4.36 Problems 3501 to 3600

Table 4.71: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

3501

\[ {}2 \left (1+x \right ) y^{\prime }+2 y+\left (1+x \right )^{4} y^{3} = 0 \]

3502

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

3503

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

3504

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

3505

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

3506

\[ {}x^{2} y^{\prime } = a +b x +c \,x^{2}+x y \]

3507

\[ {}x^{2} y^{\prime } = a +b x +c \,x^{2}-x y \]

3508

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

3509

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

3510

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

3511

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

3512

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

3513

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

3514

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

3515

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

3516

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

3517

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

3518

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

3519

\[ {}x^{2} y^{\prime } = a +b \,x^{n}+y^{2} x^{2} \]

3520

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

3521

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

3522

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

3523

\[ {}x^{2} y^{\prime } = a +b \,x^{n}+c \,x^{2} y^{2} \]

3524

\[ {}x^{2} y^{\prime } = a +b x y+c \,x^{2} y^{2} \]

3525

\[ {}x^{2} y^{\prime } = a +b x y+c \,x^{4} y^{2} \]

3526

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

3527

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

3528

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

3529

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

3530

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

3531

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

3532

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

3533

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

3534

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

3535

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

3536

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

3537

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

3538

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

3539

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

3540

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

3541

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

3542

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

3543

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

3544

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

3545

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

3546

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

3547

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

3548

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

3549

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

3550

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

3551

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

3552

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

3553

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

3554

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

3555

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

3556

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

3557

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

3558

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

3559

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

3560

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

3561

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

3562

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

3563

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

3564

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

3565

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

3566

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

3567

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

3568

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

3569

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

3570

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

3571

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

3572

\[ {}x \left (1-x \right ) y^{\prime }+2-3 x y+y = 0 \]

3573

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

3574

\[ {}\left (-2+x \right ) \left (x -3\right ) y^{\prime }+x^{2}-8 y+3 x y = 0 \]

3575

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

3576

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

3577

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

3578

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

3579

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

3580

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

3581

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

3582

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

3583

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

3584

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

3585

\[ {}2 x^{2} y^{\prime }+1+2 x y-y^{2} x^{2} = 0 \]

3586

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

3587

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

3588

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

3589

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

3590

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

3591

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

3592

\[ {}2 \left (x^{2}+x +1\right ) y^{\prime } = 1+8 x^{2}-\left (2 x +1\right ) y \]

3593

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

3594

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

3595

\[ {}\left (b \,x^{2}+a \right ) y^{\prime } = A +B y^{2} \]

3596

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

3597

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

3598

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

3599

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

3600

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