\frac {1}{8}} \\ \end{align*}

[_separable]

3.625

18487

\begin{align*} x +y y^{\prime } {\mathrm e}^{-x}&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

2.389

18488

\begin{align*} r^{\prime }&=\frac {r^{2}}{\theta } \\ r \left (1\right ) &= 2 \\ \end{align*}

[_separable]

3.578

18489

\begin{align*} y^{\prime }&=\frac {3 x}{y+x^{2} y} \\ y \left (0\right ) &= -7 \\ \end{align*}

[_separable]

5.465

18491

\begin{align*} y^{\prime }&=2 x y^{2}+4 x^{3} y^{2} \\ y \left (1\right ) &= -2 \\ \end{align*}

[_separable]

2.616

18492

\begin{align*} y^{\prime }&=x^{2} {\mathrm e}^{-3 y} \\ y \left (2\right ) &= 0 \\ \end{align*}

[_separable]

3.733

18493

\begin{align*} y^{\prime }&=\left (1+y^{2}\right ) \tan \left (2 x \right ) \\ y \left (0\right ) &= -\sqrt {3} \\ \end{align*}

[_separable]

7.183

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]

3.113

18496

\begin{align*} x^{2} y^{\prime }&=y-y x \\ y \left (1\right ) &= 2 \\ \end{align*}

[_separable]

3.020

18497

\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{-x}-{\mathrm e}^{x}}{3+4 y} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

4.751

18498

\begin{align*} 2 y y^{\prime }&=\frac {x}{\sqrt {x^{2}-4}} \\ y \left (3\right ) &= -1 \\ \end{align*}

[_separable]

5.607

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]

31.158

18500

\begin{align*} \sqrt {-x^{2}+1}\, y^{2} y^{\prime }&=\arcsin \left (x \right ) \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

3.966

18501

\begin{align*} y^{\prime }&=\frac {3 x^{2}+1}{12 y^{2}-12 y} \\ y \left (0\right ) &= 2 \\ \end{align*}

[_separable]

2.804

18502

\begin{align*} y^{\prime }&=\frac {2 x^{2}}{2 y^{2}-6} \\ y \left (1\right ) &= 0 \\ \end{align*}

[_separable]

5.227

18503

\begin{align*} y^{\prime }&=2 y^{2}+x y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

3.680

18506

\begin{align*} y^{\prime }&=2 \left (x +1\right ) \left (1+y^{2}\right ) \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

3.511

18507

\begin{align*} y^{\prime }&=\frac {t \left (4-y\right ) y}{3} \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}

[_separable]

4.519

18508

\begin{align*} y^{\prime }&=\frac {t y \left (4-y\right )}{1+t} \\ y \left (0\right ) &= 2 \\ \end{align*}

[_separable]

6.628

18546

\begin{align*} y+\left (t -4\right ) t y^{\prime }&=0 \\ y \left (2\right ) &= 1 \\ \end{align*}

[_separable]

2.505

18555

\begin{align*} y^{\prime }&=\frac {t^{2}+1}{3 y-y^{2}} \\ \end{align*}

[_separable]

1.918

18556

\begin{align*} y^{\prime }&=\frac {\cot \left (t \right ) y}{1+y} \\ \end{align*}

[_separable]

3.795

18559

\begin{align*} y^{\prime }&=-\frac {4 t}{y} \\ y \left (0\right ) &= y_{0} \\ \end{align*}

[_separable]

8.186

18560

\begin{align*} y^{\prime }&=2 t y^{2} \\ y \left (0\right ) &= y_{0} \\ \end{align*}

[_separable]

5.591

18562

\begin{align*} y^{\prime }&=\frac {t^{2}}{\left (t^{3}+1\right ) y} \\ y \left (0\right ) &= y_{0} \\ \end{align*}

[_separable]

2.648

18563

\begin{align*} y^{\prime }&=t \left (3-y\right ) y \\ \end{align*}

[_separable]

3.737

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]

3.000

18568

\begin{align*} 3+2 x +\left (-2+2 y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

6.053

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]

3.132

18579

\begin{align*} \frac {x}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}&=0 \\ \end{align*}

[_separable]

6.198

18582

\begin{align*} x^{2} y^{3}+x \left (1+y^{2}\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

2.190

18585

\begin{align*} \left (2+x \right ) \sin \left (y\right )+x \cos \left (y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

2.827

18594

\begin{align*} y y^{\prime }&=x +1 \\ \end{align*}

[_separable]

2.544

18595

\begin{align*} \left (1+y^{4}\right ) y^{\prime }&=x^{4}+1 \\ \end{align*}

[_separable]

1.933

18597

\begin{align*} x \left (x -1\right ) y^{\prime }&=y \left (1+y\right ) \\ \end{align*}

[_separable]

4.088

18610

\begin{align*} 5 \left (t^{2}+1\right ) y^{\prime }&=4 t y \left (y^{3}-1\right ) \\ \end{align*}

[_separable]

20.605

18621

\begin{align*} \frac {\sqrt {x}\, y^{\prime }}{y}&=1 \\ \end{align*}

[_separable]

3.405

19066

\begin{align*} y y^{\prime } \sqrt {x^{2}+1}+x \sqrt {1+y^{2}}&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

7.848

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]

23.530

19068

\begin{align*} y^{\prime } \sqrt {-x^{2}+1}+\sqrt {1-y^{2}}&=0 \\ \end{align*}

[_separable]

17.766

19228

\begin{align*} y^{\prime } x&=2 y \\ \end{align*}

[_separable]

4.489

19229

\begin{align*} y y^{\prime }&={\mathrm e}^{2 x} \\ \end{align*}

[_separable]

3.532

19249

\begin{align*} y y^{\prime } x&=-1+y \\ \end{align*}

[_separable]

5.973

19250

\begin{align*} x^{5} y^{\prime }+y^{5}&=0 \\ \end{align*}

[_separable]

9.207

19251

\begin{align*} y^{\prime } x&=\left (-2 x^{2}+1\right ) \tan \left (y\right ) \\ \end{align*}

[_separable]

2.951

19252

\begin{align*} y^{\prime }&=2 y x \\ \end{align*}

[_separable]

3.131

19253

\begin{align*} y^{\prime } \sin \left (y\right )&=x^{2} \\ \end{align*}

[_separable]

2.483

19255

\begin{align*} y^{\prime }+\tan \left (x \right ) y&=0 \\ \end{align*}

[_separable]

3.083

19256

\begin{align*} y^{\prime }-\tan \left (x \right ) y&=0 \\ \end{align*}

[_separable]

3.243

19257

\begin{align*} 1+y^{2}+\left (x^{2}+1\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

3.684

19258

\begin{align*} y \ln \left (y\right )-y^{\prime } x&=0 \\ \end{align*}

[_separable]

5.437

19265

\begin{align*} y^{\prime }&={\mathrm e}^{3 x -2 y} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

6.211

19267

\begin{align*} {\mathrm e}^{-y}+\left (x^{2}+1\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

2.850

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]

6.365

19270

\begin{align*} y y^{\prime } x&=\left (x +1\right ) \left (1+y\right ) \\ y \left (1\right ) &= 0 \\ \end{align*}

[_separable]

4.888

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]

4.140

19302

\begin{align*} 1+y+\left (1-x \right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

3.014

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]

4.519

19311

\begin{align*} \frac {x}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}&=0 \\ \end{align*}

[_separable]

10.148

19319

\begin{align*} \left (2+x \right ) \sin \left (y\right )+x \cos \left (y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

3.349

19327

\begin{align*} y-y^{\prime } x&=x y^{3} y^{\prime } \\ \end{align*}

[_separable]

6.444

19331

\begin{align*} y^{\prime } x -y+y^{2}&=0 \\ \end{align*}

[_separable]

4.169

19377

\begin{align*} y^{\prime } x +y&=x^{2} y^{\prime }+y^{2} \\ \end{align*}

[_separable]

6.385

19400

\begin{align*} 3 x^{2} \ln \left (y\right )+\frac {x^{3} y^{\prime }}{y}&=0 \\ \end{align*}

[_separable]

6.801

19672

\begin{align*} 1+2 x+\left (-t^{2}+4\right ) x^{\prime }&=0 \\ \end{align*}

[_separable]

8.092

19678

\begin{align*} x^{\prime }+x \tan \left (t \right )&=0 \\ \end{align*}

[_separable]

3.747

19681

\begin{align*} x^{\prime }+2 t x+t x^{4}&=0 \\ \end{align*}

[_separable]

4.255

19706

\begin{align*} y^{\prime }&=\frac {\sqrt {1-y^{2}}\, \arcsin \left (y\right )}{x} \\ \end{align*}

[_separable]

13.155

19711

\begin{align*} \sin \left (x \right ) \cos \left (y\right )^{2}+\cos \left (x \right )^{2} y^{\prime }&=0 \\ \end{align*}

[_separable]

5.000

19713

\begin{align*} y-y^{\prime } x&=b \left (1+x^{2} y^{\prime }\right ) \\ \end{align*}

[_separable]

3.919

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]

3.292

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]

26.394

19723

\begin{align*} y^{\prime }+y x&=x \\ \end{align*}

[_separable]

3.704

19740

\begin{align*} y^{\prime }&=x \left (a y^{2}+b \right ) \\ \end{align*}

[_separable]

5.885

19741

\begin{align*} n^{\prime }&=\left (n^{2}+1\right ) x \\ \end{align*}

[_separable]

4.576

19742

\begin{align*} v^{\prime }+\frac {2 v}{u}&=3 v \\ \end{align*}

[_separable]

3.356

19743

\begin{align*} \sqrt {-u^{2}+1}\, v^{\prime }&=2 u \sqrt {1-v^{2}} \\ \end{align*}

[_separable]

6.703

19745

\begin{align*} \frac {y^{\prime }}{x}&=y \sin \left (x^{2}-1\right )-\frac {2 y}{\sqrt {x}} \\ \end{align*}

