2.2.36 Problems 3501 to 3600

Table 2.89: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

Maple

Mma

Sympy

time(sec)

3501

\begin{align*} 4 z y^{\prime \prime }+2 \left (1-z \right ) y^{\prime }-y&=0 \\ \end{align*}

Series expansion around \(z=0\).

[[_2nd_order, _with_linear_symmetries]]

0.900

3502

\begin{align*} z y^{\prime \prime }-2 y^{\prime }+9 z^{5} y&=0 \\ \end{align*}

Series expansion around \(z=0\).

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

0.743

3503

\begin{align*} f^{\prime \prime }+2 \left (z -1\right ) f^{\prime }+4 f&=0 \\ \end{align*}

Series expansion around \(z=0\).

[[_2nd_order, _with_linear_symmetries]]

0.522

3504

\begin{align*} z^{2} y^{\prime \prime }-\frac {3 z y^{\prime }}{2}+\left (z +1\right ) y&=0 \\ \end{align*}

Series expansion around \(z=0\).

[[_2nd_order, _with_linear_symmetries]]

0.944

3505

\begin{align*} z y^{\prime \prime }-2 y^{\prime }+y z&=0 \\ \end{align*}

Series expansion around \(z=0\).

[_Lienard]

0.757

3506

\begin{align*} y^{\prime \prime }-2 z y^{\prime }-2 y&=0 \\ \end{align*}

Series expansion around \(z=0\).

[[_2nd_order, _exact, _linear, _homogeneous]]

0.412

3507

\begin{align*} z \left (1-z \right ) y^{\prime \prime }+\left (1-z \right ) y^{\prime }+\lambda y&=0 \\ \end{align*}

Series expansion around \(z=0\).

[_Jacobi]

1.043

3508

\begin{align*} z y^{\prime \prime }+\left (2 z -3\right ) y^{\prime }+\frac {4 y}{z}&=0 \\ \end{align*}

Series expansion around \(z=0\).

[[_2nd_order, _with_linear_symmetries]]

0.745

3509

\begin{align*} \left (z^{2}+5 z +6\right ) y^{\prime \prime }+2 y&=0 \\ \end{align*}

Series expansion around \(z=0\).

[[_2nd_order, _with_linear_symmetries]]

0.556

3510

\begin{align*} \left (z^{2}+5 z +7\right ) y^{\prime \prime }+2 y&=0 \\ \end{align*}

Series expansion around \(z=0\).

[[_Emden, _Fowler]]

0.553

3511

\begin{align*} y^{\prime \prime }+\frac {y}{z^{3}}&=0 \\ \end{align*}

Series expansion around \(z=0\).

[[_Emden, _Fowler]]

0.114

3512

\begin{align*} z y^{\prime \prime }+\left (1-z \right ) y^{\prime }+\lambda y&=0 \\ \end{align*}

Series expansion around \(z=0\).

[_Laguerre]

0.963

3513

\begin{align*} \left (-z^{2}+1\right ) y^{\prime \prime }-z y^{\prime }+m^{2} y&=0 \\ \end{align*}

Series expansion around \(z=0\).

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

0.603

3514

\begin{align*} y^{\prime }&=2 y x \\ \end{align*}

[_separable]

3.013

3515

\begin{align*} y^{\prime }&=\frac {y^{2}}{x^{2}+1} \\ \end{align*}

[_separable]

2.860

3516

\begin{align*} {\mathrm e}^{x +y} y^{\prime }-1&=0 \\ \end{align*}

[_separable]

3.357

3517

\begin{align*} y^{\prime }&=\frac {y}{x \ln \left (x \right )} \\ \end{align*}

[_separable]

2.940

3518

\begin{align*} y-\left (x -2\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

2.931

3519

\begin{align*} y^{\prime }&=\frac {2 x \left (-1+y\right )}{x^{2}+3} \\ \end{align*}

[_separable]

2.958

3520

\begin{align*} -x y^{\prime }+y&=3-2 x^{2} y^{\prime } \\ \end{align*}

[_separable]

