2.3.100 Problems 9901 to 10000

Table 2.773: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

9901

1441

\begin{align*} x_{1}^{\prime }&=-2 x_{1}+x_{2}+2 \,{\mathrm e}^{-t} \\ x_{2}^{\prime }&=x_{1}-2 x_{2}+3 t \\ \end{align*}

With initial conditions

\begin{align*} x_{1} \left (0\right ) &= \alpha _{1} \\ x_{2} \left (0\right ) &= \alpha _{2} \\ \end{align*}

0.738

9902

7096

\begin{align*} y^{\prime \prime }+9 y&=8 \cos \left (x \right ) \\ y \left (\frac {\pi }{2}\right ) &= -1 \\ y^{\prime }\left (\frac {\pi }{2}\right ) &= 1 \\ \end{align*}

0.738

9903

8614

\begin{align*} \left (x -1\right )^{2} y^{\prime \prime }-\left (x -1\right ) y^{\prime }-35 y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.738

9904

9112

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

0.738

9905

9857

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

Series expansion around \(x=2\).

0.738

9906

23525

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

0.738

9907

9505

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

Series expansion around \(x=0\).

0.739

9908

10171

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

Series expansion around \(x=0\).

0.739

9909

12357

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

0.739

9910

22713

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

0.739

9911

22785

\begin{align*} y^{\prime \prime \prime \prime }+16 y^{\prime \prime }&=64 \cos \left (4 x \right ) \\ \end{align*}

0.739

9912

23533

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

0.739

9913

25248

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

Using Laplace transform method.

0.739

9914

1829

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

0.740

9915

3495

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

0.740

9916

6945

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

0.740

9917

9804

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{x} \\ \end{align*}

0.740

9918

19031

\begin{align*} x_{1}^{\prime }&=x_{1}+x_{2}+x_{3} \\ x_{2}^{\prime }&=2 x_{1}+x_{2}-x_{3} \\ x_{3}^{\prime }&=-8 x_{1}-5 x_{2}-3 x_{3} \\ \end{align*}

0.740

9919

20709

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

0.740

9920

21296

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

0.740

9921

22163

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

0.740

9922

22777

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

0.740

9923

23979

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

0.740

9924

25550

\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&={\mathrm e}^{i \omega t} \\ \end{align*}

0.740

9925

26859

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

0.740

9926

3183

\begin{align*} y^{\prime \prime }+y&={\mathrm e}^{3 x} \left (1+\sin \left (2 x \right )\right ) \\ \end{align*}

0.741

9927

9512

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

Series expansion around \(x=0\).

0.741

9928

17705

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

Series expansion around \(x=0\).

0.741

9929

17819

\begin{align*} x^{\prime \prime }+x&=\cos \left (\frac {7 t}{10}\right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}

0.741

9930

19611

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

Series expansion around \(x=0\).

0.741

9931

20376

\begin{align*} y^{\prime \prime \prime \prime }+10 y^{\prime \prime }+9 y&=96 \sin \left (2 x \right ) \cos \left (x \right ) \\ \end{align*}

0.741

9932

22727

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

0.741

9933

26068

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

0.741

9934

1717

\begin{align*} 27 x y^{2}+8 y^{3}+\left (18 x^{2} y+12 x y^{2}\right ) y^{\prime }&=0 \\ \end{align*}

0.742

9935

3205

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

0.742

9936

3747

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=\frac {2 \,{\mathrm e}^{-3 x}}{x^{2}+1} \\ \end{align*}

0.742

9937

14788

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

With initial conditions

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

0.742

9938

14990

\begin{align*} x^{\prime }&=8 x+14 y \\ y^{\prime }&=7 x+y \\ \end{align*}

With initial conditions

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

0.742

9939

16596

\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=-18 \,{\mathrm e}^{4 x}+14 \,{\mathrm e}^{5 x} \\ \end{align*}

0.742

9940

17498

\begin{align*} y^{\prime \prime }-25 y&=\frac {1}{1-{\mathrm e}^{5 t}} \\ \end{align*}

0.742

9941

18884

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

Using Laplace transform method.

0.742

9942

21520

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

0.742

9943

22191

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

Series expansion around \(x=1\).

0.742

9944

22230

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

Using Laplace transform method.

