4.1.13 Problems 1201 to 1300

Table 4.25: First order ode

#

ODE

Mathematica

Maple

Sympy

3456

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

3457

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

3458

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

3459

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

3460

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

3461

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

3462

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

3463

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

3464

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

3465

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

3466

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

3467

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

3468

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

3469

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

3470

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

3471

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

3472

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

3473

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

3474

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

3475

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

3476

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

3477

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

3478

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

3479

\[ {} \left (5 x +y-7\right ) y^{\prime } = 3 x +3 y+3 \]

3480

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

3481

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

3482

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

3515

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

3516

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

3517

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

3518

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

3519

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

3520

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

3521

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

3522

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

3523

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

3524

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

3525

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

3526

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

3527

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

3528

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

3529

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

3530

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

3531

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

3532

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

3533

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

3534

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

3535

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

3536

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

3537

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

3538

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

3539

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

3540

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

3541

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

3542

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

3543

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

3544

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

3545

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

3546

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

3547

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

3548

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

3549

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

3550

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

3551

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

3552

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

3553

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

3554

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

3555

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

3556

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

3557

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

3561

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

3562

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

3577

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

3578

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

3579

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

3580

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

3581

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

3582

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

3583

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

3586

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

3593

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

3594

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

3595

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

3596

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

3597

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

3598

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

3599

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

3600

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

3601

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

3602

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

3603

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

3604

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

3605

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

3606

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

3607

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

3608

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

3609

\[ {} m v^{\prime } = m g -k v^{2} \]

3610

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

3611

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

3612

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