[_separable]

6.963

19747

\begin{align*} v^{\prime }+2 u v&=2 u \\ \end{align*}

[_separable]

3.799

19748

\begin{align*} 1+v^{2}+\left (u^{2}+1\right ) v v^{\prime }&=0 \\ \end{align*}

[_separable]

7.808

19749

\begin{align*} u \ln \left (u \right ) v^{\prime }+\sin \left (v\right )^{2}&=1 \\ \end{align*}

[_separable]

6.269

19797

\begin{align*} y^{\prime }+\sin \left (x \right ) y&=\sin \left (x \right ) y^{2} \\ \end{align*}

[_separable]

8.782

19798

\begin{align*} \left (-x^{2}+1\right ) y^{\prime }-y x&=a x y^{2} \\ \end{align*}

[_separable]

10.442

19802

\begin{align*} y \sqrt {x^{2}-1}+x \sqrt {-1+y^{2}}\, y^{\prime }&=0 \\ \end{align*}

[_separable]

8.472

19803

\begin{align*} \left (1+{\mathrm e}^{y}\right ) \cos \left (x \right )+{\mathrm e}^{y} \sin \left (x \right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

3.628

19804

\begin{align*} \sqrt {2 a y-y^{2}}\, \csc \left (x \right )+y \tan \left (x \right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

15.145

19805

\begin{align*} y \left (3+y\right ) y^{\prime }&=x \left (3+2 y\right ) \\ \end{align*}

[_separable]

4.413

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]

4.031

19896

\begin{align*} \left (1-x \right ) y^{\prime }-1-y&=0 \\ \end{align*}

[_separable]

4.642

19898

\begin{align*} y-y^{\prime } x&=a \left (y^{\prime }+y^{2}\right ) \\ \end{align*}

[_separable]

7.787

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]

5.323

19913

\begin{align*} a \left (y^{\prime } x +2 y\right )&=y y^{\prime } x \\ \end{align*}

[_separable]

11.903

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]

24.881

19939

\begin{align*} y^{2}+x y^{2}+\left (x^{2}-x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

8.490

19952

\begin{align*} \left (x +1\right ) y^{\prime }+1&=2 \,{\mathrm e}^{y} \\ \end{align*}

[_separable]

6.740

19958

\begin{align*} y y^{\prime }&=a x \\ \end{align*}

[_separable]

10.618

19963

\begin{align*} y-y^{\prime } x&=b \left (1+x^{2} y^{\prime }\right ) \\ \end{align*}

[_separable]

3.997

19990

\begin{align*} x y \left (y-y^{\prime } x \right )&=x +y y^{\prime } \\ \end{align*}

[_separable]

9.974

20019

\begin{align*} \sqrt {x}\, y^{\prime }&=\sqrt {y} \\ \end{align*}

[_separable]

27.980

20226

\begin{align*} x \cos \left (y\right )^{2}&=y \cos \left (x \right )^{2} y^{\prime } \\ \end{align*}

[_separable]

7.208

20227

\begin{align*} y^{\prime }&={\mathrm e}^{x -y}+x^{2} {\mathrm e}^{-y} \\ \end{align*}

[_separable]

3.540

20228

\begin{align*} x^{2} y^{\prime }+y&=1 \\ \end{align*}

[_separable]

4.259

20229

\begin{align*} 2 y+\left (x^{2}+1\right ) \arctan \left (x \right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

5.309

20230

\begin{align*} x y^{2}+x +\left (y+x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

5.447

20231

\begin{align*} y^{\prime }&={\mathrm e}^{x +y}+x^{2} {\mathrm e}^{y} \\ \end{align*}

[_separable]

2.977

20232

\begin{align*} \left (3+2 \sin \left (x \right )+\cos \left (x \right )\right ) y^{\prime }&=1+2 \sin \left (y\right )+\cos \left (y\right ) \\ \end{align*}

[_separable]

10.851

20233

\begin{align*} \frac {\cos \left (y\right )^{2} y^{\prime }}{x}+\frac {\cos \left (x \right )^{2}}{y}&=0 \\ \end{align*}

[_separable]

7.509

20234

\begin{align*} \left ({\mathrm e}^{x}+1\right ) y y^{\prime }&=\left (1+y\right ) {\mathrm e}^{x} \\ \end{align*}

[_separable]

7.845

20235

\begin{align*} \csc \left (x \right ) \ln \left (y\right ) y^{\prime }+y^{2} x^{2}&=0 \\ \end{align*}

[_separable]

10.545

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]

1.207

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]

38.473

20238

\begin{align*} y^{2}+x y^{2}+\left (x^{2}-x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

9.760

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]

7.102

20240

\begin{align*} 3 \,{\mathrm e}^{x} \tan \left (y\right )+\left (1-{\mathrm e}^{x}\right ) \sec \left (y\right )^{2} y^{\prime }&=0 \\ \end{align*}

[_separable]

5.382

20241

\begin{align*} y-y^{\prime } x&=a \left (y^{\prime }+y^{2}\right ) \\ \end{align*}

[_separable]

8.698

20282

\begin{align*} x +y^{\prime }&=x \,{\mathrm e}^{\left (n -1\right ) y} \\ \end{align*}

[_separable]

7.287

20311

\begin{align*} y^{\prime }&={\mathrm e}^{3 x -2 y}+x^{2} {\mathrm e}^{-2 y} \\ \end{align*}

[_separable]

3.293

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]

6.983

20317

\begin{align*} s^{\prime }+x^{2}&=x^{2} {\mathrm e}^{3 s} \\ \end{align*}

[_separable]

6.287

20398

\begin{align*} y&=3 x +a \ln \left (y^{\prime }\right ) \\ \end{align*}

[_separable]

16.523

20410

\begin{align*} x&=y+a \ln \left (y^{\prime }\right ) \\ \end{align*}

[_separable]

16.099

20481

\begin{align*} y-y^{\prime } x&=a \left (y^{\prime }+y^{2}\right ) \\ \end{align*}

[_separable]

10.588

20482

\begin{align*} y-y^{\prime } x&=b \left (1+x^{2} y^{\prime }\right ) \\ \end{align*}

[_separable]

5.342

20677

\begin{align*} y-y^{\prime } x&=0 \\ \end{align*}

[_separable]

4.523

20678

\begin{align*} \cot \left (y\right )-\tan \left (x \right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

3.773

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]

25.779

20682

\begin{align*} 1+y^{2}-y y^{\prime } x&=0 \\ \end{align*}

[_separable]

14.004

20728

\begin{align*} x y \left (y-y^{\prime } x \right )&=x +y y^{\prime } \\ \end{align*}

[_separable]

13.405

20811

\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{x}}{2 y} \\ \end{align*}

[_separable]

7.244

20812

\begin{align*} y^{\prime }&=y^{2} \left (t^{2}+1\right ) \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

5.754

20813

\begin{align*} y^{\prime }&=\frac {\sqrt {1-y^{2}}}{x} \\ \end{align*}

[_separable]

13.408

20814

\begin{align*} y^{\prime } x&=y \left (1-2 y\right ) \\ y \left (1\right ) &= 2 \\ \end{align*}

[_separable]

11.857

20815

\begin{align*} y^{\prime }-\sin \left (x \right ) y&=\sin \left (x \right ) \\ \end{align*}

[_separable]

5.350

20817

\begin{align*} s^{\prime }+2 s&=s t^{2} \\ s \left (0\right ) &= 1 \\ \end{align*}

[_separable]

9.768

20826

\begin{align*} y^{\prime }&=\frac {x}{y}-\frac {x}{1+y} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

5.587

20829

\begin{align*} y^{\prime }+2 y x&=2 x y^{2} \\ \end{align*}

[_separable]

10.287

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]

8.453

20970

\begin{align*} y^{\prime }&=\frac {y \ln \left (y\right )}{\sin \left (x \right )} \\ y \left (\frac {\pi }{2}\right ) &= {\mathrm e}^{{\mathrm e}} \\ \end{align*}

[_separable]

15.673

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]

5.407

20973

\begin{align*} y^{\prime }&=\frac {2 y \left (-1+y\right )}{x \left (2-y\right )} \\ \end{align*}

[_separable]

40.477

20975

\begin{align*} y^{\prime }&=f \left (x \right ) y \ln \left (\frac {1}{y}\right ) \\ \end{align*}

[_separable]

7.904

20983

\begin{align*} y&=y^{\prime } x +a y^{\prime }+b \\ \end{align*}

[_separable]

7.026

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]

26.377

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]

2.628

21009

\begin{align*} x^{\prime }+\frac {x}{t^{2}-1}&=0 \\ x \left (-2\right ) &= 1 \\ \end{align*}

[_separable]

2.157

21013

\begin{align*} x^{\prime }&=2 t x \\ x \left (0\right ) &= 4 \\ \end{align*}

[_separable]

2.033

21014

\begin{align*} x^{\prime }&=-t^{2} x \\ \end{align*}

[_separable]

1.934

21024

\begin{align*} x^{\prime }&=\frac {x}{t^{2}+1} \\ x \left (0\right ) &= 1 \\ \end{align*}

[_separable]

1.835

21031

\begin{align*} x^{\prime }+\frac {\sin \left (t \right ) x}{1+{\mathrm e}^{t}}&=0 \\ \end{align*}

[_separable]

2.763

21054

\begin{align*} x^{\prime }&=4 t^{3} x^{4} \\ \end{align*}

[_separable]

3.830

21055

\begin{align*} x^{\prime }&=-t x^{2} \\ \end{align*}

[_separable]

3.619

21056

\begin{align*} x^{\prime }&={\mathrm e}^{t} \left (x^{2}+1\right ) \\ x \left (0\right ) &= 0 \\ \end{align*}

[_separable]

3.679

21057

\begin{align*} x^{\prime }&=\frac {t}{x} \\ x \left (\sqrt {2}\right ) &= 1 \\ \end{align*}

[_separable]

