2.2.260 Problems 25901 to 26000

Table 2.537: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

Maple

Mma

Sympy

time(sec)

25901

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

[[_linear, ‘class A‘]]

3.862

25902

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

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

18.835

25903

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

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

6.392

25904

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

[_linear]

2.717

25905

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

[_linear]

3.124

25906

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

[_linear]

6.613

25907

\begin{align*} y^{\prime \prime }-y^{\prime }-12 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.482

25908

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

[[_2nd_order, _missing_x]]

1.516

25909

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

[[_2nd_order, _missing_x]]

0.338

25910

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

[[_2nd_order, _missing_x]]

0.372

25911

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

[[_2nd_order, _missing_x]]

0.369

25912

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

[[_3rd_order, _missing_x]]

0.073

25913

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

[[_2nd_order, _missing_x]]

0.346

25914

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=0 \\ \end{align*}

[[_3rd_order, _missing_x]]

0.073

25915

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

[[_3rd_order, _missing_x]]

0.079

25916

\begin{align*} y^{\prime \prime \prime \prime }-13 y^{\prime \prime }+36 y&=0 \\ \end{align*}

[[_high_order, _missing_x]]

0.085

25917

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

[[_2nd_order, _missing_x]]

0.415

25918

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

[[_high_order, _missing_x]]

0.094

25919

\begin{align*} y^{\prime \prime \prime \prime }-10 y^{\prime \prime \prime }+24 y^{\prime \prime }+10 y^{\prime }-25 y&=0 \\ \end{align*}

[[_high_order, _missing_x]]

0.086

25920

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

[[_high_order, _missing_x]]

0.063

25921

\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-9 y^{\prime \prime }+8 y^{\prime }-2 y&=0 \\ \end{align*}

[[_high_order, _missing_x]]

0.092

25922

\begin{align*} 4 y^{\left (7\right )}-35 y^{\left (5\right )}-35 y^{\prime \prime \prime \prime }+70 y^{\prime \prime \prime }+154 y^{\prime \prime }+105 y^{\prime }+25 y&=0 \\ \end{align*}

[[_high_order, _missing_x]]

0.116

25923

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

[[_3rd_order, _missing_x]]

0.131

25924

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

[[_2nd_order, _missing_x]]

2.296

25925

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

[[_high_order, _missing_x]]

0.064

25926

\begin{align*} y^{\left (6\right )}+18 y^{\prime \prime \prime \prime }+81 y^{\prime \prime }&=0 \\ \end{align*}

[[_high_order, _missing_x]]

0.109

25927

\begin{align*} y^{\left (5\right )}+3 y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }-4 y^{\prime }-4 y&=0 \\ \end{align*}

[[_high_order, _missing_x]]

0.111

25928

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

[[_3rd_order, _missing_x]]

0.078

25929

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

[[_high_order, _missing_x]]

0.091

25930

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

[[_2nd_order, _missing_x]]

0.605

25931

\begin{align*} y^{\prime \prime }-4 y&=16 x^{2} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.644

25932

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

[[_2nd_order, _missing_y]]

1.306

25933

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

[[_2nd_order, _missing_y]]

1.170

25934

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.693

25935

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

[[_2nd_order, _missing_y]]

1.249

25936

\begin{align*} y^{\prime \prime }-4 y&=8 x^{2} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.513

25937

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

[[_2nd_order, _with_linear_symmetries]]

0.542

25938

\begin{align*} 5 y+4 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-x} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.783

25939

\begin{align*} y^{\prime \prime }-y&=5 \,{\mathrm e}^{x} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.678

25940

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

[[_2nd_order, _with_linear_symmetries]]

0.608

25941

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

[[_2nd_order, _with_linear_symmetries]]

0.592

25942

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.587

25943

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.603

25944

\begin{align*} y^{\prime \prime }+2 y^{\prime }-y&=6 \sin \left (3 x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.645

25945

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.595

25946

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.697

25947

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

[[_3rd_order, _linear, _nonhomogeneous]]

0.237

25948

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.732

25949

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.115

25950

\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=2 \,{\mathrm e}^{2 x}+3 \sin \left (x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.749

