5.9.12 Problems 1101 to 1200

Table 5.651: First order ode linear in derivative

#

ODE

Mathematica

Maple

3411

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

3412

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

3413

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

3416

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

3417

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

3418

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

3419

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

3420

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

3421

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

3422

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

3423

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

3424

\[ {}y^{\prime } = \frac {t}{\sqrt {t}+1} \]

3425

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

3426

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

3427

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

3428

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

3429

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

3430

\[ {}y^{\prime } = 8 \,{\mathrm e}^{4 t}+t \]

3431

\[ {}y^{\prime } = \frac {y}{t} \]

3432

\[ {}y^{\prime } = -\frac {t}{y} \]

3433

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

3434

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

3435

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

3436

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

3437

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

3438

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

3439

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

3440

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

3441

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

3442

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

3443

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

3444

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

3445

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

3446

\[ {}y^{\prime } = \tan \left (t \right ) y+\sec \left (t \right )^{3} \]

3447

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

3448

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

3449

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

3450

\[ {}y^{\prime } = -\tan \left (t \right ) y+\sec \left (t \right ) \]

3451

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

3452

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

3453

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

3454

\[ {}t \ln \left (t \right ) y^{\prime } = t \ln \left (t \right )-y \]

3455

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

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

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

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

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

3465

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

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

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

3476

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

3477

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

3478

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

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

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

3521

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

3522

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

3523

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

3524

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

3525

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

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

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

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

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

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

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