4.950

21058

\begin{align*} x^{\prime }&=-\frac {t}{4 x^{3}} \\ x \left (1\right ) &= 1 \\ \end{align*}

[_separable]

2.857

21059

\begin{align*} x^{\prime }&=-t^{2} x^{2} \\ x \left (1\right ) &= 2 \\ \end{align*}

[_separable]

5.363

21060

\begin{align*} x^{\prime }&=5 t \sqrt {x} \\ x \left (0\right ) &= 1 \\ \end{align*}

[_separable]

6.955

21061

\begin{align*} x^{\prime }&=4 t^{3} \sqrt {x} \\ x \left (0\right ) &= 1 \\ \end{align*}

[_separable]

7.319

21062

\begin{align*} x^{\prime }&=2 t \sqrt {x} \\ x \left (a \right ) &= 0 \\ \end{align*}

[_separable]

10.878

21063

\begin{align*} x^{\prime }&=-\left (1+p \right ) t^{p} x^{2} \\ \end{align*}

[_separable]

2.820

21065

\begin{align*} 2 x^{2}+1&=\left (y^{5}-1\right ) y^{\prime } \\ \end{align*}

[_separable]

1.892

21075

\begin{align*} x -2 y^{3} y^{\prime }&=0 \\ \end{align*}

[_separable]

2.715

21083

\begin{align*} y y^{\prime } x +1+y^{2}&=0 \\ \end{align*}

[_separable]

3.211

21092

\begin{align*} x^{\prime }+2 t x&=-4 t x^{3} \\ \end{align*}

[_separable]

6.986

21333

\begin{align*} y^{\prime }&=f \left (x \right ) g \left (y\right ) \\ \end{align*}

[_separable]

1.535

21334

\begin{align*} -y+y^{\prime } x&=0 \\ \end{align*}

[_separable]

1.908

21336

\begin{align*} x +y y^{\prime }&=0 \\ \end{align*}

[_separable]

5.806

21337

\begin{align*} y^{\prime } x +y&=0 \\ \end{align*}

[_separable]

2.495

21338

\begin{align*} y^{\prime } x -2 y&=0 \\ \end{align*}

[_separable]

2.763

21340

\begin{align*} 2 x \left (1+y\right )-y y^{\prime }&=0 \\ y \left (0\right ) &= -2 \\ \end{align*}

[_separable]

3.350

21341

\begin{align*} y^{\prime }&=-\frac {x}{y} \\ \end{align*}

[_separable]

4.628

21342

\begin{align*} y^{\prime }&=\frac {2 y}{x} \\ \end{align*}

[_separable]

2.462

21343

\begin{align*} -2+2 y+x^{2} \sin \left (y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

3.073

21344

\begin{align*} y^{\prime }&=\frac {x +1}{1+y^{2}} \\ \end{align*}

[_separable]

1.681

21345

\begin{align*} y^{\prime }&=\frac {a x +b}{y^{n}+d} \\ \end{align*}

[_separable]

2.234

21346

\begin{align*} y^{\prime }&=-\frac {x}{y} \\ y \left (0\right ) &= a_{0} \\ \end{align*}

[_separable]

7.181

21347

\begin{align*} y^{\prime }&=x^{2} y \\ \end{align*}

[_separable]

2.243

21348

\begin{align*} y^{\prime }&=\frac {1+y^{2}}{x^{2}+1} \\ \end{align*}

[_separable]

3.829

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]

2.964

21350

\begin{align*} y^{\prime }&=\frac {x}{y^{3}} \\ \end{align*}

[_separable]

2.619

21351

\begin{align*} y^{\prime }&=\frac {x}{y^{2} \sqrt {x^{2}+1}} \\ \end{align*}

[_separable]

2.270

21352

\begin{align*} y^{\prime }&=2 y x \\ y \left (0\right ) &= 5 \\ \end{align*}

[_separable]

2.490

21353

\begin{align*} x y^{2}-x +\left (y+x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

2.683

21354

\begin{align*} y^{\prime }&=x^{2} y^{3} \\ \end{align*}

[_separable]

4.208

21355

\begin{align*} y^{\prime }&=\frac {y \ln \left (x \right )}{x} \\ \end{align*}

[_separable]

2.635

21356

\begin{align*} y^{\prime }&=x^{2} y \\ \end{align*}

[_separable]

2.194

21357

\begin{align*} {\mathrm e}^{x}-y y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

2.074

21371

\begin{align*} \left (x -4\right ) y^{4}-x^{3} \left (y^{2}-3\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

2.241

21372

\begin{align*} 1+y^{2}+\left (x^{2}+1\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

2.659

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]

2.503

21401

\begin{align*} y^{\prime }+2 y x&=0 \\ \end{align*}

[_separable]

2.091

21406

\begin{align*} y^{\prime }&=2 y x -x \\ \end{align*}

[_separable]

1.981

21411

\begin{align*} y-y^{\prime } x&=0 \\ \end{align*}

[_separable]

1.794

21412

\begin{align*} y^{\prime } x -y+y^{2}&=0 \\ \end{align*}

[_separable]

2.396

21427

\begin{align*} \frac {y^{\prime }}{x}-\frac {y}{x^{2}}&=0 \\ \end{align*}

[_separable]

1.813

21432

\begin{align*} y^{\prime }+q \left (x \right ) y&=0 \\ y \left (\textit {x\_0} \right ) &= y_{0} \\ \end{align*}

[_separable]

2.579

21439

\begin{align*} \left (x^{2}+1\right ) y^{\prime }+4 y x&=x \\ y \left (2\right ) &= 1 \\ \end{align*}

[_separable]

2.528

21442

\begin{align*} y^{\prime }-2 y x&=x \\ \end{align*}

[_separable]

1.997

21458

\begin{align*} y^{\prime }+y x&=x y^{2} \\ \end{align*}

[_separable]

3.414

21791

\begin{align*} x +y y^{\prime }&=0 \\ \end{align*}

[_separable]

5.795

21795

\begin{align*} y^{\prime }&=-\frac {x}{4 y} \\ \end{align*}

[_separable]

5.020

21796

\begin{align*} y^{\prime }&=\frac {x}{y} \\ \end{align*}

[_separable]

6.108

21797

\begin{align*} 3 x^{2}-2 y^{3} y^{\prime }&=0 \\ \end{align*}

[_separable]

3.527

21798

\begin{align*} 1+y+y^{2}+x \left (x^{2}-4\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

4.289

21799

\begin{align*} r^{\prime } \sin \left (t \right )+r \cos \left (t \right )&=0 \\ \end{align*}

[_separable]

3.064

21801

\begin{align*} x +y y^{\prime }&=0 \\ y \left (1\right ) &= 2 \\ \end{align*}

[_separable]

5.650

21802

\begin{align*} r^{\prime }&=r \tan \left (t \right ) \\ r \left (0\right ) &= 1 \\ \end{align*}

[_separable]

4.310

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]

25.365

21821

\begin{align*} x^{3} y^{\prime }-x^{2} y&=y x^{5} \\ \end{align*}

[_separable]

2.600

21842

\begin{align*} -y+y^{\prime } x&=y^{3} \\ \end{align*}

[_separable]

6.891

21843

\begin{align*} y^{\prime }+3 x^{2} y&=3 x^{2} \\ \end{align*}

[_separable]

2.539

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]

3.131

21926

\begin{align*} x^{2} y^{\prime }+y^{2}&=x^{2} y y^{\prime }-x y^{2} \\ \end{align*}

[_separable]

4.970

21965

\begin{align*} y^{\prime }+2 x y^{2}&=0 \\ \end{align*}

[_separable]

5.020

21977

\begin{align*} y^{\prime }&=\frac {y^{2}}{x} \\ \end{align*}

[_separable]

2.520

21980

\begin{align*} \sin \left (x \right )+y^{2} y^{\prime }&=0 \\ \end{align*}

[_separable]

2.538

21986

\begin{align*} y^{\prime }&=y x \\ \end{align*}

[_separable]

2.562

21988

\begin{align*} y^{\prime }&=\frac {x^{2}}{y^{2}} \\ \end{align*}

[_separable]

6.586

21989

\begin{align*} y^{\prime }&=-\frac {2 y}{x} \\ \end{align*}

[_separable]

3.557

21991

\begin{align*} x -y^{2} y^{\prime }&=0 \\ \end{align*}

[_separable]

3.705

21992

\begin{align*} y^{\prime }&=x^{3} y^{2} \\ \end{align*}

[_separable]

5.600

21994

\begin{align*} y^{\prime }&=\frac {x +1}{1+y^{4}} \\ \end{align*}

[_separable]

2.027

21995

\begin{align*} {\mathrm e}^{x}-y y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

3.014

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]

3.168

21997

\begin{align*} x +y y^{\prime }&=0 \\ \end{align*}

[_separable]

5.855

21998

\begin{align*} \frac {1}{x}-\frac {y^{\prime }}{y}&=0 \\ \end{align*}

[_separable]

2.516

22000

\begin{align*} x +\frac {y^{\prime }}{y}&=0 \\ \end{align*}

[_separable]

3.679

22001

\begin{align*} x^{2}+1+\left (y^{2}+y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

2.231

22002

\begin{align*} \sin \left (x \right )+y y^{\prime }&=0 \\ y \left (0\right ) &= -2 \\ \end{align*}

[_separable]

4.493

22003

\begin{align*} x^{2}+1+\frac {y^{\prime }}{y}&=0 \\ y \left (-1\right ) &= 1 \\ \end{align*}

[_separable]

3.424

22004

\begin{align*} x \,{\mathrm e}^{x}+\left (y^{5}-1\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

2.475

22005

\begin{align*} y^{\prime }&=\frac {y}{x} \\ \end{align*}

[_separable]

2.212

22006

\begin{align*} y^{\prime }&=\frac {x \,{\mathrm e}^{x}}{2 y} \\ \end{align*}

[_separable]

