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

15197

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

Using Laplace transform method.

0.686

10902

17447

\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=-78 \cos \left (3 t \right ) \\ \end{align*}

0.686

10903

20839

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

0.686

10904

26126

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

0.686

10905

1391

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

Series expansion around \(x=-4\).

0.687

10906

2084

\begin{align*} x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (3+14 x \right ) y^{\prime }+\left (6+100 x \right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.687

10907

2187

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

0.687

10908

3843

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

0.687

10909

8169

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

0.687

10910

9174

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

0.687

10911

9272

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

0.687

10912

9565

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

0.687

10913

10205

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

Series expansion around \(x=0\).

0.687

10914

14196

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

0.687

10915

17641

\begin{align*} x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-11 y^{\prime } x +16 y&=\frac {1}{x^{3}} \\ \end{align*}

0.687

10916

18388

\begin{align*} 9 \left (1-x \right ) x y^{\prime \prime }-12 y^{\prime }+4 y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.687

10917

19032

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

0.687

10918

23554

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

0.687

10919

25094

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

0.687

10920

25310

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

Using Laplace transform method.

0.687

10921

26017

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

Series expansion around \(x=0\).

0.687

10922

1413

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

0.688

10923

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*}

0.688

10924

4522

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

Using Laplace transform method.

0.688

10925

6176

\begin{align*} -12 y-2 \left (2 x +1\right ) y^{\prime }+\left (2 x +1\right )^{2} y^{\prime \prime }&=1+3 x \\ \end{align*}

0.688

10926

6517

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

0.688

10927

6745

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

0.688

10928

9401

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

Series expansion around \(x=0\).

0.688

10929

10275

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

0.688

10930

11779

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

0.688

10931

17722

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

Series expansion around \(x=0\).

0.688

10932

18113

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

0.688

10933

20580

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

0.688

10934

20853

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

0.688

10935

25380

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

With initial conditions

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

0.688

10936

3250

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

0.689

10937

3684

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

0.689

10938

8591

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

Series expansion around \(x=0\).

0.689

10939

8871

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

0.689

10940

16096

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

0.689

10941

17451

\begin{align*} y^{\prime \prime }-7 y^{\prime }+12 y&=-2 t^{3} {\mathrm e}^{4 t} \\ \end{align*}

0.689

10942

26551

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

0.689

10943

1937

\begin{align*} \left (x^{2}+4 x +3\right ) y^{\prime \prime }-\left (-x^{2}+4 x +5\right ) y^{\prime }-\left (2+x \right ) y&=0 \\ y \left (-2\right ) &= 2 \\ y^{\prime }\left (-2\right ) &= -1 \\ \end{align*}

Series expansion around \(x=-2\).

0.690

10944

2083

\begin{align*} x^{2} \left (x +1\right ) y^{\prime \prime }+3 x^{2} y^{\prime }-\left (6-x \right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.690

10945

3768

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

0.690

10946

3871

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

0.690

10947

15879

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

0.690

10948

17426

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

0.690

10949

19299

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

0.690

10950

21678

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

Series expansion around \(x=0\).

0.690

10951

26742

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

With initial conditions

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

0.690

10952

1356

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

0.691

10953

2686

\begin{align*} y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} 1 & 0\le t <4 \\ 0 & 4<t \end {array}\right . \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*}

Using Laplace transform method.

0.691

10954

3142

\begin{align*} 2 y^{\prime \prime }+5 y^{\prime }-3 y&=\sin \left (x \right )-8 x \\ y \left (0\right ) &= {\frac {1}{2}} \\ y^{\prime }\left (0\right ) &= {\frac {1}{2}} \\ \end{align*}

0.691

10955

3205

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

0.691

10956

3740

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

0.691

10957

3820

\begin{align*} x_{1}^{\prime }&=x_{1}+2 x_{2}+5 \,{\mathrm e}^{4 t} \\ x_{2}^{\prime }&=2 x_{1}+x_{2} \\ \end{align*}

0.691

10958

4548

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

0.691

10959

9733

\begin{align*} {y^{\prime }}^{2}+4 x^{5} y^{\prime }-12 x^{4} y&=0 \\ \end{align*}

0.691

10960

9878

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

Series expansion around \(x=0\).

0.691

10961

14757

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

Series expansion around \(x=0\).

0.691

10962

16885

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

Series expansion around \(x=0\).

0.691

10963

17485

\begin{align*} y^{\prime \prime }+4 y^{\prime }+20 y&=2 t \,{\mathrm e}^{-2 t} \\ \end{align*}

0.691

10964

17685

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

Series expansion around \(x=0\).

0.691

10965

18150

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

0.691

10966

22030

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

0.691

10967

23086

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

0.691

10968

25350

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

Series expansion around \(t=0\).

0.691

10969

27183

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

0.691

10970

27663

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

0.691

10971

641

\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*}

0.692

10972

3805

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

0.692

10973

5718

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

0.692

10974

9570

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (25 x^{2}-\frac {4}{9}\right ) y&=0 \\ \end{align*}

0.692

10975

13895

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

0.692

10976

16125

\begin{align*} y^{\prime \prime }+4 y^{\prime }+20 y&=3+2 \cos \left (2 t \right ) \\ \end{align*}

0.692

10977

17425

\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=-{\mathrm e}^{-9 t} \\ \end{align*}

0.692

10978

18964

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

0.692

10979

23231

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

0.692

10980

24087

\begin{align*} \left (x^{3}-8\right ) y^{\prime \prime }-4 y x&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.692

10981

25343

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

Series expansion around \(t=0\).

0.692

10982

27054

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

Using Laplace transform method.

0.692

10983

911

\begin{align*} x^{\prime \prime }+25 x&=90 \cos \left (4 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 90 \\ \end{align*}

0.693

10984

5728

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

0.693

10985

8161

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

0.693

10986

22227

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

Using Laplace transform method.

0.693

10987

26117

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

0.693

10988

15

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

0.694

10989

5769

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

0.694

10990

6201

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

0.694

10991

7658

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

Series expansion around \(x=0\).

0.694

10992

8110

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

Series expansion around \(x=0\).

0.694

10993

9522

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

Series expansion around \(x=0\).

0.694

10994

9563

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

0.694

10995

10098

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

0.694

10996

10374

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

0.694

10997

16707

\begin{align*} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }-9 y^{\prime } x +9 y&=12 x \sin \left (x^{2}\right ) \\ \end{align*}

0.694

10998

17218

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

0.694

10999

20850

\begin{align*} y^{\prime \prime }+5 y^{\prime }-6 y&=3 \,{\mathrm e}^{x} \\ \end{align*}

0.694

11000

21015

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

0.694