2.3.140 Problems 13901 to 14000

Table 2.811: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

13901

3299

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

0.931

13902

4403

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

0.931

13903

5471

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

0.931

13904

7959

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

0.931

13905

8046

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

0.931

13906

8049

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

0.931

13907

11610

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

0.931

13908

15078

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

0.931

13909

18867

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

0.931

13910

5235

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

0.932

13911

8056

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

0.932

13912

9887

\begin{align*} x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y&=0 \\ \end{align*}

0.932

13913

12965

\begin{align*} 3 y y^{\prime \prime }-5 {y^{\prime }}^{2}&=0 \\ \end{align*}

0.932

13914

22854

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

0.932

13915

18645

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

0.933

13916

21460

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

0.933

13917

23302

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

0.933

13918

842

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

0.934

13919

3707

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

0.934

13920

4601

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

0.934

13921

17728

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

0.934

13922

18106

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

0.934

13923

22330

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

0.934

13924

24876

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

0.934

13925

9591

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

0.935

13926

13704

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

0.935

13927

14249

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

0.935

13928

20634

\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*}

0.935

13929

22928

\begin{align*} 2 x^{\prime }-x+7 y^{\prime }+3 y&=90 \sin \left (2 t \right ) \\ x^{\prime }-5 x+8 y^{\prime }-3 y&=0 \\ \end{align*}

0.935

13930

7579

\begin{align*} m y^{\prime \prime }+b y^{\prime }+k y&=\cos \left (\omega t \right ) \\ \end{align*}

0.936

13931

14777

\begin{align*} x^{\prime }+y^{\prime }-x-6 y&={\mathrm e}^{3 t} \\ x^{\prime }+2 y^{\prime }-2 x-6 y&=t \\ \end{align*}

0.936

13932

15938

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

0.936

13933

4406

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

0.937

13934

5399

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

0.937

13935

6026

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

0.937

13936

13063

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

0.937

13937

15609

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

0.937

13938

18184

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

0.937

13939

20639

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

0.937

13940

25274

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

0.937

13941

5941

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

0.938

13942

9416

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

0.938

13943

9886

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

0.938

13944

13171

\(\left [\begin {array}{cccc} 22 & -9 & -8 & -8 \\ 10 & -7 & -14 & 2 \\ 10 & 0 & 8 & -10 \\ 29 & -9 & -3 & -15 \end {array}\right ]\)

N/A

N/A

N/A

0.938

13945

9953

\begin{align*} 4 y x -\left (x^{2}+7\right ) y^{\prime }+x \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.939

13946

11266

\begin{align*} 2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y&=0 \\ \end{align*}

0.939

13947

13686

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

0.939

13948

16396

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

0.939

13949

17519

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

0.939

13950

18154

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

0.939

13951

18351

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

0.939

13952

19219

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

0.939

13953

23753

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

0.939

13954

24875

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

0.939

13955

1300

\begin{align*} t^{2} y^{\prime \prime }+7 t y^{\prime }+10 y&=0 \\ \end{align*}

0.940

13956

8972

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

0.940

13957

23337

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

0.940

13958

3259

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

0.941

13959

8335

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

0.941

13960

13254

\begin{align*} x^{2} y^{\prime }&=a \,x^{2} y^{2}+b x y+c \,x^{n}+s \\ \end{align*}

0.941

13961

18185

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

0.941

13962

2797

\begin{align*} x^{\prime }&=x+y+z-2 \,{\mathrm e}^{-t} \\ y^{\prime }&=2 x+y-z-2 \,{\mathrm e}^{-t} \\ z^{\prime }&=-3 x+2 y+4 z+3 \,{\mathrm e}^{-t} \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 0 \\ z \left (0\right ) &= 0 \\ \end{align*}

0.942

13963

3913

\begin{align*} x_{1}^{\prime }&=7 x_{1}-x_{4} \\ x_{2}^{\prime }&=6 x_{2} \\ x_{3}^{\prime }&=-x_{3} \\ x_{4}^{\prime }&=2 x_{1}+5 x_{4} \\ \end{align*}

0.942

13964

20945

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

0.942

13965

8020

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

0.943

13966

20719

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

0.943

13967

6972

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

0.944

13968

2837

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

0.945

13969

5634

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

0.945

13970

7425

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

0.945

13971

9909

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

0.945

13972

14323

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

0.945

13973

16405

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

0.945

13974

18537

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

0.945

13975

18642

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

0.945

13976

18716

\begin{align*} x^{\prime }&=\frac {x \sqrt {6 x-9}}{3} \\ x \left (0\right ) &= 3 \\ \end{align*}

0.945

13977

21107

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

0.945

13978

25613

\begin{align*} y^{\prime }-a y&={\mathrm e}^{c t} \\ \end{align*}

0.945

13979

3371

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

0.946

13980

8053

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

0.946

13981

16734

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

0.946

13982

19009

\begin{align*} x_{1}^{\prime }&=-7 x_{1}+6 x_{2}-6 x_{3} \\ x_{2}^{\prime }&=-9 x_{1}+5 x_{2}-9 x_{3} \\ x_{3}^{\prime }&=-x_{2}-x_{3} \\ \end{align*}

0.946

13983

23280

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

0.946

13984

23503

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

0.946

13985

1831

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

0.947

13986

5056

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

0.947

13987

6157

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

0.947

13988

6468

\begin{align*} 1+{y^{\prime }}^{2}+2 y y^{\prime \prime }&=0 \\ \end{align*}

0.947

13989

8249

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

0.947

13990

12644

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

0.947

13991

12680

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

0.947

13992

15808

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

0.947

13993

21330

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

0.947

13994

25661

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

0.947

13995

5714

\begin{align*} y^{\prime \prime }&=\operatorname {c1} \,{\mathrm e}^{a x}+\operatorname {c2} \,{\mathrm e}^{-b x} \\ \end{align*}

0.948

13996

9496

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

0.948

13997

12674

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

0.948

13998

15616

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

0.948

13999

18842

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

0.948

14000

21692

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

0.948