2.977

3521

\begin{align*} y^{\prime }&=\frac {\cos \left (x -y\right )}{\sin \left (x \right ) \sin \left (y\right )}-1 \\ \end{align*}

[_separable]

3.485

3522

\begin{align*} y^{\prime }&=\frac {x \left (y^{2}-1\right )}{2 \left (x -2\right ) \left (x -1\right )} \\ \end{align*}

[_separable]

5.362

3523

\begin{align*} y^{\prime }&=\frac {x^{2} y-32}{-x^{2}+16}+32 \\ \end{align*}

[_linear]

2.459

3524

\begin{align*} \left (x -a \right ) \left (x -b \right ) y^{\prime }-y+c&=0 \\ \end{align*}

[_separable]

4.407

3525

\begin{align*} \left (x^{2}+1\right ) y^{\prime }+y^{2}&=-1 \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

4.089

3526

\begin{align*} \left (-x^{2}+1\right ) y^{\prime }+y x&=a x \\ y \left (0\right ) &= 2 a \\ \end{align*}

[_separable]

2.665

3527

\begin{align*} y^{\prime }&=1-\frac {\sin \left (x +y\right )}{\cos \left (x \right ) \sin \left (y\right )} \\ y \left (\frac {\pi }{4}\right ) &= \frac {\pi }{4} \\ \end{align*}

[_separable]

5.106

3528

\begin{align*} y^{\prime }&=y^{3} \sin \left (x \right ) \\ \end{align*}

[_separable]

5.170

3529

\begin{align*} y^{\prime }-y&={\mathrm e}^{2 x} \\ \end{align*}

[[_linear, ‘class A‘]]

1.750

3530

\begin{align*} x^{2} y^{\prime }-4 y x&=x^{7} \sin \left (x \right ) \\ \end{align*}

[_linear]

2.609

3531

\begin{align*} y^{\prime }+2 y x&=2 x^{3} \\ \end{align*}

[_linear]

2.825

3532

\begin{align*} y^{\prime }+\frac {2 x y}{x^{2}+1}&=4 x \\ \end{align*}

[_linear]

3.014

3533

\begin{align*} y^{\prime }+\frac {2 x y}{x^{2}+1}&=\frac {4}{\left (x^{2}+1\right )^{2}} \\ \end{align*}

[_linear]

3.165

3534

\begin{align*} 2 \cos \left (x \right )^{2} y^{\prime }+y \sin \left (2 x \right )&=4 \cos \left (x \right )^{4} \\ \end{align*}

[_linear]

4.777

3535

\begin{align*} y^{\prime }+\frac {y}{x \ln \left (x \right )}&=9 x^{2} \\ \end{align*}

[_linear]

2.494

3536

\begin{align*} y^{\prime }-y \tan \left (x \right )&=8 \sin \left (x \right )^{3} \\ \end{align*}

[_linear]

3.352

3537

\begin{align*} x^{\prime } t +2 x&=4 \,{\mathrm e}^{t} \\ \end{align*}

[_linear]

2.207

3538

\begin{align*} y^{\prime }&=\sin \left (x \right ) \left (y \sec \left (x \right )-2\right ) \\ \end{align*}

[_linear]

2.928

3539

\begin{align*} 1-y \sin \left (x \right )-\cos \left (x \right ) y^{\prime }&=0 \\ \end{align*}

[_linear]

2.872

3540

\begin{align*} y^{\prime }-\frac {y}{x}&=2 x^{2} \ln \left (x \right ) \\ \end{align*}

[_linear]

2.747

3541

\begin{align*} y^{\prime }+\alpha y&={\mathrm e}^{\beta x} \\ \end{align*}

[[_linear, ‘class A‘]]

2.081

3542

\begin{align*} y^{\prime }+\frac {m}{x}&=\ln \left (x \right ) \\ \end{align*}

[_quadrature]

