4.1.77 Problems 7601 to 7700

Table 4.153: First order ode

#

ODE

Mathematica

Maple

Sympy

18170

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

18171

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

18172

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

18173

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

18174

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

18175

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

18176

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

18177

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

18178

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

18179

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

18180

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

18181

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

18182

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

18183

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

18184

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

18185

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

18186

\[ {} y^{\prime } = \sqrt {\frac {9 y^{2}-6 y+2}{x^{2}-2 x +5}} \]

18187

\[ {} \left (5 x -7 y+1\right ) y^{\prime }+x +y-1 = 0 \]

18188

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

18189

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

18190

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

18191

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

18192

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

18197

\[ {} {y^{\prime }}^{4} = 1 \]

18212

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

18570

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

18571

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

18572

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

18573

\[ {} 2 x^{\prime }+6 x = t \,{\mathrm e}^{-3 t} \]

18574

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

18587

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

18588

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

18589

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

18590

\[ {} y^{\prime } = \frac {7 x^{2}-1}{7+5 y} \]

18591

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

18592

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

18593

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

18594

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

18595

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

18596

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

18597

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

18598

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

18599

\[ {} y^{\prime } = \left (1-12 x \right ) y^{2} \]

18600

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

18601

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

18602

\[ {} r^{\prime } = \frac {r^{2}}{\theta } \]

18603

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

18604

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

18605

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

18606

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

18607

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

18608

\[ {} y^{\prime } = \frac {x \left (x^{2}+1\right ) y^{5}}{6} \]

18609

\[ {} y^{\prime } = \frac {-{\mathrm e}^{x}+3 x^{2}}{2 y-11} \]

18610

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

18611

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

18612

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

18613

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

18614

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

18615

\[ {} y^{\prime } = \frac {3 x^{2}+1}{12 y^{2}-12 y} \]

18616

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

18617

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

18618

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

18619

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

18620

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

18621

\[ {} y^{\prime } = \frac {t \left (4-y\right ) y}{3} \]

18622

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

18623

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

18624

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

18625

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

18626

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

18627

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

18628

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

18629

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

18630

\[ {} 2 t y+y^{\prime } = 16 t \,{\mathrm e}^{-t^{2}} \]

18631

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

18632

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

18633

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

18634

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

18635

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

18636

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

18637

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

18638

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

18639

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

18640

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

18641

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

18642

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

18643

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

18644

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

18645

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

18646

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

18647

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

18648

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

18649

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

18650

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

18651

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

18652

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

18653

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

18654

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

18655

\[ {} y^{\prime }-6 y = t^{6} {\mathrm e}^{6 t} \]

18656

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