2.2.140 Problems 13901 to 14000

Table 2.281: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

time (sec)

13901

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

[[_2nd_order, _missing_x]]

1.133

13902

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

[[_3rd_order, _missing_x]]

0.107

13903

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

[[_2nd_order, _missing_x]]

0.897

13904

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

[[_high_order, _missing_x]]

0.066

13905

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.386

13906

\[ {}y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+\cot \left (x \right ) y = 0 \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

2.396

13907

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

[[_2nd_order, _with_linear_symmetries]]

1.141

13908

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.517

13909

\[ {}\sin \left (x \right ) y^{\prime \prime }+x y^{\prime }+7 y = 1 \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

1.915

13910

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.835

13911

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

[[_2nd_order, _with_linear_symmetries]]

1.310

13912

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

[[_2nd_order, _with_linear_symmetries]]

0.674

13913

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

[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]]

0.105

13914

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

[[_2nd_order, _exact, _linear, _homogeneous]]

0.948

13915

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

[[_2nd_order, _exact, _linear, _homogeneous]]

1.730

13916

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

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

1.429

13917

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

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

1.900

13918

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

[[_2nd_order, _with_linear_symmetries]]

0.528

13919

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

[[_2nd_order, _with_linear_symmetries]]

0.574

13920

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

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

1.380

13921

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

[[_2nd_order, _with_linear_symmetries]]

0.912

13922

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

[[_2nd_order, _exact, _linear, _homogeneous]]

1.453

13923

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

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

1.122

13924

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

[[_2nd_order, _linear, _nonhomogeneous]]

7.819

13925

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

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

1.010

13926

\[ {}x y^{\prime \prime }+\left (6 x y^{2}+1\right ) y^{\prime }+2 y^{3}+1 = 0 \]

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

2.049

13927

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

[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]]

1.585

13928

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

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

47.347

13929

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

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

1.192

13930

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

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

1.238

13931

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

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

1.244

13932

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

[[_2nd_order, _with_linear_symmetries]]

1.799

13933

\[ {}\left (x^{2}+2 x \right ) y^{\prime \prime }+\left (x^{2}+x +10\right ) y^{\prime } = \left (25-6 x \right ) y \]

[[_2nd_order, _with_linear_symmetries]]

3.320

13934

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

[[_2nd_order, _with_linear_symmetries]]

1.091

13935

\[ {}\left (x^{2}-x \right ) y^{\prime \prime }+\left (2 x^{2}+4 x -3\right ) y^{\prime }+8 x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

1.286

13936

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.296

13937

\[ {}\left (2 \sin \left (x \right )-\cos \left (x \right )\right ) y^{\prime \prime }+\left (7 \sin \left (x \right )+4 \cos \left (x \right )\right ) y^{\prime }+10 y \cos \left (x \right ) = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11.289

13938

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.622

13939

\[ {}y^{\prime \prime }+\left (5+2 x \right ) y^{\prime }+\left (4 x +8\right ) y = {\mathrm e}^{-2 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

1.689

13940

\[ {}y^{\prime \prime }+9 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

0.336

13941

\[ {}4 y^{\prime \prime }-4 y^{\prime }+5 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

0.372

13942

\[ {}y^{\prime \prime }+2 y^{\prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

0.285

13943

\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

0.274

13944

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

[[_2nd_order, _missing_x]]

0.296

13945

\[ {}4 y^{\prime \prime }-4 y^{\prime }+37 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

0.390

13946

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

0.307

13947

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

[[_2nd_order, _missing_x]]

0.342

13948

\[ {}4 y^{\prime \prime }-12 y^{\prime }+13 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

0.335

13949

\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

0.320

13950

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

[[_2nd_order, _missing_x]]

0.198

13951

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

[[_high_order, _missing_x]]

0.661

13952

\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

0.336

13953

\[ {}y^{\prime \prime }-20 y^{\prime }+51 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

0.236

13954

\[ {}2 y^{\prime \prime }+3 y^{\prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

0.229

13955

\[ {}3 y^{\prime \prime }+8 y^{\prime }-3 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

0.230

13956

\[ {}2 y^{\prime \prime }+20 y^{\prime }+51 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

0.318

13957

\[ {}4 y^{\prime \prime }+40 y^{\prime }+101 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

0.277

13958

\[ {}y^{\prime \prime }+6 y^{\prime }+34 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

0.381

13959

\[ {}y^{\prime \prime \prime }+8 y^{\prime \prime }+16 y^{\prime } = 0 \]
i.c.

[[_3rd_order, _missing_x]]

0.327

13960

\[ {}y^{\prime \prime \prime }+6 y^{\prime \prime }+13 y^{\prime } = 0 \]
i.c.

[[_3rd_order, _missing_x]]

0.375

13961

\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+13 y^{\prime } = 0 \]
i.c.

[[_3rd_order, _missing_x]]

0.380

13962

\[ {}y^{\prime \prime \prime }+4 y^{\prime \prime }+29 y^{\prime } = 0 \]
i.c.

