6.36 Problems 3501 to 3600

Table 6.71: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

3501

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

3502

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

3503

\[ {}z y^{\prime \prime }-2 y^{\prime }+9 z^{5} y = 0 \]

3504

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

3505

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

3506

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

3507

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

3508

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

3509

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

3510

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

3511

\[ {}\left (z^{2}+5 z +7\right ) y^{\prime \prime }+2 y = 0 \]

3512

\[ {}y^{\prime \prime }+\frac {y}{z^{3}} = 0 \]

3513

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

3514

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

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

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

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

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

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

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

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

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

3553

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

3554

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

3555

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

3556

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

3557

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

3558

\[ {}y^{\prime \prime }-25 y = 0 \]

3559

\[ {}y^{\prime \prime }+4 y = 0 \]

3560

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

3561

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

3562

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

3563

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 0 \]

3564

\[ {}y^{\prime \prime }-9 y = 0 \]

3565

\[ {}x^{2} y^{\prime \prime }+5 x y^{\prime }+3 y = 0 \]

3566

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

3567

\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+13 y = 0 \]

3568

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

3569

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = x^{4} \sin \left (x \right ) \]

3570

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

3571

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

3572

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

3573

\[ {}y^{\prime \prime }-y^{\prime }-6 y = 0 \]

3574

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 0 \]

3575

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

3576

\[ {}x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = 0 \]

3577

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

3578

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

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

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

3584

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

3585

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

3586

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

3587

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

3588

\[ {}y^{\prime \prime \prime } = 6 x \]

3589

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

3590

\[ {}y^{\prime \prime }+y^{\prime }-6 y = 0 \]

3591

\[ {}x^{2} y^{\prime \prime }-x y^{\prime }-8 y = 0 \]

3592

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

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

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

3599

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

3600

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