2.181

22007

\begin{align*} y^{\prime }&=\frac {x^{2} y-y}{1+y} \\ y \left (3\right ) &= -1 \\ \end{align*}

[_separable]

3.753

22011

\begin{align*} y^{\prime }&=y x \\ y \left (1\right ) &= -2 \\ \end{align*}

[_separable]

2.864

22022

\begin{align*} \left (x^{2}+1\right ) y^{\prime }+2 y x&=0 \\ \end{align*}

[_separable]

1.892

22026

\begin{align*} y^{\prime }&=-\frac {2 x y}{x^{2}+1} \\ y \left (2\right ) &= -5 \\ \end{align*}

[_separable]

3.053

22032

\begin{align*} y^{\prime } x +y&=0 \\ \end{align*}

[_separable]

3.137

22034

\begin{align*} \sin \left (x \right ) y+y \cos \left (x \right ) x +\left (x \sin \left (x \right )+1\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

14.796

22035

\begin{align*} y-y^{\prime } x&=0 \\ \end{align*}

[_separable]

2.328

22036

\begin{align*} y^{\prime } x -y+y^{2}&=0 \\ \end{align*}

[_separable]

3.200

22039

\begin{align*} y^{\prime }&=2 y x -x \\ \end{align*}

[_separable]

2.522

22042

\begin{align*} y+1-y^{\prime } x&=0 \\ \end{align*}

[_separable]

2.933

22043

\begin{align*} \left (1-x \right ) y^{\prime }+y&=0 \\ \end{align*}

[_separable]

3.018

22047

\begin{align*} 3 x^{2} y-x^{2}+y^{\prime }&=0 \\ \end{align*}

[_separable]

2.668

22048

\begin{align*} 1-2 y y^{\prime } x&=0 \\ \end{align*}

[_separable]

3.802

22050

\begin{align*} y+3 y^{\prime } x&=0 \\ \end{align*}

[_separable]

3.269

22051

\begin{align*} 2 x y^{2}+\frac {x}{y^{2}}+4 x^{2} y y^{\prime }&=0 \\ \end{align*}

[_separable]

4.922

22058

\begin{align*} y^{\prime }-2 y x&=x \\ \end{align*}

[_separable]

2.477

22063

\begin{align*} y^{\prime }+y x&=x y^{2} \\ \end{align*}

[_separable]

4.342

22068

\begin{align*} y^{\prime }+x^{2} y&=x^{2} \\ \end{align*}

[_separable]

2.654

22070

\begin{align*} y^{\prime }+6 y x&=0 \\ y \left (\pi \right ) &= 5 \\ \end{align*}

[_separable]

4.236

22071

\begin{align*} y^{\prime }-\frac {3 y}{x^{2}}&=\frac {1}{x^{2}} \\ \end{align*}

[_separable]

2.641

22075

\begin{align*} y^{\prime }+y x&=6 x \sqrt {y} \\ \end{align*}

[_separable]

4.917

22087

\begin{align*} y^{\prime }-2 y&=y x \\ \end{align*}

[_separable]

3.026

22090

\begin{align*} y^{\prime }-\frac {2 y}{x}&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

4.510

22091

\begin{align*} y^{\prime }-\frac {2 y}{x}&=0 \\ y \left (1\right ) &= 3 \\ \end{align*}

[_separable]

3.783

22319

\begin{align*} y^{\prime }&=\frac {-x +3}{y+5} \\ \end{align*}

[_separable]

6.559

22326

\begin{align*} y^{\prime }+\tan \left (x \right ) y&=0 \\ y \left (\pi \right ) &= 4 \\ \end{align*}

[_separable]

3.883

22352

\begin{align*} y^{\prime }&=\frac {y}{x} \\ \end{align*}

[_separable]

2.467

22359

\begin{align*} y^{\prime }&=-\frac {x}{y} \\ y \left (1\right ) &= 2 \\ \end{align*}

[_separable]

7.959

22360

\begin{align*} y^{\prime }&=-\frac {y}{x} \\ y \left (1\right ) &= 3 \\ \end{align*}

[_separable]

3.875

22361

\begin{align*} 3 x \left (1+y^{2}\right )+y \left (x^{2}+2\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

3.921

22362

\begin{align*} 2 y+{\mathrm e}^{-3 x} y^{\prime }&=0 \\ \end{align*}

[_separable]

4.362

22363

\begin{align*} y^{\prime }&=\frac {x y^{2}+x}{4 y} \\ y \left (1\right ) &= 0 \\ \end{align*}

[_separable]

3.147

22364

\begin{align*} y^{\prime } x&=1+y^{2} \\ \end{align*}

[_separable]

3.922

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]

3.882

22366

\begin{align*} x \sqrt {1+y^{2}}&=y y^{\prime } \sqrt {x^{2}+1} \\ \end{align*}

[_separable]

4.582

22367

\begin{align*} 2 \cos \left (x \right ) y+3 \sin \left (x \right ) y^{\prime }&=0 \\ y \left (\frac {\pi }{2}\right ) &= 2 \\ \end{align*}

[_separable]

4.414

22368

\begin{align*} y^{\prime }&=8 y x +3 y \\ \end{align*}

[_separable]

3.177

22370

\begin{align*} y+\left (x^{3}+x^{3} y^{2}\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

4.635

22371

\begin{align*} y^{\prime }&=-\frac {3 x +x y^{2}}{x^{2} y+2 y} \\ \end{align*}

[_separable]

3.703

22372

\begin{align*} y^{\prime }&=\frac {\left (-1+y\right ) \left (3+y\right )}{\left (-2+y\right ) \left (x +3\right )} \\ \end{align*}

[_separable]

7.609

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]

6.143

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]

5.283

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]

4.734

22410

\begin{align*} 3 x +4 y y^{\prime }&=0 \\ \end{align*}

[_separable]

8.060

22421

\begin{align*} \left (x^{2}+1\right ) y^{\prime }+2 y x&=0 \\ y \left (1\right ) &= -3 \\ \end{align*}

[_separable]

2.262

22439

\begin{align*} i^{\prime }&=\frac {t -i t}{t^{2}+1} \\ i \left (0\right ) &= 0 \\ \end{align*}

[_separable]

3.373

22508

\begin{align*} \left (x^{2}+1\right ) \left (y^{3}-1\right )&=x^{2} y^{2} y^{\prime } \\ \end{align*}

[_separable]

3.902

22512

\begin{align*} 3-y+2 y^{\prime } x&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}

[_separable]

6.731

22514

\begin{align*} s^{2} t s^{\prime }+t^{2}+4&=0 \\ \end{align*}

[_separable]

3.011

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]

4.625

22543

\begin{align*} \left (1+y\right ) y^{\prime }&=x \sqrt {y} \\ \end{align*}

[_separable]

3.125

22544

\begin{align*} \tan \left (x \right ) \sin \left (y\right )+3 y^{\prime }&=0 \\ \end{align*}

[_separable]

3.721

22548

\begin{align*} x^{2} y+\left (x^{3}+1\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

3.214

22555

\begin{align*} q^{\prime }&=\frac {p \,{\mathrm e}^{p^{2}-q^{2}}}{q} \\ \end{align*}

[_separable]

4.128

22557

\begin{align*} \left (x +x \cos \left (y\right )\right ) y^{\prime }-\sin \left (y\right )-y&=0 \\ \end{align*}

[_separable]

6.272

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]

4.577

22562

\begin{align*} u v-2 v+\left (-u^{2}+u \right ) v^{\prime }&=0 \\ \end{align*}

[_separable]

3.658

22566

\begin{align*} x \sqrt {1-y^{2}}+y \sqrt {-x^{2}+1}\, y^{\prime }&=0 \\ \end{align*}

[_separable]

6.717

22568

\begin{align*} y^{\prime }&=\frac {\left (3+y\right )^{2}}{4 x^{2}} \\ \end{align*}

[_separable]

6.763

22582

\begin{align*} {\mathrm e}^{2 x -y}+{\mathrm e}^{y-2 x} y^{\prime }&=0 \\ \end{align*}

[_separable]

2.941

22586

\begin{align*} y^{\prime } \sqrt {x^{3}+1}&=x^{2} y+x^{2} \\ \end{align*}

[_separable]

5.630

22592

\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{x -y}}{y} \\ \end{align*}

[_separable]

5.122

22594

\begin{align*} y^{\prime } \sqrt {-x^{2}+1}+\sqrt {1-y^{2}}&=0 \\ \end{align*}

[_separable]

20.517

22595

\begin{align*} 1+y^{2}+\left (x^{2}+1\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

4.638

22608

\begin{align*} y^{\prime }&=\frac {y}{x} \\ \end{align*}

[_separable]

2.892

22947

\begin{align*} y y^{\prime }&=x^{2} \\ \end{align*}

[_separable]

6.196

22948

\begin{align*} \left (x +1\right ) y^{\prime }&=1+y \\ \end{align*}

[_separable]

4.312

22949

\begin{align*} 1+y^{2}&=\left (x^{2}+1\right ) y^{\prime } \\ \end{align*}

[_separable]

4.077

22950

\begin{align*} y^{\prime } \sin \left (y\right )&=\sec \left (x \right )^{2} \\ \end{align*}

[_separable]

2.994

22951

\begin{align*} x^{\prime }&=\frac {x}{t} \\ \end{align*}

[_separable]

3.033

22952

\begin{align*} \left (-x^{2}+1\right ) y^{\prime }&=1-y^{2} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

7.132

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]

5.704

22954

\begin{align*} y^{\prime } x&=\left (x +1\right ) y^{2} \\ y \left (1\right ) &= 1 \\ \end{align*}

[_separable]

3.994

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]

4.356

22956

\begin{align*} \left (x^{2}-1\right ) y^{\prime }&=\left (-1+y\right ) x \\ \end{align*}

[_separable]

6.506

22957

\begin{align*} \left (y+2\right ) x +y \left (2+x \right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

