2.2.36 Problems 3501 to 3600

Table 2.73: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

time (sec)

3501

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

[_Gegenbauer]

0.493

3502

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

[[_2nd_order, _with_linear_symmetries]]

0.645

3503

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

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

0.561

3504

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

[[_2nd_order, _with_linear_symmetries]]

0.401

3505

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

[[_2nd_order, _with_linear_symmetries]]

0.720

3506

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

[_Lienard]

0.580

3507

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

[[_2nd_order, _exact, _linear, _homogeneous]]

0.333

3508

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

[_Jacobi]

0.807

3509

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

[[_2nd_order, _with_linear_symmetries]]

0.668

3510

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

[[_2nd_order, _with_linear_symmetries]]

0.447

3511

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

[[_Emden, _Fowler]]

0.435

3512

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

[[_Emden, _Fowler]]

0.088

3513

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

[_Laguerre]

0.763

3514

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

[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

0.515

3515

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

[_separable]

1.630

3516

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

[_separable]

1.933

3517

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

[_separable]

2.505

3518

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

[_separable]

1.517

3519

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

[_separable]

1.799

3520

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

[_separable]

1.612

3521

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

[_separable]

1.914

3522

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

[_separable]

2.799

3523

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

[_separable]

2.757

3524

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

[_linear]

1.725

3525

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

[_separable]

2.059

3526

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

[_separable]

2.896

3527

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

[_separable]

2.099

3528

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

[_separable]

3.961

3529

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

[_separable]

2.812

3530

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

[[_linear, ‘class A‘]]

1.325

3531

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

[_linear]

1.739

3532

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

[_linear]

1.585

3533

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

[_linear]

1.974

3534

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

[_linear]

2.053

3535

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

[_linear]

3.814

3536

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

[_linear]

1.256

3537

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

[_linear]

2.390

3538

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

[_linear]

1.387

3539

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

[_linear]

2.338

3540

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

[_linear]

2.069

3541

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

[_linear]

1.363

3542

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

[[_linear, ‘class A‘]]

0.933

3543

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

[_quadrature]

0.280

3544

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

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

3.293

3545

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

[[_homogeneous, ‘class A‘], _rational, _Riccati]

2.575

3546

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

[[_homogeneous, ‘class A‘], _dAlembert]

6.161

3547

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

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

88.767

3548

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

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

8.680

3549

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

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

4.010

3550

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

[[_homogeneous, ‘class A‘], _dAlembert]

4.914

3551

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

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

64.206

3552

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

[[_homogeneous, ‘class A‘]]

5.408

3553

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

[[_homogeneous, ‘class A‘], _rational, _Riccati]

2.231

3554

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

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

8.148

3555

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

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

85.574

3556

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

[[_homogeneous, ‘class A‘], _dAlembert]

3.914

3557

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

[[_homogeneous, ‘class A‘], _dAlembert]

10.397

3558

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

[[_2nd_order, _missing_x]]

1.996

3559

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

[[_2nd_order, _missing_x]]

2.230

3560

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

[[_2nd_order, _missing_x]]

0.862

3561

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

[_quadrature]

1.922

3562

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

[_separable]

2.219

3563

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

[[_2nd_order, _missing_x]]

2.484

3564

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

[[_2nd_order, _missing_x]]

1.990

3565

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

[[_2nd_order, _exact, _linear, _homogeneous]]

1.183

3566

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

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

0.869

3567

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

[[_Emden, _Fowler]]

29.071

3568

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

[[_2nd_order, _with_linear_symmetries]]

1.553

3569

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

[[_2nd_order, _linear, _nonhomogeneous]]

10.994

3570

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

[[_2nd_order, _missing_x]]

42.861

3571

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

[[_2nd_order, _missing_x]]

0.414

3572

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

[[_2nd_order, _missing_x]]

3.574

3573

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

[[_2nd_order, _missing_x]]

0.850

3574

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

[[_2nd_order, _missing_x]]

0.965

3575

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

[[_2nd_order, _exact, _linear, _homogeneous]]

1.232

3576

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

[[_Emden, _Fowler]]

0.860

3577

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

[‘y=_G(x,y’)‘]

2.091

3578

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

[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]]

1.500

3579

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

[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]

1.649

3580

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

[‘y=_G(x,y’)‘]

37.886

3581

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

[_Bernoulli]

42.810

3582

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

[_quadrature]

0.483

3583

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

[_quadrature]

0.395

3584

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

[[_2nd_order, _quadrature]]

1.833

3585

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

[[_2nd_order, _quadrature]]

1.862

3586

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

[_quadrature]

0.493

3587

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

[[_2nd_order, _quadrature]]

5.726

3588

\[ {}y^{\prime \prime \prime } = 6 x \]
i.c.

[[_3rd_order, _quadrature]]

0.174

3589

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

[[_2nd_order, _quadrature]]

1.634

3590

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

[[_2nd_order, _missing_x]]

0.846

3591

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

[[_Emden, _Fowler]]

0.751

3592

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.485

3593

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

[_separable]

1.612

3594

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

[_separable]

1.875

3595

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

[_separable]

2.489

3596

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

[_separable]

1.497

3597

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

[_separable]

1.754

3598

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

[_separable]

1.598

3599

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

[_separable]

1.829

3600

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

[_separable]

2.671