2.16.120 Problems 11901 to 12000

Table 2.256: Main lookup table. Sorted sequentially by problem number.

#

ODE

Program classification

CAS classification

Solved?

Verified?

time (sec)

11901

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

second order series method. Regular singular point. Difference not integer

[[_2nd_order, _with_linear_symmetries]]

3.424

11902

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

second order series method. Regular singular point. Complex roots

[[_2nd_order, _with_linear_symmetries]]

3.46

11903

\[ {}\left (x^{4}-2 x^{3}+x^{2}\right ) y^{\prime \prime }+2 \left (-1+x \right ) y^{\prime }+x^{2} y = 0 \]

second order series method. Irregular singular point

[[_2nd_order, _with_linear_symmetries]]

N/A

2.492

11904

\[ {}\left (x^{5}+x^{4}-6 x^{3}\right ) y^{\prime \prime }+x^{2} y^{\prime }+\left (-2+x \right ) y = 0 \]

second order series method. Irregular singular point

[[_2nd_order, _with_linear_symmetries]]

N/A

2.367

11905

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

second order series method. Regular singular point. Difference not integer

[[_2nd_order, _with_linear_symmetries]]

1.353

11906

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

second order series method. Regular singular point. Difference not integer

[[_2nd_order, _with_linear_symmetries]]

1.316

11907

\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+\left (x^{2}+\frac {8}{9}\right ) y = 0 \]

second order series method. Regular singular point. Difference not integer

[[_2nd_order, _with_linear_symmetries]]

1.349

11908

\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+\left (2 x^{2}+\frac {5}{9}\right ) y = 0 \]

second order series method. Regular singular point. Difference not integer

[[_2nd_order, _with_linear_symmetries]]

1.355

11909

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{9}\right ) y = 0 \]

second order series method. Regular singular point. Difference not integer

[[_2nd_order, _with_linear_symmetries]]

1.317

11910

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

second order series method. Regular singular point. Difference not integer

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

1.344

11911

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

second order series method. Regular singular point. Difference not integer

[[_2nd_order, _with_linear_symmetries]]

1.746

11912

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

second order series method. Regular singular point. Difference is integer

[_Lienard]

1.28

11913

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

second order series method. Regular singular point. Difference is integer

[[_2nd_order, _with_linear_symmetries]]

1.358

11914

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

second order series method. Regular singular point. Difference is integer

[[_2nd_order, _with_linear_symmetries]]

1.565

11915

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

second order series method. Regular singular point. Difference is integer

[_Lienard]

1.503

11916

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

second order series method. Regular singular point. Difference is integer

[[_2nd_order, _with_linear_symmetries]]

1.303

11917

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

second order series method. Regular singular point. Difference is integer

[[_2nd_order, _with_linear_symmetries]]

1.867

11918

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

second order series method. Regular singular point. Difference is integer

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

1.119

11919

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

second order series method. Regular singular point. Difference is integer

[[_2nd_order, _with_linear_symmetries]]

3.758

11920

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

second order series method. Regular singular point. Difference is integer

[[_2nd_order, _with_linear_symmetries]]

3.982

11921

\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+8 \left (x^{2}-1\right ) y = 0 \]

second order series method. Regular singular point. Difference is integer

[[_2nd_order, _with_linear_symmetries]]

3.838

11922

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

second order series method. Regular singular point. Difference is integer

[[_2nd_order, _with_linear_symmetries]]

4.026

11923

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

second order series method. Regular singular point. Repeated root

[[_Emden, _Fowler]]

1.232

11924

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

second order series method. Regular singular point. Difference is integer

[[_Emden, _Fowler]]

3.831

11925

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

second order series method. Regular singular point. Repeated root

[[_2nd_order, _with_linear_symmetries]]

1.334

11926

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

second order series method. Regular singular point. Difference is integer

[[_2nd_order, _with_linear_symmetries]]