9.332

22958

\begin{align*} x y \left (x^{2}+1\right ) y^{\prime }-y^{2}&=1 \\ \end{align*}

[_separable]

9.118

22959

\begin{align*} y^{\prime } x +y&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}

[_separable]

4.791

22960

\begin{align*} y^{\prime } x -1+y&=0 \\ y \left (1\right ) &= 2 \\ \end{align*}

[_separable]

3.287

22962

\begin{align*} x^{2} y^{\prime }+2 y x&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}

[_separable]

5.565

22963

\begin{align*} x \cos \left (y\right ) y^{\prime }+\sin \left (y\right )&=5 \\ \end{align*}

[_separable]

6.904

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]

3.623

22965

\begin{align*} x \sec \left (y\right )^{2} y^{\prime }+1+\tan \left (y\right )&=0 \\ \end{align*}

[_separable]

35.374

22966

\begin{align*} {\mathrm e}^{y} \left (y^{\prime } x +1\right )&=5 \\ \end{align*}

[_separable]

5.783

22977

\begin{align*} y^{\prime }+2 y x&=x \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

4.720

22978

\begin{align*} y^{\prime }-2 y x&=3 x \\ y \left (1\right ) &= 1 \\ \end{align*}

[_separable]

3.343

22986

\begin{align*} y^{\prime }-\sin \left (x \right ) y&=\sin \left (x \right ) \\ y \left (0\right ) &= 2 \\ \end{align*}

[_separable]

4.198

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]

5.703

23056

\begin{align*} \frac {r^{\prime }}{r}&=\tan \left (\theta \right ) \\ \end{align*}

[_separable]

4.086

23057

\begin{align*} \left (1+\cos \left (\theta \right )\right ) r^{\prime }&=-r \sin \left (\theta \right ) \\ \end{align*}

[_separable]

4.885

23058

\begin{align*} \cot \left (\theta \right ) r^{\prime }&=r+b \\ \end{align*}

[_separable]

3.491

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]

5.979

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]

6.147

23127

\begin{align*} x^{\prime }&=\frac {a x^{{5}/{6}}}{\left (-B t +b \right )^{{3}/{2}}} \\ \end{align*}

[_separable]

66.891

23128

\begin{align*} -y+y^{\prime } x&=1 \\ y \left (2\right ) &= 3 \\ \end{align*}

[_separable]

5.163

23130

\begin{align*} y^{\prime } x +y^{2}&=1 \\ y \left (-2\right ) &= 1 \\ \end{align*}

[_separable]

6.678

23132

\begin{align*} y^{\prime }&=y x \\ y \left (1\right ) &= 2 \\ \end{align*}

[_separable]

3.777

23134

\begin{align*} y^{\prime } x +\left (x +1\right ) y&=0 \\ \end{align*}

[_separable]

2.804

23137

\begin{align*} y^{\prime } x +y&=3 \\ \end{align*}

[_separable]

3.145

23142

\begin{align*} y^{\prime }&=x -y x -y+1 \\ \end{align*}

[_separable]

3.782

23143

\begin{align*} \left (x^{2}+4\right ) y^{\prime }+3 y x&=0 \\ \end{align*}

[_separable]

3.533

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]

9.267

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]

6.177

23150

\begin{align*} y^{\prime }&=\frac {\left (a -x \right ) y}{d \,x^{2}+c x +b} \\ \end{align*}

[_separable]

10.445

23151

\begin{align*} y^{\prime } x +y&=3 \\ \end{align*}

[_separable]

3.112

23154

\begin{align*} y^{\prime } x +\left (x +1\right ) y&=0 \\ \end{align*}

[_separable]

2.777

23162

\begin{align*} y^{\prime }-\frac {x}{x^{2}+1}&=-\frac {x y}{x^{2}+1} \\ \end{align*}

[_separable]

3.055

23167

\begin{align*} y^{\prime }-2 y x&=4 x \sqrt {y} \\ \end{align*}

[_separable]

6.477

23171

\begin{align*} y^{\prime } x -\frac {y}{\ln \left (x \right )}&=0 \\ y \left ({\mathrm e}\right ) &= -1 \\ \end{align*}

[_separable]

3.935

23172

\begin{align*} \left (x^{2}+1\right ) y^{\prime }+2 y x&=-2 x \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

3.875

23185

\begin{align*} \cos \left (y\right )+\sin \left (x \right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

3.611

23194

\begin{align*} y-y^{\prime } x&=0 \\ \end{align*}

[_separable]

3.191

23203

\begin{align*} y^{\prime } x +y&=3 \\ \end{align*}

[_separable]

3.237

23256

\begin{align*} 7 y^{\prime }-y x&=0 \\ \end{align*}

[_separable]

4.476

23269

\begin{align*} y^{\prime } x +y&=0 \\ \end{align*}

[_separable]

5.201

23849

\begin{align*} 2 y^{\prime } x +y&=0 \\ \end{align*}

[_separable]

4.990

23850

\begin{align*} \left (x^{2}+1\right ) y y^{\prime }+4&=0 \\ \end{align*}

[_separable]

3.973

23851

\begin{align*} x^{2} y+\left (x +1\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}

[_separable]

5.652

23852

\begin{align*} y x +{\mathrm e}^{x} y^{\prime }&=0 \\ \end{align*}

[_separable]

5.852

23853

\begin{align*} y^{3}+y^{\prime } \sqrt {-x^{2}+1}&=0 \\ \end{align*}

[_separable]

8.241

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]

7.702

23855

\begin{align*} \left (x^{2}-1\right ) y+\left (1+y^{2}\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

4.013

23856

\begin{align*} y x +\ln \left (y\right ) y^{\prime }&=0 \\ y \left (2\right ) &= 1 \\ \end{align*}

[_separable]

4.269

23857

\begin{align*} \left (x^{3}+1\right ) y^{\prime }+x y^{2}&=0 \\ \end{align*}

[_separable]

4.245

23858

\begin{align*} y^{2} \sec \left (x \right )^{2} y^{\prime }+x&=0 \\ \end{align*}

[_separable]

5.068

23919

\begin{align*} y^{\prime }+y x&=x y^{5} \\ \end{align*}

[_separable]

5.466

23941

\begin{align*} y^{\prime }&=x^{2} y \\ \end{align*}

[_separable]

5.217

23948

\begin{align*} x \sqrt {a^{2}+x^{2}}&=y \sqrt {y^{2}-a^{2}}\, y^{\prime } \\ \end{align*}

[_separable]

7.228

23956

\begin{align*} y^{\prime }&=\sin \left (y\right )^{3} \cos \left (x \right )^{2} \\ \end{align*}

[_separable]

5.753

23957

\begin{align*} y x -x&=\left (x y^{2}+x -y^{2}-1\right ) y^{\prime } \\ \end{align*}

[_separable]

3.802

23963

\begin{align*} {\mathrm e}^{2 x +3 y}+{\mathrm e}^{4 x -5 y} y^{\prime }&=0 \\ \end{align*}

[_separable]

4.237

23971

\begin{align*} y^{\prime }-y x&=x \\ \end{align*}

[_separable]

3.964

24120

\begin{align*} \left (1-x \right ) y^{\prime }&=y^{2} \\ \end{align*}

[_separable]

3.944

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]

4.424

24122

\begin{align*} x y^{3}+{\mathrm e}^{x^{2}} y^{\prime }&=0 \\ \end{align*}

[_separable]

7.381

24123

\begin{align*} 2 y-3 y^{\prime } x&=0 \\ \end{align*}

[_separable]

6.232

24124

\begin{align*} m y-n x y^{\prime }&=0 \\ \end{align*}

[_separable]

5.904

24125

\begin{align*} y^{\prime }&=x y^{2} \\ \end{align*}

[_separable]

10.465

24126

\begin{align*} v^{\prime }&=-\frac {v}{p} \\ \end{align*}

[_separable]

5.394

24127

\begin{align*} {\mathrm e}^{2 x} y-\left (4+{\mathrm e}^{2 x}\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

8.824

24128

\begin{align*} 1&=b \left (\cos \left (y\right )+x \sin \left (y\right ) y^{\prime }\right ) \\ \end{align*}

[_separable]

8.256

24129

\begin{align*} y x -\left (2+x \right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

5.400

24130

\begin{align*} x^{2}+y \left (x -1\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

4.312

24131

\begin{align*} y x +x -\left (1+x^{2}+y^{2}+y^{2} x^{2}\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

4.234

24132

\begin{align*} x \cos \left (y\right )^{2}+\tan \left (y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

40.918

24133

\begin{align*} x y^{3}+\left (1+y\right ) {\mathrm e}^{-x} y^{\prime }&=0 \\ \end{align*}

[_separable]

12.542

24134

\begin{align*} \theta ^{\prime }&=z \left (-z^{2}+1\right ) \sec \left (\theta \right )^{2} \\ \end{align*}

[_separable]

3.596

24135

\begin{align*} x^{\prime }&=\sin \left (x\right )^{2} \cos \left (t \right )^{3} \\ \end{align*}

[_separable]

5.402

24136

\begin{align*} y^{\prime } x +y+x y \left (1+y^{\prime }\right )&=0 \\ \end{align*}

[_separable]

6.292

24137

\begin{align*} \cos \left (y\right )&=y^{\prime } x \\ \end{align*}

[_separable]

6.270

24142

\begin{align*} y-\left ({\mathrm e}^{3 x}+1\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

9.616

24143

\begin{align*} y \ln \left (x \right ) \ln \left (y\right )+y^{\prime }&=0 \\ \end{align*}

[_separable]

5.675

24144

\begin{align*} y y^{\prime } x -y^{2}&=1 \\ y \left (2\right ) &= 1 \\ \end{align*}

[_separable]

11.057

24145

\begin{align*} r^{\prime }&=-2 r t \\ r \left (0\right ) &= r_{0} \\ \end{align*}

[_separable]

