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]

0.659

3502

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

[[_2nd_order, _with_linear_symmetries]]

0.696

3503

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

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

0.622

3504

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

[[_2nd_order, _with_linear_symmetries]]

0.500

3505

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

[[_2nd_order, _with_linear_symmetries]]

0.851

3506

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

[_Lienard]

0.641

3507

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

[[_2nd_order, _exact, _linear, _homogeneous]]

0.419

3508

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

[_Jacobi]

0.936

3509

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

[[_2nd_order, _with_linear_symmetries]]

0.716

3510

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

[[_2nd_order, _with_linear_symmetries]]

0.554

3511

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

[[_Emden, _Fowler]]

0.562

3512

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

[[_Emden, _Fowler]]

0.171

3513

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

[_Laguerre]

0.924

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)]‘]]

0.555

3515

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

[_separable]

1.193

3516

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

[_separable]

1.420

3517

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

[_separable]

2.348

3518

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

[_separable]

1.256

3519

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

[_separable]

1.422

3520

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

[_separable]

1.327

3521

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

[_separable]

1.744

3522

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

[_separable]

2.678

3523

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

[_separable]

3.105

3524

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

[_linear]

1.759

3525

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

[_separable]

2.391

3526

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

[_separable]

2.291

3527

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

[_separable]

1.441

3528

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

[_separable]

3.481

3529

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

[_separable]

2.526

3530

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

[[_linear, ‘class A‘]]

1.088

3531

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

[_linear]

1.599

3532

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

[_linear]

1.462

3533

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

[_linear]

1.678

3534

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

[_linear]

1.840

3535

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

[_linear]

3.730

3536

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

[_linear]

1.392

3537

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

[_linear]

2.471

3538

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

[_linear]

1.302

3539

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

[_linear]

2.328

3540

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

[_linear]

1.897

3541

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

[_linear]

1.147

3542

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

[[_linear, ‘class A‘]]

1.202

3543

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

[_quadrature]

0.336

3544

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

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

2.952

3545

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

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

2.140

3546

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

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

6.512

3547

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

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

145.614

3548

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

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

5.702

3549

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

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

5.645

3550

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

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

3.814

3551

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

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

6.125

3552

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

[[_homogeneous, ‘class A‘]]

4.777

3553

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

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

1.760

3554

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

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

6.901

3555

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

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

3.923

3556

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

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

3.932

3557

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

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

31.187

3558

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

[[_2nd_order, _missing_x]]

1.590

3559

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

[[_2nd_order, _missing_x]]

1.431

3560

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

[[_2nd_order, _missing_x]]

0.361

3561

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

[_quadrature]

1.505

3562

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

[_separable]

1.598

3563

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

[[_2nd_order, _missing_x]]

0.591

3564

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

[[_2nd_order, _missing_x]]

1.601

3565

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

[[_2nd_order, _exact, _linear, _homogeneous]]

1.218

3566

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

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

0.984

3567

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

[[_Emden, _Fowler]]

1.064

3568

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

[[_2nd_order, _with_linear_symmetries]]

1.467

3569

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

[[_2nd_order, _linear, _nonhomogeneous]]

7.378

3570

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

[[_2nd_order, _missing_x]]

0.812

3571

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

[[_2nd_order, _missing_x]]

0.390

3572

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

[[_2nd_order, _missing_x]]

0.535

3573

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

[[_2nd_order, _missing_x]]

0.351

3574

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

[[_2nd_order, _missing_x]]

0.392

3575

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

[[_2nd_order, _exact, _linear, _homogeneous]]

1.290

3576

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

[[_Emden, _Fowler]]

0.998

3577

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

[‘y=_G(x,y’)‘]

2.352

3578

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

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

1.614

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)]‘]]

1.712

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’)‘]

47.456

3581

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

[_Bernoulli]

43.771

3582

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

[_quadrature]

0.379

3583

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

[_quadrature]

0.347

3584

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

[[_2nd_order, _quadrature]]

0.916

3585

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

[[_2nd_order, _quadrature]]

1.076

3586

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

[_quadrature]

0.565

3587

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

[[_2nd_order, _quadrature]]

2.995

3588

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

[[_3rd_order, _quadrature]]

0.206

3589

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

[[_2nd_order, _quadrature]]

1.409

3590

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

[[_2nd_order, _missing_x]]

0.353

3591

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

[[_Emden, _Fowler]]

0.713

3592

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.543

3593

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

[_separable]

1.186

3594

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

[_separable]

1.409

3595

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

[_separable]

2.370

3596

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

[_separable]

1.225

3597

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

[_separable]

1.441

3598

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

[_separable]

1.297

3599

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

[_separable]

1.560

3600

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

[_separable]

2.581