2.3.110 Problems 10901 to 11000

Table 2.763: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

10901

22833

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

0.785

10902

24575

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

0.785

10903

3351

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

0.786

10904

3903

\begin{align*} x_{1}^{\prime }&=2 x_{1}-4 x_{2}+3 x_{3} \\ x_{2}^{\prime }&=-9 x_{1}-3 x_{2}-9 x_{3} \\ x_{3}^{\prime }&=4 x_{1}+4 x_{2}+3 x_{3} \\ \end{align*}

0.786

10905

4163

\begin{align*} 9 y^{\prime \prime }-6 y^{\prime }+y&=\left (4 x^{2}+24 x +18\right ) {\mathrm e}^{x} \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*}

0.786

10906

7575

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

0.786

10907

7699

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

0.786

10908

8974

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

0.786

10909

9567

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

0.786

10910

9985

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

0.786

10911

12624

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

0.786

10912

16871

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

0.786

10913

20505

\begin{align*} y+3 y^{\prime } x +9 x^{2} y^{\prime \prime }+6 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime }&=4 x \\ \end{align*}

0.786

10914

22728

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

0.786

10915

10341

\begin{align*} y^{\prime } t +y&=t \\ y \left (1\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

0.787

10916

15654

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

0.787

10917

18291

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

0.787

10918

19568

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

0.787

10919

19771

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

0.787

10920

20599

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

0.787

10921

7300

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

0.788

10922

8971

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

0.788

10923

9460

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

0.788

10924

9568

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

0.788

10925

12982

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

0.788

10926

15758

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

0.788

10927

15992

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

0.788

10928

17704

\begin{align*} y^{\prime \prime }-\cos \left (x \right ) y&=\sin \left (x \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Series expansion around \(x=0\).

0.788

10929

21528

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

0.788

10930

21661

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

0.788

10931

2828

\begin{align*} x_{1}^{\prime }&=x_{1}-4 x_{2} \\ x_{2}^{\prime }&=-8 x_{1}+4 x_{2} \\ \end{align*}

0.789

10932

4018

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

0.789

10933

4416

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

0.789

10934

7647

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

0.789

10935

9268

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

0.789

10936

9876

\begin{align*} 2 x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.789

10937

9879

\begin{align*} 2 x^{2} y^{\prime \prime }+5 y^{\prime } x -2 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.789

10938

17004

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

0.789

10939

17697

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

0.789

10940

18125

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

0.789

10941

21688

\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x -\left (x^{2}+\frac {5}{4}\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.789

10942

22215

\begin{align*} -y+y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.789

10943

23600

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

0.789

10944

25338

\begin{align*} t y^{\prime \prime }+\left (1-t \right ) y^{\prime }+4 t y&=0 \\ \end{align*}
Series expansion around \(t=0\).

0.789

10945

4013

\begin{align*} 4 x^{2} y^{\prime \prime }+3 y^{\prime } x +y x&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.790

10946

4041

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

0.790

10947

6381

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

0.790

10948

10122

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

0.790

10949

10340

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

0.790

10950

19112

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

0.790

10951

21803

\begin{align*} {\mathrm e}^{x} \sec \left (y\right )+\left ({\mathrm e}^{x}+1\right ) \sec \left (y\right ) \tan \left (y\right ) y^{\prime }&=0 \\ y \left (3\right ) &= \frac {\pi }{3} \\ \end{align*}

0.790

10952

3822

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

0.791

10953

4137

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

0.791

10954

6255

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

0.791

10955

9471

\begin{align*} x^{\prime }&=x+y-5 t +2 \\ y^{\prime }&=4 x-2 y-8 t -8 \\ \end{align*}

0.791

10956

9739

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

0.791

10957

10080

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

0.791

10958

23288

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

0.791

10959

38

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

0.792

10960

891

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

0.792

10961

1995

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

0.792

10962

7775

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

0.792

10963

9575

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

0.792

10964

10302

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

0.792

10965

1955

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

0.793

10966

3842

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

0.793

10967

4187

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

0.793

10968

4685

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

0.793

10969

10081

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

0.793

10970

11835

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

0.793

10971

13728

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

0.793

10972

14639

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

0.793

10973

15777

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

0.793

10974

16723

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

0.793

10975

16886

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

0.793

10976

18872

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

0.793

10977

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*}

0.793

10978

19605

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

0.793

10979

20842

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

0.793

10980

595

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

0.794

10981

2754

\begin{align*} x_{1}^{\prime }&=-4 x_{1}-4 x_{2} \\ x_{2}^{\prime }&=10 x_{1}+9 x_{2}+x_{3} \\ x_{3}^{\prime }&=-4 x_{1}-3 x_{2}+x_{3} \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= 2 \\ x_{2} \left (0\right ) &= 1 \\ x_{3} \left (0\right ) &= -1 \\ \end{align*}

0.794

10982

7177

\begin{align*} \left (a^{2}+x^{2}\right ) y^{\prime \prime }+y^{\prime } x -n^{2} y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.794

10983

10293

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

0.794

10984

19370

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

0.794

10985

19617

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

0.794

10986

20009

\begin{align*} {y^{\prime }}^{3}-4 y y^{\prime } x +8 y^{2}&=0 \\ \end{align*}

0.794

10987

24823

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

0.794

10988

9643

\begin{align*} y^{\prime \prime }+16 y&=\delta \left (t -2 \pi \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.795

10989

16085

\begin{align*} y^{\prime \prime }+4 y^{\prime }+20 y&={\mathrm e}^{-\frac {t}{2}} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.795

10990

22176

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

0.795

10991

3848

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

0.796

10992

7885

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

0.796

10993

8757

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

0.796

10994

9708

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

0.796

10995

13777

\begin{align*} x^{2} y^{\prime \prime }-\left (a \,x^{3}+\frac {5}{16}\right ) y&=0 \\ \end{align*}

0.796

10996

14293

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

0.796

10997

15778

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

0.796

10998

16403

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

0.796

10999

16926

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

0.796

11000

1438

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

0.797