5.888

24146

\begin{align*} x y^{2}+{\mathrm e}^{x} y^{\prime }&=0 \\ y \left (\infty \right ) &= {\frac {1}{2}} \\ \end{align*}

[_separable]

6.589

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]

8.978

24148

\begin{align*} y^{\prime }&=x \,{\mathrm e}^{-y-x^{2}} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

3.404

24187

\begin{align*} 2 y x -y+\left (x^{2}+x \right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

2.204

24190

\begin{align*} 1+y^{2}+\left (y+x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

3.078

24212

\begin{align*} y \left (1+y^{2}\right )+x \left (-1+y^{2}\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

4.847

24243

\begin{align*} y^{\prime }&=-2 y x +x \\ \end{align*}

[_separable]

1.874

24268

\begin{align*} y^{\prime }&={\mathrm e}^{x +y} \\ \end{align*}

[_separable]

1.431

24271

\begin{align*} x^{2}+1+x^{2} y^{2} y^{\prime }&=0 \\ \end{align*}

[_separable]

1.388

24274

\begin{align*} y^{\prime }-\cos \left (x \right )&=\tan \left (y\right )^{2} \cos \left (x \right ) \\ \end{align*}

[_separable]

2.445

24278

\begin{align*} y^{\prime }&=\sec \left (x \right )^{2} \sec \left (y\right )^{3} \\ \end{align*}

[_separable]

1.889

24281

\begin{align*} y x +\sqrt {x^{2}+1}\, y^{\prime }&=0 \\ \end{align*}

[_separable]

2.064

24286

\begin{align*} x^{\prime }&=\cos \left (x\right ) \cos \left (t \right )^{2} \\ \end{align*}

[_separable]

2.355

24292

\begin{align*} a^{2} \left (y^{\prime }-1\right )&=x^{2} y^{\prime }+y^{2} \\ \end{align*}

[_separable]

2.571

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]

8.159

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]

7.674

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]

7.776

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]

8.174

24337

\begin{align*} -y+y^{\prime } x&=x^{k} y \\ \end{align*}

[_separable]

1.908

24338

\begin{align*} -y+y^{\prime } x&=y \\ \end{align*}

[_separable]

2.167

24909

\begin{align*} y^{\prime } t&=y \\ \end{align*}

[_separable]

2.056

24918

\begin{align*} y^{\prime }&=2 t y \\ \end{align*}

[_separable]

2.325

24920

\begin{align*} \left (1+t \right ) y^{\prime }+y&=0 \\ \end{align*}

[_separable]

2.077

24931

\begin{align*} \left (1+t \right ) y^{\prime }+y&=0 \\ y \left (1\right ) &= -9 \\ \end{align*}

[_separable]

4.257

24940

\begin{align*} y^{\prime }&=-t y \\ \end{align*}

[_separable]

2.249

24942

\begin{align*} y^{\prime }&=t y^{2} \\ \end{align*}

[_separable]

4.684

24943

\begin{align*} y^{\prime }&=\frac {t y}{1+y} \\ \end{align*}

[_separable]

2.677

24952

\begin{align*} y^{\prime } t&=y-2 t y \\ \end{align*}

[_separable]

1.668

24953

\begin{align*} y^{\prime }&=t y^{2}-y^{2}+t -1 \\ \end{align*}

[_separable]

3.263

24956

\begin{align*} {\mathrm e}^{t} y^{\prime }&=y^{3}-y \\ \end{align*}

[_separable]

5.415

24958

\begin{align*} 1-y^{2}-t y y^{\prime }&=0 \\ \end{align*}

[_separable]

9.423

24959

\begin{align*} y^{3} y^{\prime }&=t \\ \end{align*}

[_separable]

3.326

24960

\begin{align*} y^{4} y^{\prime }&=t +2 \\ \end{align*}

[_separable]

2.309

24961

\begin{align*} y^{\prime }&=t y^{2} \\ \end{align*}

[_separable]

3.941

24962

\begin{align*} \tan \left (t \right ) y+y^{\prime }&=\tan \left (t \right ) \\ \end{align*}

[_separable]

2.670

24963

\begin{align*} y^{\prime }&=t^{m} y^{n} \\ \end{align*}

[_separable]

33.399

24967

\begin{align*} t y y^{\prime }+t^{2}+1&=0 \\ \end{align*}

[_separable]

2.072

24968

\begin{align*} y+1+\left (y-1\right ) \left (t^{2}+1\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

4.169

24969

\begin{align*} 2 y y^{\prime }&={\mathrm e}^{t} \\ \end{align*}

[_separable]

2.116

24970

\begin{align*} \left (1-t \right ) y^{\prime }&=y^{2} \\ \end{align*}

[_separable]

2.144

24972

\begin{align*} y^{\prime }&=4 t y^{2} \\ y \left (1\right ) &= 0 \\ \end{align*}

[_separable]

4.397

24973

\begin{align*} y^{\prime }&=\frac {y x +2 y}{x} \\ y \left (1\right ) &= {\mathrm e} \\ \end{align*}

[_separable]

2.508

24974

\begin{align*} 2 t y+y^{\prime }&=0 \\ y \left (0\right ) &= 4 \\ \end{align*}

[_separable]

2.717

24975

\begin{align*} y^{\prime }&=\frac {\cot \left (y\right )}{t} \\ y \left (1\right ) &= \frac {\pi }{4} \\ \end{align*}

[_separable]

5.488

24976

\begin{align*} \frac {\left (u^{2}+1\right ) y^{\prime }}{y}&=u \\ y \left (0\right ) &= 2 \\ \end{align*}

[_separable]

3.194

24977

\begin{align*} t y-\left (t +2\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

2.711

24978

\begin{align*} y^{\prime }&=\frac {1+y^{2}}{t} \\ y \left (1\right ) &= \sqrt {3} \\ \end{align*}

[_separable]

3.358

24987

\begin{align*} t \left (1+t \right ) y^{\prime }&=2+y \\ \end{align*}

[_separable]

2.165

24990

\begin{align*} y \cos \left (t \right )+y^{\prime }&=\cos \left (t \right ) \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

4.091

24997

\begin{align*} y^{\prime } t +2 y \ln \left (t \right )&=4 \ln \left (t \right ) \\ \end{align*}

[_separable]

3.430

25013

\begin{align*} t y+y^{\prime }&=t y^{3} \\ \end{align*}

[_separable]

5.709

25015

\begin{align*} \left (-t^{2}+1\right ) y^{\prime }-t y&=5 t y^{2} \\ \end{align*}

[_separable]

5.266

25038

\begin{align*} y^{\prime }&=t y \\ y \left (1\right ) &= 1 \\ \end{align*}

[_separable]

2.546

25042

\begin{align*} y^{\prime }&=t y \\ y \left (1\right ) &= 1 \\ \end{align*}

[_separable]

2.508

25398

\begin{align*} y^{\prime }&=a \left (t \right ) y \\ \end{align*}

[_separable]

2.657

25430

\begin{align*} y^{\prime }-a \left (t \right ) y&=0 \\ \end{align*}

[_separable]

2.673

25465

\begin{align*} y^{\prime }&=\sin \left (t \right ) y+Q \sin \left (t \right ) \\ \end{align*}

[_separable]

2.615

25466

\begin{align*} y^{\prime }&=\sin \left (t \right ) y \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

3.778

25468

\begin{align*} y^{\prime }&=\frac {y}{1+t} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

3.875

25490

\begin{align*} y^{\prime }&=a \left (t \right ) y \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

3.076

25491

\begin{align*} y^{\prime }&=t y \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

2.681

25492

\begin{align*} y^{\prime }&=t^{m} y^{n} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

12.447

25493

\begin{align*} y^{\prime }&=a \left (t \right ) y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

2.963

25495

\begin{align*} y^{\prime }&=\frac {y}{t} \\ \end{align*}

[_separable]

2.288

25497

\begin{align*} y^{\prime }&=\frac {y^{2}}{t^{2}} \\ \end{align*}

[_separable]

4.963

25498

\begin{align*} y^{\prime }&={\mathrm e}^{y+t} \\ \end{align*}

[_separable]

2.223

25499

\begin{align*} y^{\prime }&=t y+t +y+1 \\ \end{align*}

[_separable]

2.772

25500

\begin{align*} y^{\prime }&=\left (y+4\right ) \cos \left (t \right ) \\ \end{align*}

[_separable]

2.855

25501

\begin{align*} y^{\prime }&={\mathrm e}^{t} y \\ \end{align*}

[_separable]

3.744

25502

\begin{align*} y^{\prime }&=-4 t y \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

5.212

25503

\begin{align*} y^{\prime }&=t y^{3} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

9.428

25504

\begin{align*} \left (1+t \right ) y^{\prime }&=4 y \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

3.414

25656

\begin{align*} y^{2}-1+y^{\prime } x&=0 \\ \end{align*}

[_separable]

4.810

25663

\begin{align*} y^{\prime }&=2 x y^{2} \\ \end{align*}

[_separable]

7.872

25664

\begin{align*} 2 y^{\prime }&=y^{3} \cos \left (x \right ) \\ \end{align*}

[_separable]

4.490

25675

\begin{align*} y^{\prime } x -2 y&=0 \\ \end{align*}

[_separable]

3.817

25676

\begin{align*} y^{\prime }&=-\frac {x}{y} \\ \end{align*}

[_separable]

8.842

25683

\begin{align*} 3 y^{\prime } x +5 y&=10 \\ \end{align*}

[_separable]

4.200

25693

\begin{align*} y^{\prime }+2 x y^{2}&=0 \\ y \left (2\right ) &= {\frac {1}{3}} \\ \end{align*}

[_separable]

7.039

25694

\begin{align*} y^{\prime }+2 x y^{2}&=0 \\ y \left (-2\right ) &= {\frac {1}{2}} \\ \end{align*}

[_separable]

4.507

25695

\begin{align*} y^{\prime }+2 x y^{2}&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