25951

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.813

25952

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

[[_3rd_order, _missing_y]]

0.262

25953

\begin{align*} y^{\prime \prime }-9 y&={\mathrm e}^{3 x} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.625

25954

\begin{align*} y^{\prime \prime }+5 y^{\prime }&={\mathrm e}^{x} \\ \end{align*}

[[_2nd_order, _missing_y]]

1.210

25955

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

[[_high_order, _with_linear_symmetries]]

0.205

25956

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

[[_3rd_order, _missing_y]]

0.168

25957

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

[[_3rd_order, _missing_y]]

0.169

25958

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.539

25959

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

[[_2nd_order, _missing_y]]

1.269

25960

\begin{align*} y^{\prime \prime }+16 y&=14 \cos \left (3 x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.629

25961

\begin{align*} y^{\prime \prime }+y&=12 \cos \left (2 x \right )-\sin \left (x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.874

25962

\begin{align*} y^{\prime \prime }+y^{\prime }&=8 \sin \left (4 x \right ) \\ \end{align*}

[[_2nd_order, _missing_y]]

1.296

25963

\begin{align*} y^{\prime \prime }+y&=x^{5}-2 x^{2}+6 \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.546

25964

\begin{align*} y^{\prime \prime }+y^{\prime }&=x^{2}+2 x -6 \\ \end{align*}

[[_2nd_order, _missing_y]]

1.206

25965

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.559

25966

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

[[_3rd_order, _missing_y]]

0.167

25967

\begin{align*} y^{\left (6\right )}+y^{\prime \prime \prime \prime }-y&=4 x^{5}-6 x^{2}+2 \\ \end{align*}

[[_high_order, _linear, _nonhomogeneous]]

0.310

25968

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.678

25969

\begin{align*} y^{\prime \prime }-y^{\prime }&=1 \\ \end{align*}

[[_2nd_order, _missing_x]]

1.424

25970

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

[[_linear, ‘class A‘]]

2.484

25971

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.570

25972

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.790

25973

\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{3 x} \sin \left (3 x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.747

25974

\begin{align*} y^{\prime \prime \prime }+4 y^{\prime \prime }&={\mathrm e}^{-4 x} \\ \end{align*}

[[_3rd_order, _missing_y]]

0.173

25975

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.679

25976

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

[[_2nd_order, _missing_y]]

1.470

25977

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.573

25978

\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=72 x \,{\mathrm e}^{-x} \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.531

25979

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

[[_3rd_order, _linear, _nonhomogeneous]]

0.175

25980

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.540

25981

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.625

25982

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

[[_2nd_order, _with_linear_symmetries]]

0.515

25983

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.884

25984

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.760

25985

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.919

25986

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.710

25987

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.744

25988

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

system_of_ODEs

0.535

25989

\begin{align*} x^{\prime }+y^{\prime }-x&=0 \\ x^{\prime }+2 y^{\prime }&=4 \,{\mathrm e}^{t} \\ \end{align*}

system_of_ODEs

0.698

25990

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

system_of_ODEs

0.494

25991

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

system_of_ODEs

0.484

25992

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

system_of_ODEs

0.299

25993

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

system_of_ODEs

0.049

25994

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

system_of_ODEs

0.734

25995

\begin{align*} -y+y^{\prime }&={\mathrm e}^{3 t} \\ y \left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

[[_linear, ‘class A‘]]

0.467

25996

\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}
Using Laplace transform method.

[[_2nd_order, _missing_x]]

0.194

25997

\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=t \,{\mathrm e}^{-2 t} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}
Using Laplace transform method.

[[_2nd_order, _linear, _nonhomogeneous]]

0.332

25998

\begin{align*} y^{\prime \prime }+4 y&=12 \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= -3 \\ \end{align*}
Using Laplace transform method.

[[_2nd_order, _missing_x]]

0.310

25999

\begin{align*} y^{\prime \prime }+2 y^{\prime }&=8 t \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

[[_2nd_order, _missing_y]]

0.311

26000

\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=4 t^{2} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

[[_2nd_order, _with_linear_symmetries]]

0.342