2.3.110 Problems 10901 to 11000

Table 2.793: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

10901

5814

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

0.839

10902

7377

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

0.839

10903

9267

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

0.839

10904

9845

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

Series expansion around \(x=0\).

0.839

10905

13984

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

0.839

10906

16647

\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&=x^{3} {\mathrm e}^{2 x} \sin \left (x \right ) \\ \end{align*}

0.839

10907

17479

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

0.839

10908

17680

\begin{align*} x^{2} y^{\prime \prime }-2 x y^{\prime }+7 y&=0 \\ \end{align*}

Series expansion around \(x=1\).

0.839

10909

18022

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

0.839

10910

18430

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

With initial conditions

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

0.839

10911

18456

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

Using Laplace transform method.

0.839

10912

24862

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

0.839

10913

25377

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

With initial conditions

\begin{align*} y_{1} \left (0\right ) &= 1 \\ y_{2} \left (0\right ) &= 3 \\ \end{align*}

0.839

10914

6950

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

0.840

10915

14604

\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 7 \\ \end{align*}

0.840

10916

985

\begin{align*} x_{1}^{\prime }&=5 x_{1}-6 x_{3} \\ x_{2}^{\prime }&=2 x_{1}-x_{2}-2 x_{3} \\ x_{3}^{\prime }&=4 x_{1}-2 x_{2}-4 x_{3} \\ \end{align*}

0.841

10917

2787

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

With initial conditions

\begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 1 \\ x_{3} \left (0\right ) &= 1 \\ x_{4} \left (0\right ) &= 1 \\ \end{align*}

0.841

10918

3805

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

0.841

10919

4186

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

Series expansion around \(x=0\).

0.841

10920

12657

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

0.841

10921

15574

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

0.841

10922

18672

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

With initial conditions

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

0.841

10923

25994

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

0.841

10924

598

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

0.842

10925

2030

\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-3 x \left (-x^{2}+1\right ) y^{\prime }+4 y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.842

10926

4505

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

0.842

10927

5717

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

0.842

10928

8258

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

0.842

10929

9077

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

0.842

10930

9588

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

Series expansion around \(x=0\).

0.842

10931

10206

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

Series expansion around \(x=0\).

0.842

10932

12977

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

0.842

10933

14288

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

0.842

10934

23742

\begin{align*} 2 \left (x +3\right )^{2} y^{\prime \prime }-\left (x^{2}+5 x +6\right ) y^{\prime }-y&=0 \\ \end{align*}

Series expansion around \(x=-3\).

0.842

10935

26512

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

0.842

10936

475

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

Series expansion around \(x=0\).

0.843

10937

2781

\begin{align*} x_{1}^{\prime }&=2 x_{1}-2 x_{2} \\ x_{2}^{\prime }&=4 x_{1}-2 x_{2}+\delta \left (t -\pi \right ) \\ \end{align*}

With initial conditions

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

0.843

10938

3416

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

0.843

10939

3628

\begin{align*} y^{\prime }-2 y&=\left \{\begin {array}{cc} 1 & x \le 1 \\ 0 & 1<x \end {array}\right . \\ y \left (0\right ) &= 3 \\ \end{align*}

0.843

10940

5813

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

0.843

10941

10209

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

Series expansion around \(x=0\).

0.843

10942

1430

\begin{align*} x_{1}^{\prime }&=2 x_{1}-5 x_{2}-\cos \left (t \right ) \\ x_{2}^{\prime }&=x_{1}-2 x_{2}+\sin \left (t \right ) \\ \end{align*}

0.844

10943

19455

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

0.844

10944

26648

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

0.844

10945

27134

\(\left [\begin {array}{ccc} \frac {\sqrt {2}}{2} & \frac {i \sqrt {2}}{2} & 0 \\ -\frac {\sqrt {2}}{2} & \frac {i \sqrt {2}}{2} & 0 \\ 0 & 0 & 1 \end {array}\right ]\)

N/A

N/A

N/A

0.844

10946

1456

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

0.845

10947

3402

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

0.845

10948

4024

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

Series expansion around \(x=0\).

0.845

10949

4155

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

0.845

10950

11813

\begin{align*} {y^{\prime }}^{3}-x y^{4} y^{\prime }-y^{5}&=0 \\ \end{align*}

0.845

10951

13064

\begin{align*} a x^{\prime }+b y^{\prime }&=\alpha x+\beta y \\ b x^{\prime }-a y^{\prime }&=\beta x-\alpha y \\ \end{align*}

0.845

10952

18270

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

0.845

10953

22263

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

With initial conditions

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

0.845

10954

26023

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

Series expansion around \(x=0\).

0.845

10955

1981

\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*}

Series expansion around \(x=0\).

0.846

10956

1999

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

Series expansion around \(x=0\).

0.846

10957

2467

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

Series expansion around \(t=0\).

0.846

10958

5783

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

0.846

10959

14603

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

0.846

10960

18679

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

0.846

10961

22206

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

Series expansion around \(x=0\).

0.846

10962

22839

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

Series expansion around \(x=0\).

0.846

10963

1971

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

Series expansion around \(x=0\).

0.847

10964

3355

\begin{align*} 9 x^{2} y^{\prime \prime }+\left (3 x +2\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.847

10965

11710

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

0.847

10966

20998

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

0.847

10967

481

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

Series expansion around \(x=0\).

0.848

10968

1957

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

Series expansion around \(x=0\).

0.848

10969

1973

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

Series expansion around \(x=0\).

0.848

10970

3359

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

Series expansion around \(x=0\).

0.848

10971

4065

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

Series expansion around \(x=0\).

0.848

10972

9665

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

0.848

10973

18673

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

0.848

10974

18914

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

With initial conditions

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

0.848

10975

21243

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

0.848

10976

27725

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

0.848

10977

1974

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

Series expansion around \(x=0\).

0.849

10978

5522

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

0.849

10979

8185

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

0.849

10980

16881

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

Series expansion around \(x=1\).

0.849

10981

17480

\begin{align*} 4 y^{\prime \prime }+4 y^{\prime }+37 y&=\cos \left (3 t \right ) \\ y \left (0\right ) &= a \\ y^{\prime }\left (\pi \right ) &= a \\ \end{align*}

0.849

10982

3313

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

0.850

10983

9793

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

0.850

10984

10165

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

Series expansion around \(x=0\).

0.850

10985

14103

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

0.850

10986

14307

\begin{align*} x^{\prime \prime }+7 x&=t \,{\mathrm e}^{3 t} \\ \end{align*}

0.850

10987

18413

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

With initial conditions

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

0.850

10988

21167

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

0.850

10989

2639

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

Series expansion around \(t=0\).

0.851

10990

3249

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

0.851

10991

3830

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

0.851

10992

4568

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

With initial conditions

\begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= -2 \\ x_{3} \left (0\right ) &= 0 \\ \end{align*}

0.851

10993

8087

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

Series expansion around \(x=\infty \).

0.851

10994

10187

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

Series expansion around \(x=0\).

0.851

10995

10208

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

Series expansion around \(x=0\).

0.851

10996

14070

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

0.851

10997

20522

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

0.851

10998

22811

\begin{align*} y^{\prime \prime }+9 y&=20 \,{\mathrm e}^{-t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

Using Laplace transform method.

0.851

10999

476

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

Series expansion around \(x=0\).

0.852

11000

498

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

Series expansion around \(x=0\).

0.852