2.3.40 Problems 3901 to 4000

Table 2.653: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

3901

10512

\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }-8 x y^{\prime }+20 y&=0 \\ \end{align*}

0.317

3902

10984

\begin{align*} 2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }-x \left (-7 x^{2}+12\right ) y^{\prime }+\left (3 x^{2}+7\right ) y&=0 \\ \end{align*}

0.317

3903

17736

\begin{align*} y^{\prime \prime }+7 y^{\prime }+10 y&=0 \\ \end{align*}

0.317

3904

20042

\begin{align*} y^{\prime \prime }+8 y^{\prime }+25 y&=0 \\ \end{align*}

0.317

3905

23791

\begin{align*} x^{\prime }&=5 x-6 y \\ y^{\prime }&=6 x-7 y \\ \end{align*}

0.317

3906

1766

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

0.318

3907

9978

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

0.318

3908

10978

\begin{align*} x^{2} \left (x +2\right ) y^{\prime \prime }+5 x \left (1-x \right ) y^{\prime }-\left (2-8 x \right ) y&=0 \\ \end{align*}

0.318

3909

14637

\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y&=3 \,{\mathrm e}^{x} x^{2}-7 \,{\mathrm e}^{x} \\ \end{align*}

0.318

3910

15079

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

0.318

3911

18089

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

0.318

3912

19030

\begin{align*} x_{1}^{\prime }&=-3 x_{1}+\frac {5 x_{2}}{2} \\ x_{2}^{\prime }&=-\frac {5 x_{1}}{2}+2 x_{2} \\ \end{align*}

0.318

3913

19646

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

0.318

3914

23029

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

0.318

3915

27194

\begin{align*} x_{1}^{\prime }&=4 x_{1}-x_{2} \\ x_{2}^{\prime }&=x_{1}+2 x_{2} \\ \end{align*}

0.318

3916

260

\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&=2 x \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 8 \\ \end{align*}

0.319

3917

309

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

0.319

3918

1063

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

Series expansion around \(x=0\).

0.319

3919

1088

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

Series expansion around \(x=0\).

0.319

3920

1310

\begin{align*} 16 y^{\prime \prime }+24 y^{\prime }+9 y&=0 \\ \end{align*}

0.319

3921

1362

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

Series expansion around \(x=0\).

0.319

3922

1445

\begin{align*} x_{1}^{\prime }&=x_{1}-4 x_{2} \\ x_{2}^{\prime }&=4 x_{1}-7 x_{2} \\ \end{align*}

0.319

3923

2196

\begin{align*} y^{\prime \prime \prime }-y^{\prime }&=-2 x -2+4 \,{\mathrm e}^{x}-6 \,{\mathrm e}^{-x}+96 \,{\mathrm e}^{3 x} \\ \end{align*}

0.319

3924

2671

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

Using Laplace transform method.

0.319

3925

3762

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

0.319

3926

7050

\begin{align*} y^{\prime \prime }+4 k y^{\prime }-12 k^{2} y&=0 \\ \end{align*}

0.319

3927

7240

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

0.319

3928

7371

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

0.319

3929

7587

\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=0 \\ \end{align*}

0.319

3930

8073

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

Series expansion around \(x=0\).

0.319

3931

10511

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

0.319

3932

10987

\begin{align*} x \left (x^{2}+1\right ) y^{\prime \prime }+\left (7 x^{2}+4\right ) y^{\prime }+8 y x&=0 \\ \end{align*}

0.319

3933

13164

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

N/A

N/A

N/A

0.319

3934

14709

\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-10 x y^{\prime }-8 y&=0 \\ \end{align*}

0.319

3935

17741

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

0.319

3936

17744

\begin{align*} 12 y^{\prime \prime }+8 y^{\prime }+y&=0 \\ \end{align*}

0.319

3937

25097

\begin{align*} y^{\prime \prime }+y^{\prime }-12 y&=0 \\ \end{align*}

0.319

3938

26413

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

0.319

3939

830

\begin{align*} 9 y^{\prime \prime }-12 y^{\prime }+4 y&=0 \\ \end{align*}

0.320

3940

1277

\begin{align*} y^{\prime \prime }+6 y^{\prime }+13 y&=0 \\ \end{align*}

0.320

3941

1763

\begin{align*} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y&=8 \,{\mathrm e}^{-x \left (x +2\right )} \\ \end{align*}

0.320

3942

6729

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

0.320

3943

9338

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

0.320

3944

9462

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

0.320

3945

10808

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

0.320

3946

14708

\begin{align*} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y&=0 \\ \end{align*}

0.320

3947

16771

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

Using Laplace transform method.

0.320

3948

16773

\begin{align*} y^{\prime \prime }+9 y&=27 t^{3} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

0.320

3949

19651

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

0.320

3950

19865

\begin{align*} \left (x^{3}+x^{2}-3 x +1\right ) y^{\prime \prime \prime }+\left (9 x^{2}+6 x -9\right ) y^{\prime \prime }+\left (18 x +6\right ) y^{\prime }+6 y&=x^{3} \\ \end{align*}

0.320

3951

21665

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

Series expansion around \(t=-{\frac {1}{2}}\).