3.7

11927

\[ {}\left [\begin {array}{c} x^{\prime }+y^{\prime }-2 x-4 y={\mathrm e}^{t} \\ x^{\prime }+y^{\prime }-y={\mathrm e}^{4 t} \end {array}\right ] \]

system of linear ODEs

system of linear ODEs

0.43

11928

\[ {}\left [\begin {array}{c} x^{\prime }+y^{\prime }-x=-2 t \\ x^{\prime }+y^{\prime }-3 x-y=t^{2} \end {array}\right ] \]

system of linear ODEs

system of linear ODEs

0.462

11929

\[ {}\left [\begin {array}{c} x^{\prime }+y^{\prime }-x-3 y={\mathrm e}^{t} \\ x^{\prime }+y^{\prime }+x={\mathrm e}^{3 t} \end {array}\right ] \]

system of linear ODEs

system of linear ODEs

0.526

11930

\[ {}\left [\begin {array}{c} x^{\prime }+y^{\prime }-x-2 y=2 \,{\mathrm e}^{t} \\ x^{\prime }+y^{\prime }-3 x-4 y={\mathrm e}^{2 t} \end {array}\right ] \]

system of linear ODEs

system of linear ODEs

0.21

11931

\[ {}\left [\begin {array}{c} 2 x^{\prime }+y^{\prime }-x-y={\mathrm e}^{-t} \\ x^{\prime }+2 x+y^{\prime }+y={\mathrm e}^{t} \end {array}\right ] \]

system of linear ODEs

system of linear ODEs

1.411

11932

\[ {}\left [\begin {array}{c} 2 x^{\prime }+y^{\prime }-3 x-y=t \\ x^{\prime }+y^{\prime }-4 x-y={\mathrm e}^{t} \end {array}\right ] \]

system of linear ODEs

system of linear ODEs

0.979

11933

\[ {}\left [\begin {array}{c} x^{\prime }+y^{\prime }-x-6 y={\mathrm e}^{3 t} \\ x^{\prime }+2 y^{\prime }-2 x-6 y=t \end {array}\right ] \]

system of linear ODEs

system of linear ODEs

1.345

11934

\[ {}\left [\begin {array}{c} x^{\prime }+y^{\prime }-x-3 y=3 t \\ x^{\prime }+2 y^{\prime }-2 x-3 y=1 \end {array}\right ] \]

system of linear ODEs

system of linear ODEs

1.229

11935

\[ {}\left [\begin {array}{c} x^{\prime }+y^{\prime }+2 y=\sin \left (t \right ) \\ x^{\prime }+y^{\prime }-x-y=0 \end {array}\right ] \]

system of linear ODEs

system of linear ODEs

0.807

11936

\[ {}\left [\begin {array}{c} x^{\prime }-y^{\prime }-2 x+4 y=t \\ x^{\prime }+y^{\prime }-x-y=1 \end {array}\right ] \]

system of linear ODEs

system of linear ODEs

1.054

11937

\[ {}\left [\begin {array}{c} 2 x^{\prime }+y^{\prime }+x+5 y=4 t \\ x^{\prime }+y^{\prime }+2 x+2 y=2 \end {array}\right ] \]

system of linear ODEs

system of linear ODEs

0.969

11938

\[ {}\left [\begin {array}{c} x^{\prime }+y^{\prime }-x+5 y=t^{2} \\ x^{\prime }+2 y^{\prime }-2 x+4 y=1+2 t \end {array}\right ] \]

system of linear ODEs

system of linear ODEs

3.727

11939

\[ {}\left [\begin {array}{c} 2 x^{\prime }+y^{\prime }+x+y=t^{2}+4 t \\ x^{\prime }+y^{\prime }+2 x+2 y=2 t^{2}-2 t \end {array}\right ] \]

system of linear ODEs

system of linear ODEs

1.026

11940

\[ {}\left [\begin {array}{c} 3 x^{\prime }+2 y^{\prime }-x+y=-1+t \\ x^{\prime }+y^{\prime }-x=2+t \end {array}\right ] \]

system of linear ODEs

system of linear ODEs

1.704

11941

\[ {}\left [\begin {array}{c} 2 x^{\prime }+4 y^{\prime }+x-y=3 \,{\mathrm e}^{t} \\ x^{\prime }+y^{\prime }+2 x+2 y={\mathrm e}^{t} \end {array}\right ] \]

system of linear ODEs

system of linear ODEs

1.049

11942

\[ {}\left [\begin {array}{c} 2 x^{\prime }+y^{\prime }-x-y=-2 t \\ x^{\prime }+y^{\prime }+x-y=t^{2} \end {array}\right ] \]

system of linear ODEs

system of linear ODEs

0.976

11943

\[ {}\left [\begin {array}{c} 2 x^{\prime }+y^{\prime }-x-y=1 \\ x^{\prime }+y^{\prime }+2 x-y=t \end {array}\right ] \]

system of linear ODEs

system of linear ODEs

0.957

11944

\[ {}\left [\begin {array}{c} x^{\prime }=3 x+4 y \\ y^{\prime }=2 x+y \end {array}\right ] \]

i.c.

