2.2.89 Problems 8801 to 8900

Table 2.179: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

time (sec)

8801

\[ {}y^{\prime \prime }+y^{\prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

2.149

8802

\[ {}y^{\prime \prime }+y^{\prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

2.980

8803

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

[[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]

6.595

8804

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

[_Riccati]

6.290

8805

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

[[_2nd_order, _with_linear_symmetries]]

2.786

8806

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

[[_2nd_order, _with_linear_symmetries]]

2.790

8807

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

[[_2nd_order, _with_linear_symmetries]]

2.795

8808

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

[[_2nd_order, _with_linear_symmetries]]

1.285

8809

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.376

8810

\[ {}y^{\prime \prime }-x y^{\prime }-x y-x^{4}-6 = 0 \]

[[_2nd_order, _linear, _nonhomogeneous]]

1.389

8811

\[ {}y^{\prime \prime }-x y^{\prime }-x y-x^{5}+24 = 0 \]

[[_2nd_order, _linear, _nonhomogeneous]]

1.379

8812

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

[[_2nd_order, _with_linear_symmetries]]

2.893

8813

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

[[_2nd_order, _with_linear_symmetries]]

1.260

8814

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.297

8815

\[ {}y^{\prime \prime }-a x y^{\prime }-b x y-c x = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.658

8816

\[ {}y^{\prime \prime }-a x y^{\prime }-b x y-c \,x^{2} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.666

8817

\[ {}y^{\prime \prime }-a x y^{\prime }-b x y-c \,x^{3} = 0 \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.667

8818

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

[[_2nd_order, _with_linear_symmetries]]

1.033

8819

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.991

8820

\[ {}y^{\prime \prime }-y^{\prime }-x y-x^{2}-1 = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.401

8821

\[ {}y^{\prime \prime }-y^{\prime }-x y-x^{2}-1 = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.397

8822

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

[[_2nd_order, _with_linear_symmetries]]

0.399

8823

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

[[_2nd_order, _with_linear_symmetries]]

0.400

8824

\[ {}y^{\prime \prime }-y^{\prime }-x y-x^{3}+1 = 0 \]

[[_2nd_order, _linear, _nonhomogeneous]]

1.031

8825

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.403

8826

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.406

8827

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.403

8828

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.402

8829

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.404

8830

\[ {}y^{\prime \prime }-8 y^{\prime }-x y-x^{3}+2 = 0 \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.407

8831

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.412

8832

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.079

8833

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

[[_2nd_order, _linear, _nonhomogeneous]]

2.906

8834

\[ {}y^{\prime \prime }-x y-x^{6}+64 = 0 \]

[[_2nd_order, _linear, _nonhomogeneous]]

7.520

8835

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

[[_2nd_order, _with_linear_symmetries]]

1.377

8836

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

[[_2nd_order, _with_linear_symmetries]]

5.676

8837

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

[[_2nd_order, _linear, _nonhomogeneous]]

4.191

8838

\[ {}y^{\prime \prime }-x y-x^{6}-x^{3}+42 = 0 \]

[[_2nd_order, _linear, _nonhomogeneous]]

8.675

8839

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

[[_2nd_order, _with_linear_symmetries]]

2.755

8840

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

[[_2nd_order, _with_linear_symmetries]]

73.569

8841

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

[[_2nd_order, _linear, _nonhomogeneous]]

3.659

8842

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

[[_2nd_order, _linear, _nonhomogeneous]]

8.338

8843

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

[[_2nd_order, _linear, _nonhomogeneous]]

9.227

8844

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

[[_2nd_order, _with_linear_symmetries]]

14.740

8845

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

[[_2nd_order, _with_linear_symmetries]]

333.730

8846

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

[[_2nd_order, _with_linear_symmetries]]

0.721

8847

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

[[_2nd_order, _with_linear_symmetries]]

0.747

8848

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

[[_2nd_order, _with_linear_symmetries]]