0.320

3952

26939

\begin{align*} y^{\prime \prime }+10 y^{\prime }+26 y&=0 \\ \end{align*}

0.320

3953

27105

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

N/A

N/A

N/A

0.320

3954

27121

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

N/A

N/A

N/A

0.320

3955

27538

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

0.320

3956

1042

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

Series expansion around \(x=0\).

0.321

3957

1886

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

Series expansion around \(x=0\).

0.321

3958

10562

\begin{align*} 4 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+x \left (-19 x^{2}+7\right ) y^{\prime }-\left (14 x^{2}+1\right ) y&=0 \\ \end{align*}

0.321

3959

19588

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

Series expansion around \(x=0\).

0.321

3960

20900

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

Series expansion around \(x=0\).

0.321

3961

23250

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

0.321

3962

1075

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

Series expansion around \(x=0\).

0.322

3963

1383

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

Series expansion around \(x=0\).

0.322

3964

12336

\begin{align*} y^{\prime \prime }+\sqrt {x}\, y^{\prime }+\left (\frac {1}{4 \sqrt {x}}+\frac {x}{4}-9\right ) y-x \,{\mathrm e}^{-\frac {x^{{3}/{2}}}{3}}&=0 \\ \end{align*}

0.322

3965

14994

\(\left [\begin {array}{cc} 7 & 1 \\ -4 & 11 \end {array}\right ]\)

N/A

N/A

N/A

0.322

3966

15196

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -3 \\ \end{align*}

Using Laplace transform method.

0.322

3967

18315

\begin{align*} x^{2} y^{\prime \prime }-x y^{\prime }-3 y&=5 x^{4} \\ \end{align*}

0.322

3968

22791

\begin{align*} s^{\prime \prime \prime \prime }-2 s^{\prime \prime }+s&=100 \cos \left (3 t \right ) \\ \end{align*}

0.322

3969

25096

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

0.322

3970

25099

\begin{align*} y^{\prime \prime }-4 y^{\prime }-12 y&=0 \\ \end{align*}

0.322

3971

27761

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

Series expansion around \(x=0\).

0.322

3972

829

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

0.323

3973

1282

\begin{align*} y^{\prime \prime }+4 y^{\prime }+\frac {25 y}{4}&=0 \\ \end{align*}

0.323

3974

1367

\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }-4 x y^{\prime }+6 y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.323

3975

7260

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

0.323

3976

7718

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

0.323

3977

10058

\begin{align*} x^{\prime }&=x-3 y \\ y^{\prime }&=3 x+7 y \\ \end{align*}

0.323

3978

16793

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

Using Laplace transform method.

0.323

3979

16847

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

Series expansion around \(x=0\).

0.323

3980

17743

\begin{align*} 20 y^{\prime \prime }+y^{\prime }-y&=0 \\ \end{align*}

0.323

3981

18467

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

Using Laplace transform method.

0.323

3982

20602

\begin{align*} \left (x^{3}-4 x \right ) y^{\prime \prime \prime }+\left (9 x^{2}-4\right ) y^{\prime \prime }+18 x y^{\prime }+6 y&=6 \\ \end{align*}

0.323

3983

25092

\begin{align*} y^{\prime \prime }-7 y^{\prime }+10 y&=0 \\ \end{align*}

0.323

3984

25107

\begin{align*} y^{\prime \prime }-4 y^{\prime }-21 y&=0 \\ \end{align*}

0.323

3985

851

\begin{align*} 4 y^{\prime \prime }-12 y^{\prime }+9 y&=0 \\ \end{align*}

0.324

3986

1011

\begin{align*} x_{1}^{\prime }&=3 x_{1}-x_{2} \\ x_{2}^{\prime }&=x_{1}+5 x_{2} \\ \end{align*}

0.324

3987

1090

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

Series expansion around \(x=0\).

0.324

3988

11195

\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+12 y&=0 \\ \end{align*}

0.324

3989

14830

\begin{align*} t^{3} x^{\prime \prime \prime }-3 t^{2} x^{\prime \prime }+6 x^{\prime } t -6 x&=0 \\ \end{align*}

0.324

3990

14949

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

0.324

3991

16513

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

0.324

3992

25321

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

Using Laplace transform method.

0.324

3993

25947

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

0.324

3994

26944

\begin{align*} y^{\prime \prime }-6 y^{\prime }+7 y&=0 \\ \end{align*}

0.324

3995

273

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

0.325

3996

1081

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

Series expansion around \(x=0\).

0.325

3997

7461

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

0.325

3998

9535

\begin{align*} x^{3} \left (x^{2}-25\right ) \left (x -2\right )^{2} y^{\prime \prime }+3 x \left (x -2\right ) y^{\prime }+7 \left (5+x \right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.325

3999

10606

\begin{align*} 3 x^{2} \left (x^{2}+3\right ) y^{\prime \prime }+x \left (11 x^{2}+3\right ) y^{\prime }+\left (5 x^{2}+1\right ) y&=0 \\ \end{align*}

0.325

4000

12621

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

0.325