2.3.140 Problems 13901 to 14000

Table 2.853: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

13901

3392

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

Series expansion around \(x=0\).

2.585

13902

18109

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

2.585

13903

24082

\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +56 y&=0 \\ \end{align*}

Series expansion around \(x=0\).

2.585

13904

2298

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

2.586

13905

9429

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

Series expansion around \(x=0\).

2.586

13906

10166

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

Series expansion around \(x=0\).

2.586

13907

13033

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

2.586

13908

5831

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

2.587

13909

5435

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

2.588

13910

10361

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

2.588

13911

10171

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

Series expansion around \(x=0\).

2.589

13912

23733

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

Series expansion around \(x=0\).

2.589

13913

4361

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

2.590

13914

4623

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

2.590

13915

7141

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

2.590

13916

11711

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

2.590

13917

12299

\begin{align*} y^{\prime \prime }-\left (4 a^{2} b^{2} x^{2} {\mathrm e}^{2 b \,x^{2}}-1\right ) y&=0 \\ \end{align*}

2.590

13918

27091

\(\left [\begin {array}{cc} 6 & -2 \\ -3 & 4 \end {array}\right ]\)

N/A

N/A

N/A

2.591

13919

1144

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

2.592

13920

15444

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

2.592

13921

23695

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

Series expansion around \(x=1\).

2.592

13922

27636

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

2.592

13923

6561

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

2.593

13924

10180

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

Series expansion around \(x=0\).

2.593

13925

25629

\begin{align*} y^{\prime \prime }+8 y^{\prime }+16 y&=0 \\ \end{align*}

Using Laplace transform method.

2.594

13926

1821

\begin{align*} y^{\prime \prime } x -y^{\prime }-4 x^{3} y&=8 x^{5} \\ \end{align*}

2.595

13927

9241

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

2.595

13928

1531

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

2.596

13929

12527

\begin{align*} x \left (x +3\right ) y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y-\left (20 x +30\right ) \left (x^{2}+3 x \right )^{{7}/{3}}&=0 \\ \end{align*}

2.596

13930

5696

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

2.598

13931

17186

\begin{align*} y^{\prime }-3 y&=27 t^{2} \\ \end{align*}

2.598

13932

17216

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

2.598

13933

1565

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

2.599

13934

2515

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

2.599

13935

16964

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

2.599

13936

17061

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

2.599

13937

17184

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

2.599

13938

21673

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

Series expansion around \(x=0\).

2.599

13939

6691

\begin{align*} y+y^{\prime } x +\left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime \prime }+x \left (\operatorname {b0} x +\operatorname {a0} \right ) y^{\prime \prime \prime }&=f \left (x \right ) \\ \end{align*}

2.600

13940

18031

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

2.601

13941

2486

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

2.602

13942

4190

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

2.602

13943

13697

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

2.602

13944

14186

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

2.602

13945

16410

\begin{align*} y^{\prime \prime } x -y^{\prime }&=6 x^{5} \\ \end{align*}

2.602

13946

20034

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

2.602

13947

21609

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

2.602

13948

23744

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

Series expansion around \(x=0\).

2.602

13949

24898

\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*}

2.602

13950

3220

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

2.603

13951

98

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

2.604

13952

17195

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

2.604

13953

23510

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

2.605

13954

25166

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

With initial conditions

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

2.605

13955

26600

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

2.605

13956

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 \(x=0\).

2.606

13957

25952

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

2.606

13958

9000

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

Series expansion around \(x=0\).

2.608

13959

5929

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

2.609

13960

10175

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

Series expansion around \(x=0\).

2.609

13961

23725

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

Series expansion around \(x=0\).

2.609

13962

25973

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

2.609

13963

1228

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

2.611

13964

6760

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

2.611

13965

2496

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

2.612

13966

8105

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

Series expansion around \(x=0\).

2.612

13967

9256

\begin{align*} 4 y+y^{\prime \prime }&=4 \cos \left (2 x \right )+6 \cos \left (x \right )+8 x^{2}-4 x \\ \end{align*}

2.612

13968

9598

\begin{align*} y^{\prime \prime }+x^{2} y^{\prime }+2 y x&=10 x^{3}-2 x +5 \\ \end{align*}

Series expansion around \(x=0\).

2.612

13969

10046

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

2.612

13970

25324

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

Series expansion around \(t=0\).

2.612

13971

24715

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

2.613

13972

16123

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

2.614

13973

19703

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

2.614

13974

4640

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

2.615

13975

8884

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

2.615

13976

8974

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

2.615

13977

16880

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

Series expansion around \(x=0\).

2.615

13978

21903

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

Series expansion around \(x=0\).

2.615

13979

12353

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

2.616

13980

14659

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

2.616

13981

22331

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

2.616

13982

3631

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

2.617

13983

9238

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

2.617

13984

10173

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

Series expansion around \(x=0\).

2.617

13985

25749

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

2.617

13986

10343

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

Using Laplace transform method.

2.618

13987

18302

\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x -3 y&=-\frac {16 \ln \left (x \right )}{x} \\ \end{align*}

2.618

13988

20187

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

2.618

13989

27107

\(\left [\begin {array}{cc} -13 & 1 \\ 1 & 4 \end {array}\right ]\)

N/A

N/A

N/A

2.618

13990

1224

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

2.619

13991

4742

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

2.619

13992

9750

\begin{align*} y&=x^{6} {y^{\prime }}^{3}-y^{\prime } x \\ \end{align*}

2.619

13993

10168

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

Series expansion around \(x=0\).

2.619

13994

10169

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

Series expansion around \(x=0\).

2.619

13995

27105

\(\left [\begin {array}{cc} -3 & 5 \\ 5 & 4 \end {array}\right ]\)

N/A

N/A

N/A

2.619

13996

1122

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

2.620

13997

9400

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

Series expansion around \(x=0\).

2.621

13998

16653

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

2.621

13999

16870

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

Series expansion around \(x=0\).

2.621

14000

20163

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

2.621