0.742

9945

22840

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

Series expansion around \(x=0\).

0.742

9946

3243

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

0.743

9947

3502

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

Series expansion around \(z=0\).

0.743

9948

5742

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

0.743

9949

6398

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

0.743

9950

13069

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

0.743

9951

16753

\begin{align*} 3 y^{\prime \prime }+8 y^{\prime }-3 y&=123 x \sin \left (3 x \right ) \\ \end{align*}

0.743

9952

22717

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

0.743

9953

22742

\begin{align*} y^{\prime \prime }-y&=2 x^{4}-3 x +1 \\ \end{align*}

0.743

9954

23745

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

Series expansion around \(x=0\).

0.743

9955

24108

\begin{align*} x^{2} y^{\prime \prime }+5 x y^{\prime }+\left (2 x +4\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.743

9956

24637

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

0.743

9957

923

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

0.744

9958

1501

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

Using Laplace transform method.

0.744

9959

2800

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

0.744

9960

3906

\begin{align*} x_{1}^{\prime }&=-7 x_{1}-6 x_{2}-7 x_{3} \\ x_{2}^{\prime }&=-3 x_{1}-3 x_{2}-3 x_{3} \\ x_{3}^{\prime }&=7 x_{1}+6 x_{2}+7 x_{3} \\ \end{align*}

0.744

9961

5946

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

0.744

9962

5958

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

0.744

9963

7111

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

0.744

9964

8013

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

0.744

9965

8549

\begin{align*} 4 x^{2} y^{\prime \prime }+\left (16 x^{2}+1\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.744

9966

14352

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

Using Laplace transform method.

0.744

9967

16897

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

Series expansion around \(x=0\).

0.744

9968

19700

\begin{align*} x^{\prime \prime }+4 x^{\prime }+3 x&=t \sin \left (t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}

0.744

9969

21498

\begin{align*} y^{\prime \prime }-6 y^{\prime }+25 y&=0 \\ y \left (0\right ) &= -3 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}

0.744

9970

21774

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

0.744

9971

25243

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

Using Laplace transform method.

0.744

9972

26702

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

0.744

9973

27724

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

0.744

9974

1435

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

0.745

9975

3508

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

Series expansion around \(z=0\).

0.745

9976

5776

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

0.745

9977

11319

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

0.745

9978

15003

\begin{align*} x^{\prime }&=x+20 y \\ y^{\prime }&=40 x-19 y \\ \end{align*}

0.745

9979

16943

\begin{align*} x^{\prime }&=8 x+2 y+7 \,{\mathrm e}^{2 t} \\ y^{\prime }&=4 x+y-7 \,{\mathrm e}^{2 t} \\ \end{align*}

With initial conditions

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

0.745

9980

16945

\begin{align*} x^{\prime }&=-y \\ y^{\prime }&=4 x+24 t \\ \end{align*}

With initial conditions

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

0.745

9981

17510

\begin{align*} y^{\prime \prime }+8 y^{\prime }+16 y&=\frac {{\mathrm e}^{-4 t}}{t^{2}+1} \\ \end{align*}

0.745

9982

19410

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

0.745

9983

20362

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

0.745

9984

26024

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

Series expansion around \(x=0\).

0.745

9985

26726

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

0.745

9986

26990

\begin{align*} y^{\prime \prime }+6 y^{\prime }+2 y&=4 \cos \left (3 x \right ) \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.745

9987

27037

\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&=4 \delta \left (-3+t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

0.745

9988

1340

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

0.746

9989

2053

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

Series expansion around \(x=0\).

0.746

9990

3376

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

Series expansion around \(x=0\).

0.746

9991

3396

\begin{align*} 9 x^{2} y^{\prime \prime }+10 x y^{\prime }+y&=x -1 \\ \end{align*}

Series expansion around \(x=0\).

0.746

9992

5383

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

0.746

9993

8585

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

Series expansion around \(x=0\).

0.746

9994

12971

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

0.746

9995

13073

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

0.746

9996

15267

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

0.746

9997

17367

\begin{align*} y^{\prime \prime }+9 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -4 \\ \end{align*}

0.746

9998

20549

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

0.746

9999

27081

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

Series expansion around \(x=0\).

0.746

10000

233

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

0.747