7.667

25696

\begin{align*} y^{\prime }+2 x y^{2}&=0 \\ y \left (\frac {1}{2}\right ) &= -4 \\ \end{align*}

[_separable]

7.635

25706

\begin{align*} y^{\prime } x&=2 y \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

5.533

25709

\begin{align*} y^{\prime } x&=y \\ \end{align*}

[_separable]

2.480

25711

\begin{align*} \left (4-y^{2}\right ) y^{\prime }&=x^{2} \\ \end{align*}

[_separable]

2.269

25712

\begin{align*} \left (y^{3}+1\right ) y^{\prime }&=x^{2} \\ \end{align*}

[_separable]

2.176

25719

\begin{align*} y^{\prime } x&=y \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

3.013

25722

\begin{align*} y y^{\prime }&=3 x \\ y \left (-2\right ) &= 3 \\ \end{align*}

[_separable]

7.742

25732

\begin{align*} y^{\prime }&=x \sqrt {y} \\ y \left (2\right ) &= 1 \\ \end{align*}

[_separable]

13.259

25735

\begin{align*} y^{\prime } x&=2 y \\ \end{align*}

[_separable]

3.905

25736

\begin{align*} y^{\prime } x&=2 y \\ \end{align*}

[_separable]

4.405

25738

\begin{align*} y^{\prime } x&=y \\ \end{align*}

[_separable]

2.526

25743

\begin{align*} 3 y^{\prime } x -2 y&=0 \\ \end{align*}

[_separable]

3.929

25744

\begin{align*} \left (-2+2 y\right ) y^{\prime }&=2 x -1 \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

11.106

25757

\begin{align*} y^{\prime } x +y&=\frac {1}{y^{2}} \\ \end{align*}

[_separable]

6.723

25779

\begin{align*} y^{\prime }&=\cos \left (y\right ) \sin \left (x \right ) \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

6.652

25780

\begin{align*} y^{\prime }&=\cos \left (y\right ) \sin \left (x \right ) \\ y \left (1\right ) &= 0 \\ \end{align*}

[_separable]

2.786

25781

\begin{align*} y^{\prime }&=\cos \left (y\right ) \sin \left (x \right ) \\ y \left (3\right ) &= 3 \\ \end{align*}

[_separable]

3.700

25782

\begin{align*} y^{\prime }&=\cos \left (y\right ) \sin \left (x \right ) \\ y \left (0\right ) &= -{\frac {5}{2}} \\ \end{align*}

[_separable]

6.556

25787

\begin{align*} y y^{\prime }&=-x \\ y \left (1\right ) &= 1 \\ \end{align*}

[_separable]

8.423

25788

\begin{align*} y y^{\prime }&=-x \\ y \left (0\right ) &= 4 \\ \end{align*}

[_separable]

8.062

25793

\begin{align*} y^{\prime }&=x \,{\mathrm e}^{y} \\ y \left (0\right ) &= -2 \\ \end{align*}

[_separable]

3.746

25794

\begin{align*} y^{\prime }&=x \,{\mathrm e}^{y} \\ y \left (1\right ) &= {\frac {5}{2}} \\ \end{align*}

[_separable]

4.852

25819

\begin{align*} y^{\prime } x&=4 y \\ \end{align*}

[_separable]

4.231

25820

\begin{align*} y^{\prime }+2 x y^{2}&=0 \\ \end{align*}

[_separable]

6.050

25821

\begin{align*} y^{\prime }&={\mathrm e}^{3 x +2 y} \\ \end{align*}

[_separable]

2.630

25822

\begin{align*} y \,{\mathrm e}^{x} y^{\prime }&={\mathrm e}^{-y}+{\mathrm e}^{-2 x -y} \\ \end{align*}

[_separable]

4.208

25823

\begin{align*} y^{\prime }&=\frac {y \ln \left (x \right ) x^{2}}{\left (1+y\right )^{2}} \\ \end{align*}

[_separable]

3.431

25824

\begin{align*} y^{\prime }&=\frac {\left (3+2 y\right )^{2}}{\left (5+4 x \right )^{2}} \\ \end{align*}

[_separable]

6.872

25825

\begin{align*} \csc \left (y\right )+\sec \left (x \right )^{2} y^{\prime }&=0 \\ \end{align*}

[_separable]

2.965

25826

\begin{align*} \sin \left (3 x \right )+2 y \cos \left (3 x \right )^{3} y^{\prime }&=0 \\ \end{align*}

[_separable]

6.809

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]

4.638

25828

\begin{align*} x \sqrt {1+y^{2}}&=y y^{\prime } \sqrt {x^{2}+1} \\ \end{align*}

[_separable]

4.875

25830

\begin{align*} y^{\prime }&=\frac {y \left (\cos \left (x \right ) x +\sin \left (x \right )-1\right )}{3 x -3 x \sin \left (x \right )} \\ \end{align*}

[_separable]

8.618

25833

\begin{align*} x +y y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

9.141

25835

\begin{align*} y^{\prime }&=-\frac {2 x y}{x^{2}+1} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

2.276

25836

\begin{align*} y^{\prime }&=-\frac {y}{x -3} \\ y \left (-2\right ) &= 1 \\ \end{align*}

[_separable]

2.982

25837

\begin{align*} 2 y y^{\prime } x -1-y^{2}&=0 \\ y \left (2\right ) &= 3 \\ \end{align*}

[_separable]

5.793

25838

\begin{align*} x^{2} \left (1-y\right ) y^{\prime }+\left (1-x \right ) y&=0 \\ \end{align*}

[_separable]

6.163

25839

\begin{align*} 2 x y \left (4-y^{2}\right )+\left (-1+y\right ) \left (x^{2}+2\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

12.540

25840

\begin{align*} \left (2 x^{2}+1\right ) y y^{\prime }&=2 x \left (1+y^{2}\right ) \\ \end{align*}

[_separable]

6.388

25841

\begin{align*} x^{2} y+\left (x +1\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

3.966

25842

\begin{align*} y^{3}+y^{\prime } \sqrt {-x^{2}+1}&=0 \\ \end{align*}

[_separable]

7.056

25843

\begin{align*} y x -x +\left (y x +y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

3.964

25844

\begin{align*} y^{\prime }+\left (-1+y\right ) \cos \left (x \right )&=0 \\ \end{align*}

[_separable]

3.092

25852

\begin{align*} \sec \left (x \right )^{2} \tan \left (y\right )+\sec \left (y\right )^{2} \tan \left (x \right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

26.049

25855

\begin{align*} 3-2 y+\left (x^{2}-1\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

3.258

25889

\begin{align*} y-y^{\prime } x&=a y^{2}+a y^{\prime } \\ \end{align*}

[_separable]

5.406

25895

\begin{align*} y^{\prime } x +y&=y y^{\prime } x -y x \\ \end{align*}

[_separable]

4.725

25898

\begin{align*} \sin \left (x \right ) \cos \left (y\right )^{2}+\cos \left (x \right )^{2} y^{\prime }&=0 \\ \end{align*}

[_separable]

4.717

26061

\begin{align*} y&=y^{\prime } x +y^{\prime }-1 \\ \end{align*}

[_separable]

3.553

26077

\begin{align*} y^{\prime }&=\left (-1+y\right ) x \\ \end{align*}

[_separable]

3.151

26078

\begin{align*} y^{\prime }&=2 y x \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

4.154

26079

\begin{align*} 2 y y^{\prime } x +1+y^{2}&=0 \\ \end{align*}

[_separable]

5.095

26080

\begin{align*} {\mathrm e}^{3 y} \sin \left (x \right )^{2}+\cos \left (x \right )^{2} y^{\prime }&=0 \\ \end{align*}

[_separable]

4.280

26147

\begin{align*} \left (-x^{2}+1\right ) y^{\prime }+y x&=2 x \\ \end{align*}

[_separable]

6.440

26148

\begin{align*} y y^{\prime }&=-2 x^{3}+x \\ \end{align*}

[_separable]

3.546

26149

\begin{align*} y^{\prime } x&=y \tan \left (\ln \left (y\right )\right ) \\ \end{align*}

[_separable]

13.599

26153

\begin{align*} x +y y^{\prime }&=0 \\ \end{align*}

[_separable]

9.092

26155

\begin{align*} y-y^{\prime } x&=0 \\ \end{align*}

[_separable]

3.096

26160

\begin{align*} y^{\prime }-\tan \left (x \right ) y&=0 \\ \end{align*}

[_separable]

3.727

26162

\begin{align*} y^{\prime }&={\mathrm e}^{x -y} \\ \end{align*}

[_separable]

2.991

26167

\begin{align*} y^{\prime } x +1&={\mathrm e}^{y} \\ \end{align*}

[_separable]

5.948

26175

\begin{align*} y^{\prime }&=\frac {x}{y} \\ \end{align*}

[_separable]

9.940

26189

\begin{align*} y^{\prime }&=\left (-1+y\right ) x \\ \end{align*}

[_separable]

3.227

26194

\begin{align*} y^{\prime }&=\frac {1+y}{x -1} \\ \end{align*}

[_separable]

3.326

26198

\begin{align*} y^{\prime }&=\left (1-y\right ) \left (1-x \right ) \\ \end{align*}

[_separable]

3.678

26202

\begin{align*} y^{\prime }&=\frac {x -1}{y} \\ \end{align*}

[_separable]

6.975

26203

\begin{align*} y^{\prime }&=-\frac {y}{x} \\ \end{align*}

[_separable]

4.215

26204

\begin{align*} y^{\prime }&=\frac {y}{x} \\ y \left (1\right ) &= 1 \\ \end{align*}

[_separable]

3.451

26205

\begin{align*} y^{\prime }&=\frac {y x}{2} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

4.486

26209

\begin{align*} 1+y^{2}+\left (x^{2}+1\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

4.836

26210

\begin{align*} y y^{\prime } x +1+y^{2}&=0 \\ \end{align*}

[_separable]