system of linear ODEs

system of linear ODEs

0.393

11945

\[ {}\left [\begin {array}{c} x^{\prime }=5 x+3 y \\ y^{\prime }=4 x+y \end {array}\right ] \]

i.c.

system of linear ODEs

system of linear ODEs

0.423

11946

\[ {}\left [\begin {array}{c} x^{\prime }=5 x+2 y+5 t \\ y^{\prime }=3 x+4 y+17 t \end {array}\right ] \]

system of linear ODEs

system of linear ODEs

1.084

11947

\[ {}\left [\begin {array}{c} x^{\prime }=5 x-2 y \\ y^{\prime }=4 x-y \end {array}\right ] \]

system of linear ODEs

system of linear ODEs

0.416

11948

\[ {}\left [\begin {array}{c} x^{\prime }=5 x-y \\ y^{\prime }=3 x+y \end {array}\right ] \]

system of linear ODEs

system of linear ODEs

0.416

11949

\[ {}\left [\begin {array}{c} x^{\prime }=-2 x+7 y \\ y^{\prime }=3 x+2 y \end {array}\right ] \]

i.c.

system of linear ODEs

system of linear ODEs

0.392

11950

\[ {}\left [\begin {array}{c} x^{\prime }=-2 x+y \\ y^{\prime }=7 x+4 y \end {array}\right ] \]

i.c.

system of linear ODEs

system of linear ODEs

0.469

11951

\(\left [\begin {array}{cc} 1 & 2 \\ 3 & 2 \end {array}\right ]\)

Eigenvectors

N/A

N/A

0.167

11952

\(\left [\begin {array}{cc} 3 & 2 \\ 6 & -1 \end {array}\right ]\)

Eigenvectors

N/A

N/A

0.165

11953

\(\left [\begin {array}{cc} 3 & 1 \\ 12 & 2 \end {array}\right ]\)

Eigenvectors

N/A

N/A

0.185

11954

\(\left [\begin {array}{cc} -2 & 7 \\ 3 & 2 \end {array}\right ]\)

Eigenvectors

N/A

N/A

0.173

11955

\(\left [\begin {array}{cc} 3 & 4 \\ 5 & 2 \end {array}\right ]\)

Eigenvectors

N/A

N/A

0.169

11956

\(\left [\begin {array}{cc} 3 & -5 \\ -4 & 2 \end {array}\right ]\)

Eigenvectors

N/A

N/A

0.176

11957

\(\left [\begin {array}{ccc} 1 & 1 & -1 \\ 2 & 3 & -4 \\ 4 & 1 & -4 \end {array}\right ]\)

Eigenvectors

N/A

N/A

0.283

11958

\(\left [\begin {array}{ccc} 1 & -1 & -1 \\ 1 & 3 & 1 \\ -3 & -6 & 6 \end {array}\right ]\)

Eigenvectors

N/A

N/A

0.304

11959

\(\left [\begin {array}{ccc} 1 & -1 & -1 \\ 1 & 3 & 1 \\ -3 & 1 & -1 \end {array}\right ]\)

Eigenvectors

N/A

N/A

0.292

11960

\(\left [\begin {array}{ccc} 1 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 1 \end {array}\right ]\)

Eigenvectors

N/A

N/A

0.251

11961

\(\left [\begin {array}{ccc} 1 & 3 & -6 \\ 0 & 2 & 2 \\ 0 & -1 & 5 \end {array}\right ]\)

Eigenvectors

N/A

N/A

0.264

11962

\(\left [\begin {array}{ccc} -5 & -12 & 6 \\ 1 & 5 & -1 \\ -7 & -10 & 8 \end {array}\right ]\)

Eigenvectors

N/A

N/A

0.285

11963

\(\left [\begin {array}{ccc} -2 & 5 & 5 \\ -1 & 4 & 5 \\ 3 & -3 & 2 \end {array}\right ]\)

