2.3.120 Problems 11901 to 12000

Table 2.771: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

11901

21155

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

0.664

11902

21698

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

0.664

11903

22172

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

0.664

11904

23726

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

0.664

11905

4456

\begin{align*} y^{\prime \prime }-8 y^{\prime }+17 y&={\mathrm e}^{4 x} \left (x^{2}-3 x \sin \left (x \right )\right ) \\ \end{align*}

0.665

11906

5733

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

0.665

11907

6521

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

0.665

11908

10187

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

0.665

11909

16942

\begin{align*} x^{\prime }&=8 x+2 y-17 \\ y^{\prime }&=4 x+y-13 \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 0 \\ \end{align*}

0.665

11910

18120

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

0.665

11911

19511

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

0.665

11912

23301

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

0.665

11913

23668

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

0.665

11914

24571

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

0.665

11915

24944

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

0.665

11916

25219

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

0.665

11917

25622

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

0.665

11918

2262

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

0.666

11919

3368

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

0.666

11920

8613

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

0.666

11921

15825

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

0.666

11922

20905

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

0.666

11923

22279

\begin{align*} x_{1}^{\prime }&=x_{2} \\ x_{2}^{\prime }&=x_{3} \\ x_{3}^{\prime }&=6 t \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= 0 \\ x_{2} \left (0\right ) &= 0 \\ x_{3} \left (0\right ) &= 12 \\ \end{align*}

0.666

11924

23097

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

0.666

11925

1029

\begin{align*} x_{1}^{\prime }&=x_{1}+3 x_{2}+7 x_{3} \\ x_{2}^{\prime }&=-x_{2}-4 x_{3} \\ x_{3}^{\prime }&=x_{2}+3 x_{3} \\ x_{4}^{\prime }&=-6 x_{2}-14 x_{3}+x_{4} \\ \end{align*}

0.667

11926

1850

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

0.667

11927

7171

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

0.667

11928

7914

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

0.667

11929

9578

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

0.667

11930

16329

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

0.667

11931

17489

\begin{align*} y^{\prime \prime }+2 y^{\prime }+50 y&={\mathrm e}^{-t} \csc \left (7 t \right ) \\ \end{align*}

0.667

11932

25290

\begin{align*} y+y^{\prime }&=\left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\pi \\ 0 & \pi \le t <\infty \end {array}\right . \\ y \left (\pi \right ) &= -1 \\ \end{align*}
Using Laplace transform method.

0.667

11933

25292

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

0.667

11934

25414

\begin{align*} y^{\prime }-5 y&=3 \operatorname {Heaviside}\left (t -4\right ) \\ \end{align*}

0.667

11935

665

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

0.668

11936

2197

\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+9 y^{\prime }-10 y&=10 \,{\mathrm e}^{2 x}+20 \,{\mathrm e}^{x} \sin \left (2 x \right )-10 \\ \end{align*}

0.668

11937

2261

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

0.668

11938

2543

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

0.668

11939

5216

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

0.668

11940

5593

\begin{align*} \left (x^{2}-4 y^{2}\right ) {y^{\prime }}^{2}+6 x y^{\prime } y-4 x^{2}+y^{2}&=0 \\ \end{align*}

0.668

11941

6284

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

0.668

11942

8600

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

0.668

11943

8656

\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=25 t -100 \delta \left (t -\pi \right ) \\ y \left (0\right ) &= -2 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}
Using Laplace transform method.

0.668

11944

9548

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

0.668

11945

9958

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

0.668

11946

10366

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

0.668

11947

16065

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

0.668

11948

16137

\begin{align*} y^{\prime \prime }+3 y&=\operatorname {Heaviside}\left (t -4\right ) \cos \left (5 t -20\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*}
Using Laplace transform method.

0.668

11949

16425

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

0.668

11950

18435

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

0.668

11951

19011

\begin{align*} x_{1}^{\prime }&=x_{1}+x_{2}+x_{3} \\ x_{2}^{\prime }&=2 x_{1}+x_{2}-x_{3} \\ x_{3}^{\prime }&=-8 x_{1}-5 x_{2}-3 x_{3} \\ \end{align*}

0.668

11952

19584

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

0.668

11953

20379

\begin{align*} y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=24 \cos \left (x \right ) x \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 12 \\ \end{align*}

0.668

11954

20871

\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=20 \,{\mathrm e}^{-2 x} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.668

11955

21272

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

0.668

11956

7958

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

0.669

11957

9414

\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 \(x=0\).

0.669

11958

18038

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

0.669

11959

20895

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

0.669

11960

21268

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

0.669

11961

23206

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

0.669

11962

7644

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

0.670

11963

9800

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

0.670

11964

10084

\begin{align*} y^{\prime \prime }-y^{\prime } x -y x -x^{4}-6&=0 \\ \end{align*}

0.670

11965

17493

\begin{align*} y^{\prime \prime }-6 y^{\prime }+34 y&={\mathrm e}^{3 t} \tan \left (5 t \right ) \\ \end{align*}

0.670

11966

17708

\begin{align*} \left (x^{2}-25\right )^{2} y^{\prime \prime }-\left (x +5\right ) y^{\prime }+10 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.670

11967

18309

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

0.670

11968

20207

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

0.670

11969

21923

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

0.670

11970

22092

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

0.670

11971

1949

\begin{align*} x^{2} \left (10 x^{2}+x +5\right ) y^{\prime \prime }+x \left (48 x^{2}+3 x +4\right ) y^{\prime }+\left (36 x^{2}+x \right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.671

11972

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 \(x=0\).

0.671

11973

2627

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

0.671

11974

10146

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

0.671

11975

12645

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

0.671

11976

14427

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

0.671

11977

14937

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

0.671

11978

15503

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

0.671

11979

16404

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

0.671

11980

22495

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

0.671

11981

24639

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

0.671

11982

24648

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

0.671

11983

837

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

0.672

11984

6340

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

0.672

11985

9884

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

0.672

11986

15274

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

0.672

11987

21518

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

0.672

11988

23544

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

0.672

11989

501

\begin{align*} 5 y^{\prime \prime } x +\left (30+3 x \right ) y^{\prime }+3 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.673

11990

1961

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

0.673

11991

18956

\begin{align*} 4 y^{\prime \prime }+4 y^{\prime }+17 y&=g \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.673

11992

19269

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

0.673

11993

20669

\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }-\left (4 x^{2}-3 x -5\right ) y^{\prime }+\left (4 x^{2}-6 x -5\right ) y&={\mathrm e}^{2 x} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}

0.673

11994

21526

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

0.673

11995

23730

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

0.673

11996

25378

\begin{align*} y_{1}^{\prime }&=-y_{1}+2 y_{2}+5 \\ y_{2}^{\prime }&=-2 y_{1}-y_{2} \\ \end{align*}
With initial conditions
\begin{align*} y_{1} \left (0\right ) &= 1 \\ y_{2} \left (0\right ) &= 0 \\ \end{align*}

0.673

11997

1942

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

0.674

11998

2453

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

0.674

11999

4482

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

0.674

12000

6745

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

0.674