[[_3rd_order, _missing_x]]

0.394

13963

\[ {}y^{\prime \prime \prime }+6 y^{\prime \prime }+25 y^{\prime } = 0 \]
i.c.

[[_3rd_order, _missing_x]]

0.395

13964

\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+10 y^{\prime } = 0 \]
i.c.

[[_3rd_order, _missing_x]]

0.389

13965

\[ {}y^{\prime \prime \prime \prime }+13 y^{\prime \prime }+36 y = 0 \]
i.c.

[[_high_order, _missing_x]]

0.477

13966

\[ {}y^{\prime \prime }+2 y^{\prime }+3 y = 9 t \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

0.398

13967

\[ {}4 y^{\prime \prime }+16 y^{\prime }+17 y = 17 t -1 \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

0.357

13968

\[ {}4 y^{\prime \prime }+5 y^{\prime }+4 y = 3 \,{\mathrm e}^{-t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

0.570

13969

\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = t^{2} {\mathrm e}^{2 t} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

0.312

13970

\[ {}y^{\prime \prime }+9 y = {\mathrm e}^{-2 t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

0.384

13971

\[ {}2 y^{\prime \prime }-3 y^{\prime }+17 y = 17 t -1 \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

0.599

13972

\[ {}y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

0.251

13973

\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = t +2 \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

0.410

13974

\[ {}2 y^{\prime }+y = {\mathrm e}^{-\frac {t}{2}} \]
i.c.

[[_linear, ‘class A‘]]

0.382

13975

\[ {}y^{\prime \prime }+8 y^{\prime }+20 y = \sin \left (2 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

0.417

13976

\[ {}4 y^{\prime \prime }-4 y^{\prime }+y = t^{2} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

0.336

13977

\[ {}2 y^{\prime \prime }+y^{\prime }-y = 4 \sin \left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

0.404

13978

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

[[_linear, ‘class A‘]]

0.407

13979

\[ {}3 y^{\prime \prime }+5 y^{\prime }-2 y = 7 \,{\mathrm e}^{-2 t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

0.329

13980

\[ {}y^{\prime }+y = \operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -2\right ) \]
i.c.

[[_linear, ‘class A‘]]

0.563

13981

\[ {}y^{\prime }-2 y = 4 t \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -2\right )\right ) \]
i.c.

[[_linear, ‘class A‘]]

1.189

13982

\[ {}y^{\prime \prime }+9 y = 24 \sin \left (t \right ) \left (\operatorname {Heaviside}\left (t \right )+\operatorname {Heaviside}\left (t -\pi \right )\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

0.725

13983

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.967

13984

\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = 5 \cos \left (t \right ) \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right )\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1.782

13985

\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = 36 t \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -1\right )\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1.177

13986

\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = 39 \operatorname {Heaviside}\left (t \right )-507 \left (t -2\right ) \operatorname {Heaviside}\left (t -2\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1.578

13987

\[ {}y^{\prime \prime }+4 y = 3 \operatorname {Heaviside}\left (t \right )-3 \operatorname {Heaviside}\left (-4+t \right )+\left (2 t -5\right ) \operatorname {Heaviside}\left (-4+t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

0.771

13988

\[ {}4 y^{\prime \prime }+4 y^{\prime }+5 y = 25 t \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right )\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

4.297

13989

\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = \operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -1\right )+\operatorname {Heaviside}\left (t -2\right )-\operatorname {Heaviside}\left (t -3\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

2.216

13990

\[ {}y^{\prime \prime }-2 y^{\prime } = \left \{\begin {array}{cc} 4 & 0\le t <1 \\ 6 & 1\le t \end {array}\right . \]
i.c.

[[_2nd_order, _missing_y]]

0.933

13991

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = \left \{\begin {array}{cc} 0 & 0\le t <1 \\ 1 & 1\le t <2 \\ -1 & 2\le t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1.423

13992

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & 0\le t <2 \\ -1 & 2\le t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

0.925

13993

\[ {}y^{\prime \prime }+y = \left \{\begin {array}{cc} t & 0\le t <\pi \\ -t & \pi \le t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1.041

13994

\[ {}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 8 t & 0\le t <\frac {\pi }{2} \\ 8 \pi & \frac {\pi }{2}\le t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

4.168

13995

\[ {}y^{\prime \prime }+4 \pi ^{2} y = 3 \delta \left (t -\frac {1}{3}\right )-\delta \left (t -1\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

2.791

13996

\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = 3 \delta \left (t -1\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

0.874

13997

\[ {}y^{\prime \prime }+4 y^{\prime }+29 y = 5 \delta \left (t -\pi \right )-5 \delta \left (t -2 \pi \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1.510

13998

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 1-\delta \left (t -1\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

0.783

13999

\[ {}4 y^{\prime \prime }+4 y^{\prime }+y = {\mathrm e}^{-\frac {t}{2}} \delta \left (t -1\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

0.588

14000

\[ {}y^{\prime \prime }-7 y^{\prime }+6 y = \delta \left (t -1\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

0.642