0.363

3543

\begin{align*} \left (3 x -y\right ) y^{\prime }&=3 y \\ \end{align*}

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

11.626

3544

\begin{align*} y^{\prime }&=\frac {\left (x +y\right )^{2}}{2 x^{2}} \\ \end{align*}

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

5.314

3545

\begin{align*} \sin \left (\frac {y}{x}\right ) \left (x y^{\prime }-y\right )&=x \cos \left (\frac {y}{x}\right ) \\ \end{align*}

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

18.925

3546

\begin{align*} x y^{\prime }&=\sqrt {16 x^{2}-y^{2}}+y \\ \end{align*}

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

29.000

3547

\begin{align*} x y^{\prime }-y&=\sqrt {9 x^{2}+y^{2}} \\ \end{align*}

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

8.997

3548

\begin{align*} x \left (x^{2}-y^{2}\right )-x \left (x^{2}+y^{2}\right ) y^{\prime }&=0 \\ \end{align*}

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

9.711

3549

\begin{align*} x y^{\prime }+y \ln \left (x \right )&=\ln \left (y\right ) y \\ \end{align*}

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

10.879

3550

\begin{align*} y^{\prime }&=\frac {y^{2}+2 y x -2 x^{2}}{x^{2}-y x +y^{2}} \\ \end{align*}

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

1.969

3551

\begin{align*} 2 x y y^{\prime }-2 y^{2}-x^{2} {\mathrm e}^{-\frac {y^{2}}{x^{2}}}&=0 \\ \end{align*}

[[_homogeneous, ‘class A‘]]

6.289

3552

\begin{align*} x^{2} y^{\prime }&=y^{2}+3 y x +x^{2} \\ \end{align*}

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

5.512

3553

\begin{align*} y y^{\prime }&=\sqrt {x^{2}+y^{2}}-x \\ \end{align*}

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

13.547

3554

\begin{align*} 2 x \left (2 x +y\right ) y^{\prime }&=y \left (4 x -y\right ) \\ \end{align*}

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

14.490

3555

\begin{align*} x y^{\prime }&=x \tan \left (\frac {y}{x}\right )+y \\ \end{align*}

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

11.890

3556

\begin{align*} y^{\prime }&=\frac {x \sqrt {x^{2}+y^{2}}+y^{2}}{y x} \\ \end{align*}

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

26.484

3557

\begin{align*} y^{\prime \prime }-25 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

2.396

3558

\begin{align*} 4 y+y^{\prime \prime }&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

1.677

3559

\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.294

3560

\begin{align*} y^{\prime }&=-y^{2} \\ \end{align*}

[_quadrature]

2.285

3561

\begin{align*} y^{\prime }&=\frac {y}{2 x} \\ \end{align*}

[_separable]

3.737

3562

\begin{align*} 5 y+2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.347

3563

\begin{align*} y^{\prime \prime }-9 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

2.059

3564

\begin{align*} x^{2} y^{\prime \prime }+5 x y^{\prime }+3 y&=0 \\ \end{align*}

[[_2nd_order, _exact, _linear, _homogeneous]]

1.987

3565

\begin{align*} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y&=0 \\ \end{align*}

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

1.303

3566

\begin{align*} x^{2} y^{\prime \prime }-3 x y^{\prime }+13 y&=0 \\ \end{align*}

[[_Emden, _Fowler]]

1.896

3567

\begin{align*} 2 x^{2} y^{\prime \prime }-x y^{\prime }+y&=9 x^{2} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

2.598

3568

\begin{align*} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y&=x^{4} \sin \left (x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

7.527

3569

\begin{align*} y^{\prime \prime }-\left (a +b \right ) y^{\prime }+a b y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.516

3570

\begin{align*} y^{\prime \prime }-2 a y^{\prime }+a^{2} y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.358

3571

\begin{align*} y^{\prime \prime }-2 a y^{\prime }+\left (a^{2}+b^{2}\right ) y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.635

3572

\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.285

3573

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.363

3574

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-y&=0 \\ \end{align*}

[[_2nd_order, _exact, _linear, _homogeneous]]

