2.36 Problems 3501 to 3600

Table 2.36: Main lookup table

#

ODE

Mathematica result

Maple result

3501

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

3502

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

3503

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

3504

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

3505

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

3506

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

3507

\[ {}\left (y^{\prime }\right )^{2}-5 y^{\prime }+6 = 0 \]

3508

\[ {}\left (y^{\prime }\right )^{2}-7 y^{\prime }+12 = 0 \]

3509

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

3510

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

3511

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

3512

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

3513

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

3514

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

3515

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

3516

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

3517

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

3518

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

3519

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

3520

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

3521

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

3522

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

3523

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

3524

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

3525

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

3526

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

3527

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

3528

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

3529

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

3530

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

3531

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

3532

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

3533

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

3534

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

3535

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

3536

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

3537

\[ {}\left (y^{\prime }\right )^{2}+4 x^{5} y^{\prime }-12 x^{4} y = 0 \]

3538

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

3539

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

3540

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

3541

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

3542

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

3543

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

3544

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

3545

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

3546

\[ {}\left (y^{\prime }\right )^{2}-2 \left (1-3 y\right ) y^{\prime }-\left (4-9 y\right ) y = 0 \]

3547

\[ {}\left (y^{\prime }\right )^{2}+\left (a +6 y\right ) y^{\prime }+y \left (3 a +b +9 y\right ) = 0 \]

3548

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

3549

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

3550

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

3551

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

3552

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

3553

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

3554

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

3555

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

3556

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

3557

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

3558

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

3559

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

3560

\[ {}\left (y^{\prime }\right )^{2}-3 x y^{\frac {2}{3}} y^{\prime }+9 y^{\frac {5}{3}} = 0 \]

3561

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

3562

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

3563

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

3564

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

3565

\[ {}2 \left (y^{\prime }\right )^{2}+2 \left (6 y-1\right ) y^{\prime }+3 y \left (6 y-1\right ) = 0 \]

3566

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

3567

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

3568

\[ {}4 \left (y^{\prime }\right )^{2} = 9 x \]

3569

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

3570

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

3571

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

3572

\[ {}5 \left (y^{\prime }\right )^{2}+6 x y^{\prime }-2 y = 0 \]

3573

\[ {}9 \left (y^{\prime }\right )^{2}+3 x y^{4} y^{\prime }+y^{5} = 0 \]

3574

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

3575

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

3576

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

3577

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

3578

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

3579

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

3580

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

3581

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

3582

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

3583

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

3584

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

3585

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

3586

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

3587

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

3588

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

3589

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

3590

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

3591

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

3592

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

3593

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

3594

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

3595

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

3596

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

3597

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

3598

\[ {}x \left (y^{\prime }\right )^{2}-3 y y^{\prime }+9 x^{2} = 0 \]

3599

\[ {}x \left (y^{\prime }\right )^{2}-\left (2 x +3 y\right ) y^{\prime }+6 y = 0 \]

3600

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