2.955

8849

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

[[_2nd_order, _with_linear_symmetries]]

0.847

8850

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

[[_2nd_order, _with_linear_symmetries]]

0.727

8851

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

[[_2nd_order, _with_linear_symmetries]]

0.732

8852

\[ {}y^{\prime \prime }-\frac {y^{\prime }}{x}-x y-x^{2}-\frac {1}{x} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

167.143

8853

\[ {}y^{\prime \prime }-\frac {y^{\prime }}{x}-x^{2} y-x^{3}-\frac {1}{x} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

4.793

8854

\[ {}y^{\prime \prime }-\frac {y^{\prime }}{x}-x^{3} y-x^{4}-\frac {1}{x} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

488.635

8855

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

[[_2nd_order, _with_linear_symmetries]]

0.747

8856

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

[[_2nd_order, _with_linear_symmetries]]

0.767

8857

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

[[_2nd_order, _with_linear_symmetries]]

0.760

8858

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

[[_3rd_order, _with_linear_symmetries]]

0.037

8859

\[ {}y^{\prime \prime }+c y^{\prime }+k y = 0 \]

[[_2nd_order, _missing_x]]

3.228

8860

\[ {}w^{\prime } = -\frac {1}{2}-\frac {\sqrt {1-12 w}}{2} \]
i.c.

[_quadrature]

17.113

8861

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

[[_2nd_order, _linear, _nonhomogeneous]]

2.957

8862

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

[[_2nd_order, _linear, _nonhomogeneous]]

2.834

8863

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

[[_2nd_order, _linear, _nonhomogeneous]]

3.155

8864

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

[[_2nd_order, _linear, _nonhomogeneous]]

2.937

8865

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

[[_2nd_order, _linear, _nonhomogeneous]]

2.887

8866

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

[[_2nd_order, _linear, _nonhomogeneous]]

2.665

8867

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

[[_2nd_order, _linear, _nonhomogeneous]]

2.956

8868

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

[[_2nd_order, _linear, _nonhomogeneous]]

2.664

8869

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

[[_2nd_order, _linear, _nonhomogeneous]]

63.447

8870

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

[[_2nd_order, _linear, _nonhomogeneous]]

75.008

8871

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

[[_2nd_order, _linear, _nonhomogeneous]]

38.453

8872

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

[[_3rd_order, _with_linear_symmetries]]

0.591

8873

\[ {}x^{4} y^{\prime \prime }+x^{3} y^{\prime }-4 x^{2} y = 1 \]

[[_2nd_order, _with_linear_symmetries]]

1.699

8874

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

[[_2nd_order, _with_linear_symmetries]]

1.648

8875

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

[[_2nd_order, _with_linear_symmetries]]

1.208

8876

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

[[_3rd_order, _with_linear_symmetries]]

0.163

8877

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

[[_3rd_order, _with_linear_symmetries]]

4.302

8878

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

[[_high_order, _with_linear_symmetries]]

0.328

8879

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

[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]

0.790

8880

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

[[_2nd_order, _missing_y]]

1843.976

8881

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

[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]

0.425

8882

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

[NONE]

0.118

8883

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

[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]

0.552

8884

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

[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

0.441

8885

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

[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]

0.826

8886

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

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

2.191

8887

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

[[_homogeneous, ‘class D‘]]

3.556

8888

\[ {}4 x^{2} y^{\prime \prime }+y = 8 \sqrt {x}\, \left (1+\ln \left (x \right )\right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.755

8889

\[ {}v v^{\prime } = \frac {2 v^{2}}{r^{3}}+\frac {\lambda r}{3} \]

[_rational, _Bernoulli]

1.716

8890

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

[[_2nd_order, _with_linear_symmetries]]

0.615

8891

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.689

8892

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.712

8893

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.642

8894

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.694

8895

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.679

8896

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.725

8897

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.684

8898

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.660

8899

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.713

8900

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.737