1.799

3575

\begin{align*} x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y&=0 \\ \end{align*}

[[_Emden, _Fowler]]

1.289

3576

\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{x}-\sin \left (y\right )}{x \cos \left (y\right )} \\ \end{align*}

[‘y=_G(x,y’)‘]

3.214

3577

\begin{align*} y^{\prime }&=\frac {1-y^{2}}{2 y x +2} \\ \end{align*}

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

4.129

3578

\begin{align*} y^{\prime }&=\frac {\left (1-y \,{\mathrm e}^{y x}\right ) {\mathrm e}^{-y x}}{x} \\ y \left (1\right ) &= 0 \\ \end{align*}

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

1.840

3579

\begin{align*} 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 )} \\ \end{align*}

[‘y=_G(x,y’)‘]

30.479

3580

\begin{align*} y^{\prime }&=\frac {\cos \left (x \right )-2 x y^{2}}{2 x^{2} y} \\ y \left (\pi \right ) &= \frac {1}{\pi } \\ \end{align*}

[_Bernoulli]

26.490

3581

\begin{align*} y^{\prime }&=\sin \left (x \right ) \\ \end{align*}

[_quadrature]

0.385

3582

\begin{align*} y^{\prime }&=\frac {1}{x^{{2}/{3}}} \\ \end{align*}

[_quadrature]

0.701

3583

\begin{align*} y^{\prime \prime }&=x \,{\mathrm e}^{x} \\ \end{align*}

[[_2nd_order, _quadrature]]

0.938

3584

\begin{align*} y^{\prime \prime }&=x^{n} \\ \end{align*}

[[_2nd_order, _quadrature]]

0.997

3585

\begin{align*} y^{\prime }&=x^{2} \ln \left (x \right ) \\ y \left (1\right ) &= 2 \\ \end{align*}

[_quadrature]

0.606

3586

\begin{align*} y^{\prime \prime }&=\cos \left (x \right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

[[_2nd_order, _quadrature]]

1.218

3587

\begin{align*} y^{\prime \prime \prime }&=6 x \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ y^{\prime \prime }\left (0\right ) &= -4 \\ \end{align*}

[[_3rd_order, _quadrature]]

0.168

3588

\begin{align*} y^{\prime \prime }&=x \,{\mathrm e}^{x} \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*}

[[_2nd_order, _quadrature]]

1.214

3589

\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.298

3590

\begin{align*} x^{2} y^{\prime \prime }-x y^{\prime }-8 y&=0 \\ \end{align*}

[[_Emden, _Fowler]]

0.934

3591

\begin{align*} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y&=x^{2} \ln \left (x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

5.175

3592

\begin{align*} y^{\prime }&=2 y x \\ \end{align*}

[_separable]

3.108

3593

\begin{align*} y^{\prime }&=\frac {y^{2}}{x^{2}+1} \\ \end{align*}

[_separable]

3.056

3594

\begin{align*} {\mathrm e}^{x +y} y^{\prime }-1&=0 \\ \end{align*}

[_separable]

3.372

3595

\begin{align*} y^{\prime }&=\frac {y}{x \ln \left (x \right )} \\ \end{align*}

[_separable]

2.974

3596

\begin{align*} y-\left (x -1\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

3.202

3597

\begin{align*} y^{\prime }&=\frac {2 x \left (-1+y\right )}{x^{2}+3} \\ \end{align*}

[_separable]

3.204

3598

\begin{align*} -x y^{\prime }+y&=3-2 x^{2} y^{\prime } \\ \end{align*}

[_separable]

3.250

3599

\begin{align*} y^{\prime }&=\frac {\cos \left (x -y\right )}{\sin \left (x \right ) \sin \left (y\right )}-1 \\ \end{align*}

[_separable]

3.687

3600

\begin{align*} y^{\prime }&=\frac {x \left (y^{2}-1\right )}{2 \left (x -2\right ) \left (x -1\right )} \\ \end{align*}

[_separable]

5.800