7.523

26211

\begin{align*} \left (y^{2}+x y^{2}\right ) y^{\prime }+x^{2}-x^{2} y&=0 \\ \end{align*}

[_separable]

3.044

26212

\begin{align*} 1+y^{2}&=y^{\prime } x \\ \end{align*}

[_separable]

5.278

26213

\begin{align*} y y^{\prime } \sqrt {x^{2}+1}+x \sqrt {1+y^{2}}&=0 \\ \end{align*}

[_separable]

5.494

26214

\begin{align*} x \sqrt {1-y^{2}}+y \sqrt {-x^{2}+1}\, y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

9.500

26216

\begin{align*} y \ln \left (y\right )+y^{\prime } x&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}

[_separable]

6.496

26217

\begin{align*} y^{\prime }&=a^{x +y} \\ \end{align*}

[_separable]

4.376

26218

\begin{align*} {\mathrm e}^{y} \left (x^{2}+1\right ) y^{\prime }-2 x \left (1+{\mathrm e}^{y}\right )&=0 \\ \end{align*}

[_separable]

7.685

26219

\begin{align*} \left ({\mathrm e}^{x}+1\right ) y y^{\prime }&={\mathrm e}^{y} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

5.202

26220

\begin{align*} \left (1+y^{2}\right ) {\mathrm e}^{2 x}-\left (1+y^{2}\right ) {\mathrm e}^{y} y^{\prime }-\left (1+y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

5.034

26221

\begin{align*} x y^{2}-y^{2}+x -1+\left (x^{2} y-2 y x +x^{2}+2 y-2 x +2\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

5.013

26226

\begin{align*} 1+y^{2}&=\left (y-\sqrt {1+y^{2}}\right ) \left (x^{2}+1\right )^{{3}/{2}} y^{\prime } \\ \end{align*}

[_separable]

6.713

26235

\begin{align*} y-y^{\prime } x&=a \left (1+x^{2} y^{\prime }\right ) \\ \end{align*}

[_separable]

3.758

26236

\begin{align*} a^{2}+y^{2}+2 x \sqrt {a x -x^{2}}\, y^{\prime }&=0 \\ y \left (a \right ) &= 0 \\ \end{align*}

[_separable]

10.381

26237

\begin{align*} y^{\prime }+\sin \left (\frac {x}{2}+\frac {y}{2}\right )&=\sin \left (\frac {x}{2}-\frac {y}{2}\right ) \\ \end{align*}

[_separable]

11.601

26238

\begin{align*} y^{\prime }&=\frac {y}{x} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

4.319

26248

\begin{align*} x^{2} y^{\prime } \cos \left (y\right )+1&=0 \\ y \left (\infty \right ) &= 2 \pi \\ \end{align*}

[_separable]

4.994

26251

\begin{align*} 2 \left (x^{2}+1\right ) y^{\prime }-\cos \left (2 y\right )^{2}&=0 \\ y \left (-\infty \right ) &= \frac {7 \pi }{2} \\ \end{align*}

[_separable]

3.624

26323

\begin{align*} \frac {x y}{\sqrt {x^{2}+1}}+2 y x -\frac {y}{x}+\left (\sqrt {x^{2}+1}+x^{2}-\ln \left (x \right )\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

32.718

26395

\begin{align*} y^{\prime }+\cos \left (\frac {x}{2}+\frac {y}{2}\right )&=\cos \left (\frac {x}{2}-\frac {y}{2}\right ) \\ \end{align*}

[_separable]

16.443

26404

\begin{align*} \left (x -1\right ) \left (y^{2}-y+1\right )&=\left (1+y\right ) \left (x^{2}+x +1\right ) y^{\prime } \\ \end{align*}

[_separable]

8.388

26857

\begin{align*} y^{\prime }&=\frac {2 x y}{-x^{2}+2} \\ \end{align*}

[_separable]

3.464

26860

\begin{align*} 3 y^{\prime }&=\frac {4 x}{y^{2}} \\ \end{align*}

[_separable]

6.864

26861

\begin{align*} y^{\prime } x +y&=0 \\ \end{align*}

[_separable]

5.436

26863

\begin{align*} {\mathrm e}^{x +y} y^{\prime }&=3 x \\ \end{align*}

[_separable]

3.651

26864

\begin{align*} y^{\prime } x +y&=y^{2} \\ \end{align*}

[_separable]

9.042

26866

\begin{align*} x \sin \left (y\right ) y^{\prime }&=\cos \left (y\right ) \\ \end{align*}

[_separable]

16.908

26867

\begin{align*} \frac {x y^{\prime }}{y}&=\frac {2 y^{2}+1}{x +1} \\ \end{align*}

[_separable]

12.227

26870

\begin{align*} y^{2} y^{\prime } x&=1+y \\ y \left (3 \,{\mathrm e}^{2}\right ) &= 2 \\ \end{align*}

[_separable]

7.562

26871

\begin{align*} y^{\prime }&=3 x^{2} \left (y+2\right ) \\ y \left (2\right ) &= 8 \\ \end{align*}

[_separable]

9.849

26873

\begin{align*} 2 y y^{\prime }&={\mathrm e}^{x -y^{2}} \\ y \left (4\right ) &= -2 \\ \end{align*}

[_separable]

2.684

26874

\begin{align*} y y^{\prime }&=2 x \sec \left (3 y\right ) \\ y \left (\frac {2}{3}\right ) &= \frac {\pi }{3} \\ \end{align*}

[_separable]

6.684

26891

\begin{align*} 4 y^{4}-1+12 x y^{3} y^{\prime }&=0 \\ y \left (1\right ) &= 2 \\ \end{align*}

[_separable]

8.134

26895

\begin{align*} y-y^{\prime } x&=0 \\ \end{align*}

[_separable]

4.026

26896

\begin{align*} y^{\prime }-\frac {y}{x}&=0 \\ \end{align*}

[_separable]

3.877

26901

\begin{align*} y^{\prime }+y x&=x y^{2} \\ \end{align*}

[_separable]

7.901

26904

\begin{align*} y^{\prime }&=\frac {y^{2}}{2 x}-\frac {y}{x}-\frac {4}{x} \\ \end{align*}

[_separable]

17.893

26909

\begin{align*} y^{\prime }&=-\frac {y^{2}}{x}+\frac {2 y}{x} \\ \end{align*}

[_separable]

13.781

26912

\begin{align*} y^{\prime }+\frac {2 y}{x}&=\frac {3 y^{2}}{x} \\ \end{align*}

[_separable]

12.980

27203

\begin{align*} x +y y^{\prime }&=0 \\ \end{align*}

[_separable]

11.609

27204

\begin{align*} y^{\prime } x&=2 y \\ \end{align*}

[_separable]

6.688

27205

\begin{align*} y^{\prime } x +y&=0 \\ \end{align*}

[_separable]

5.592

27207

\begin{align*} \left (1+y^{2}\right ) y^{\prime }+x&=0 \\ \end{align*}

[_separable]

3.595

27208

\begin{align*} y^{\prime }&=\frac {x}{y} \\ \end{align*}

[_separable]

15.268

27211

\begin{align*} x^{2}+y^{2} y^{\prime }&=1 \\ \end{align*}

[_separable]

3.757

27213

\begin{align*} \left (x +1\right ) y^{\prime }+y x&=0 \\ \end{align*}

[_separable]

5.754

27214

\begin{align*} \sqrt {1+y^{2}}&=y y^{\prime } x \\ \end{align*}

[_separable]

14.355

27215

\begin{align*} \left (x^{2}-1\right ) y^{\prime }+2 x y^{2}&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

6.025

27216

\begin{align*} \cot \left (x \right ) y^{\prime }+y&=2 \\ y \left (0\right ) &= -1 \\ \end{align*}

[_separable]

7.447

27218

\begin{align*} y^{\prime } x +y&=y^{2} \\ y \left (1\right ) &= {\frac {1}{2}} \\ \end{align*}

[_separable]

13.109

27219

\begin{align*} 2 x^{2} y y^{\prime }+y^{2}&=2 \\ \end{align*}

[_separable]

8.253

27220

\begin{align*} y^{\prime }-x y^{2}&=2 y x \\ \end{align*}

[_separable]

7.692

27222

\begin{align*} z^{\prime }&=10^{x +z} \\ \end{align*}

[_separable]

5.507

27223

\begin{align*} x x^{\prime }+t&=1 \\ \end{align*}

[_separable]

8.352

27229

\begin{align*} 3 y^{2} y^{\prime }+16 x&=2 x y^{3} \\ y \left (\infty \right ) &= 2 \\ \end{align*}

[_separable]

11.564

27230

\begin{align*} y^{\prime }&=\left (\frac {1+y^{2}}{x^{4}+1}\right )^{{1}/{3}} \\ \end{align*}

[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]

7.974

27399

\begin{align*} y&=y^{\prime } x -y^{\prime }-2 \\ \end{align*}

[_separable]

5.366

27408

\begin{align*} 2 y^{\prime } x +y^{2}&=1 \\ \end{align*}

[_separable]

8.821

27411

\begin{align*} y-y^{\prime }&=y^{\prime } x +y^{2} \\ \end{align*}

[_separable]

11.781

27415

\begin{align*} \left (-x^{2}+1\right ) y^{\prime }+y x&=0 \\ \end{align*}

[_separable]

5.506

27418

\begin{align*} x^{2} y^{\prime }-2 y x&=3 y \\ \end{align*}

[_separable]

7.136

27428

\begin{align*} y^{\prime } x&={\mathrm e}^{y}+2 y^{\prime } \\ \end{align*}

[_separable]

4.285

27430

\begin{align*} y^{\prime }+y x -x y^{3}&=0 \\ \end{align*}

[_separable]

13.983

27435

\begin{align*} \left (-x^{2}+1\right ) y^{\prime }-2 x y^{2}&=y x \\ \end{align*}

[_separable]

13.075

27437

\begin{align*} x y^{2}-x +\left (y x +y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

11.102