Eigenvectors

N/A

N/A

0.296

11964

\(\left [\begin {array}{ccc} -2 & 6 & -18 \\ 12 & -23 & 66 \\ 5 & -10 & 29 \end {array}\right ]\)

Eigenvectors

N/A

N/A

0.299

11965

\[ {}\left [\begin {array}{c} x^{\prime }=x+y-z \\ y^{\prime }=2 x+3 y-4 z \\ z^{\prime }=4 x+y-4 z \end {array}\right ] \]

system of linear ODEs

system of linear ODEs

0.762

11966

\[ {}\left [\begin {array}{c} x^{\prime }=x-y-z \\ y^{\prime }=x+3 y+z \\ z^{\prime }=-3 x-6 y+6 z \end {array}\right ] \]

system of linear ODEs

system of linear ODEs

0.722

11967

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

quadrature

[_quadrature]

0.577

11968

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

quadrature

[_quadrature]

0.266

11969

\[ {}u^{\prime } = 4 \ln \left (t \right ) t \]

quadrature

[_quadrature]

0.192

11970

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

quadrature

[_quadrature]

0.252

11971

\[ {}T^{\prime } = {\mathrm e}^{-t} \sin \left (2 t \right ) \]

quadrature

[_quadrature]

0.674

11972

\[ {}x^{\prime } = \sec \left (t \right )^{2} \]

i.c.

quadrature

[_quadrature]

0.694

11973

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

i.c.

quadrature

[_quadrature]

0.395

11974

\[ {}x^{\prime } = 2 \sin \left (t \right )^{2} \]

i.c.

quadrature

[_quadrature]

0.806

11975

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

i.c.

quadrature

[_quadrature]

0.411

11976

\[ {}x^{\prime } {\mathrm e}^{3 t}+3 x \,{\mathrm e}^{3 t} = {\mathrm e}^{-t} \]

i.c.

exact, linear, first_order_ode_lie_symmetry_lookup

[[_linear, ‘class A‘]]

1.396

11977

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

quadrature

[_quadrature]

0.435

11978

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

quadrature

[_quadrature]

1.095

11979

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

quadrature

[_quadrature]

1.213

11980

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

quadrature

[_quadrature]

2.863

11981

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

quadrature

[_quadrature]

1.005

11982

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

i.c.

exact, linear, separable, first_order_ode_lie_symmetry_lookup

[_separable]

1.519

11983

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

i.c.

exact, riccati, separable, first_order_ode_lie_symmetry_lookup

[_separable]

4.773

11984

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

exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup

[_separable]

1.078

11985

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

quadrature

[_quadrature]

0.176

11986

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

exact, riccati, separable, first_order_ode_lie_symmetry_lookup

[_separable]

1.004

11987

\[ {}x^{\prime }+p x = q \]

quadrature

[_quadrature]

0.811

11988

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

exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup

[_separable]

2.334

11989

\[ {}i^{\prime } = p \left (t \right ) i \]

exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup

[_separable]

1.553

11990

\[ {}x^{\prime } = \lambda x \]

quadrature

[_quadrature]

0.863

11991

\[ {}m v^{\prime } = -m g +k v^{2} \]

quadrature

[_quadrature]

0.623

11992

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

i.c.

quadrature

[_quadrature]

2.006

11993

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

i.c.

quadrature

[_quadrature]

3.913

11994

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

i.c.

exact, linear, differentialType, first_order_ode_lie_symmetry_lookup

[_linear]

N/A

1.396

11995

\[ {}x^{\prime }+x t = 4 t \]

i.c.

exact, linear, separable, first_order_ode_lie_symmetry_lookup

[_separable]

2.01

11996

\[ {}z^{\prime } = z \tan \left (y \right )+\sin \left (y \right ) \]

linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup

[_linear]

1.334

11997

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

i.c.

linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup

[_linear]

1.697

11998

\[ {}x^{\prime }+x \tanh \left (t \right ) = 3 \]

linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup

[_linear]

1.259

11999

\[ {}y^{\prime }+2 y \cot \left (x \right ) = 5 \]

i.c.

linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup

[_linear]

2.536

12000

\[ {}x^{\prime }+5 x = t \]

linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup

[[_linear, ‘class A‘]]

0.875