2.3.120 Problems 11901 to 12000

Table 2.813: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

11901

644

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

0.971

11902

1299

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

0.971

11903

1951

\begin{align*} 18 x^{2} \left (x +1\right ) y^{\prime \prime }+3 x \left (x^{2}+11 x +5\right ) y^{\prime }-\left (-5 x^{2}-2 x +1\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.971

11904

8294

\begin{align*} y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \\ y \left (0\right ) &= 1 \\ \end{align*}

0.971

11905

8601

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

Series expansion around \(x=0\).

0.971

11906

10253

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

Series expansion around \(x=0\).

0.971

11907

10268

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

0.971

11908

12584

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

0.971

11909

21667

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

Series expansion around \(x=0\).

0.971

11910

22100

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

0.971

11911

25339

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

Series expansion around \(t=0\).

0.971

11912

22914

\begin{align*} x^{\prime }+5 x+3 y^{\prime }-11 y&=0 \\ x^{\prime }+3 x+y^{\prime }-7 y&=0 \\ \end{align*}

0.972

11913

24070

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

0.972

11914

4541

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

0.973

11915

7318

\begin{align*} x^{2} y^{\prime \prime }+7 x y^{\prime }+9 y&=0 \\ \end{align*}

0.973

11916

10357

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

Series expansion around \(x=0\).

0.973

11917

12524

\begin{align*} x \left (x -1\right ) y^{\prime \prime }+\left (\left (\operatorname {a1} +\operatorname {b1} +1\right ) x -\operatorname {d1} \right ) y^{\prime }+\operatorname {a1} \operatorname {b1} \operatorname {d1}&=0 \\ \end{align*}

0.973

11918

14808

\(\left [\begin {array}{ccc} -2 & 6 & -18 \\ 12 & -23 & 66 \\ 5 & -10 & 29 \end {array}\right ]\)

N/A

N/A

N/A

0.973

11919

27687

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

0.973

11920

2741

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

0.974

11921

7571

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

0.974

11922

9854

\begin{align*} \left (3 x^{2}+1\right ) y^{\prime \prime }+13 x y^{\prime }+7 y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.974

11923

10065

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

0.974

11924

15269

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

0.974

11925

16726

\begin{align*} x^{2} y^{\prime \prime }+2 x y^{\prime }-30 y&=0 \\ \end{align*}

0.974

11926

22874

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

Series expansion around \(x=0\).

0.974

11927

24871

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

0.974

11928

5485

\begin{align*} \left (1+3 x \right ) {y^{\prime }}^{2}-3 \left (y+2\right ) y^{\prime }+9&=0 \\ \end{align*}

0.975

11929

14625

\begin{align*} y^{\prime \prime }+2 y^{\prime }+10 y&=5 \,{\mathrm e}^{-2 x} x \\ \end{align*}

0.975

11930

17435

\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&=2 t \,{\mathrm e}^{-2 t} \sin \left (3 t \right ) \\ \end{align*}

0.975

11931

17494

\begin{align*} y^{\prime \prime }-10 y^{\prime }+34 y&={\mathrm e}^{5 t} \cot \left (3 t \right ) \\ \end{align*}

0.975

11932

3348

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

Series expansion around \(x=\frac {\pi }{2}\).

0.976

11933

7317

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

0.976

11934

15487

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

0.976

11935

24727

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

0.976

11936

24885

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

0.976

11937

27564

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

0.976

11938

1307

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

0.977

11939

1633

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

0.977

11940

8616

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

Series expansion around \(x=0\).

0.977

11941

9684

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

With initial conditions

\begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 3 \\ z \left (0\right ) &= 0 \\ \end{align*}

0.977

11942

10409

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

0.977

11943

10445

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

0.977

11944

15661

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

0.977

11945

15825

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

0.977

11946

19616

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

Series expansion around \(x=0\).

0.977

11947

20778

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

0.977

11948

21484

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

0.977

11949

24838

\begin{align*} 9 y^{2} {y^{\prime }}^{2}-3 x y^{\prime }+y&=0 \\ \end{align*}

0.977

11950

27685

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

0.977

11951

3955

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

Using Laplace transform method.

0.978

11952

4126

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

0.978

11953

8556

\begin{align*} 16 x^{2} y^{\prime \prime }+32 x y^{\prime }+\left (x^{4}-12\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.978

11954

9583

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

0.978

11955

1283

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

0.979

11956

15067

\begin{align*} y^{\prime \prime }-6 y^{\prime }+10 y&=100 \\ y \left (0\right ) &= 10 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}

0.979

11957

22921

\begin{align*} 2 x^{\prime }-6 x+3 y^{\prime }-2 y&=0 \\ 7 x^{\prime }+4 x+7 y^{\prime }+20 y&=0 \\ \end{align*}

0.979

11958

23226

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

0.979

11959

24905

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

0.979

11960

3367

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

Series expansion around \(x=0\).

0.980

11961

8295

\begin{align*} y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \\ y \left (0\right ) &= -4 \\ \end{align*}

0.980

11962

17116

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

0.980

11963

17490

\begin{align*} y^{\prime \prime }+6 y^{\prime }+25 y&={\mathrm e}^{-3 t} \left (\sec \left (4 t \right )+\csc \left (4 t \right )\right ) \\ \end{align*}

0.980

11964

20087

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

0.980

11965

22778

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

0.980

11966

22827

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

Series expansion around \(x=0\).

0.980

11967

26503

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

0.980

11968

3371

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

Series expansion around \(x=0\).

0.981

11969

8603

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

Series expansion around \(x=0\).

0.981

11970

3351

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

Series expansion around \(x=0\).

0.982

11971

4661

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

0.982

11972

6189

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

0.982

11973

12447

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

0.982

11974

12536

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

0.982

11975

15465

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

0.982

11976

18646

\begin{align*} x^{\prime }&=-5 x+4 y-35 \\ y^{\prime }&=-2 x+y-11 \\ \end{align*}

0.982

11977

2002

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

Series expansion around \(x=0\).

0.983

11978

3889

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

0.983

11979

5721

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

0.983

11980

14426

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

0.983

11981

22268

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

With initial conditions

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

0.983

11982

4068

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

Series expansion around \(x=0\).

0.984

11983

4154

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

0.984

11984

6863

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

0.984

11985

8051

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

0.984

11986

8296

\begin{align*} y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \\ y \left (8\right ) &= -4 \\ \end{align*}

0.984

11987

8522

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

Series expansion around \(x=0\).

0.984

11988

20588

\begin{align*} x^{2} y^{\prime \prime }+4 y^{2}-6 y&=x^{4} {y^{\prime }}^{2} \\ \end{align*}

0.984

11989

21289

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

Using Laplace transform method.

0.984

11990

22693

\begin{align*} s^{\prime \prime }-3 s^{\prime }+2 s&=8 t^{2}+12 \,{\mathrm e}^{-t} \\ s \left (0\right ) &= 0 \\ s^{\prime }\left (0\right ) &= 2 \\ \end{align*}

0.984

11991

26186

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

0.984

11992

2006

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

Series expansion around \(x=0\).

0.985

11993

2600

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=\left (3 t^{7}-5 t^{4}\right ) {\mathrm e}^{3 t} \\ \end{align*}

0.985

11994

2812

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

0.985

11995

4604

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

Series expansion around \(x=0\).

0.985

11996

26504

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

0.985

11997

26518

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

0.985

11998

6689

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

0.986

11999

9373

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

Series expansion around \(x=0\).

0.986

12000

19995

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

0.986