2.3.111 Problems 11001 to 11100

Table 2.795: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

11001

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*}

0.852

11002

1429

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

0.852

11003

1989

\begin{align*} 8 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+2 x \left (34 x^{2}+5\right ) y^{\prime }-\left (-30 x^{2}+1\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.852

11004

2738

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

With initial conditions

\begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 4 \\ x_{3} \left (0\right ) &= -7 \\ \end{align*}

0.852

11005

4023

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

Series expansion around \(x=0\).

0.852

11006

8103

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

Series expansion around \(x=0\).

0.852

11007

9326

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

0.852

11008

9785

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

0.852

11009

10082

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

0.852

11010

10088

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

0.852

11011

11757

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

0.852

11012

14930

\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 27 \\ y^{\prime }\left (0\right ) &= -54 \\ \end{align*}

0.852

11013

16403

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

0.852

11014

16591

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=169 \sin \left (2 x \right ) \\ y \left (0\right ) &= -10 \\ y^{\prime }\left (0\right ) &= 9 \\ \end{align*}

0.852

11015

18668

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

0.852

11016

22650

\begin{align*} s^{\prime \prime }+16 s^{\prime }+64 s&=0 \\ s \left (0\right ) &= 0 \\ s^{\prime }\left (0\right ) &= -4 \\ \end{align*}

0.852

11017

26064

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

0.852

11018

5735

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

0.853

11019

9850

\begin{align*} 2 y^{\prime \prime }+9 x y^{\prime }-36 y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.853

11020

14674

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

0.853

11021

15768

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

0.853

11022

19203

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

0.853

11023

21227

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

0.853

11024

25749

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

0.853

11025

3380

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

Series expansion around \(x=0\).

0.854

11026

15260

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

0.854

11027

20370

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

0.854

11028

20857

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

0.854

11029

504

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

Series expansion around \(x=0\).

0.855

11030

1992

\begin{align*} 28 x^{2} \left (-3 x +1\right ) y^{\prime \prime }-7 x \left (5+9 x \right ) y^{\prime }+7 \left (2+9 x \right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.855

11031

2014

\begin{align*} 36 x^{2} \left (1-2 x \right ) y^{\prime \prime }+24 x \left (1-9 x \right ) y^{\prime }+\left (1-70 x \right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.855

11032

9183

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

0.855

11033

10084

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

0.855

11034

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*}

0.855

11035

473

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

Series expansion around \(x=0\).

0.856

11036

499

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

Series expansion around \(x=0\).

0.856

11037

505

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

Series expansion around \(x=0\).

0.856

11038

3165

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

0.856

11039

3283

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

0.856

11040

3365

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

Series expansion around \(x=0\).

0.856

11041

4485

\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=5 \cos \left (x \right )+10 \sin \left (2 x \right ) \\ \end{align*}

0.856

11042

6923

\begin{align*} 3 x^{2} y+8 x y^{2}+\left (x^{3}+8 x^{2} y+12 y^{2}\right ) y^{\prime }&=0 \\ \end{align*}

0.856

11043

14312

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

0.856

11044

15573

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

0.856

11045

18911

\begin{align*} y_{1}^{\prime }&=5 y_{1}-2 y_{2} \\ y_{2}^{\prime }&=6 y_{1}-2 y_{2} \\ \end{align*}

With initial conditions

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

0.856

11046

21944

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

0.856

11047

26474

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

0.856

11048

9595

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

Series expansion around \(x=1\).

0.857

11049

9779

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

0.857

11050

12526

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

0.857

11051

15436

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

0.857

11052

22141

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

0.857

11053

23284

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

0.857

11054

988

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

0.858

11055

3740

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

0.858

11056

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*}

0.858

11057

4540

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

0.858

11058

8942

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

0.858

11059

9833

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

Series expansion around \(x=0\).

0.858

11060

18313

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

0.858

11061

18888

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

Using Laplace transform method.

0.858

11062

19605

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

Series expansion around \(x=0\).

0.858

11063

20999

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

0.858

11064

22887

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

With initial conditions

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

0.858

11065

23764

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

0.858

11066

26045

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

0.858

11067

1954

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

Series expansion around \(x=0\).

0.859

11068

2019

\begin{align*} x^{2} \left (9+4 x \right ) y^{\prime \prime }+3 x y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.859

11069

5966

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

0.859

11070

8066

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

0.859

11071

9260

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

0.859

11072

16899

\begin{align*} \left (-9 x^{4}+x^{2}\right ) y^{\prime \prime }-6 x y^{\prime }+10 y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.859

11073

16909

\begin{align*} \left (9 x^{3}+9 x^{2}\right ) y^{\prime \prime }+\left (27 x^{2}+9 x \right ) y^{\prime }+\left (8 x -1\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.859

11074

18667

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

0.859

11075

20872

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

0.859

11076

22221

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

Series expansion around \(x=0\).

0.859

11077

22724

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

0.859

11078

23680

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

Series expansion around \(x=0\).

0.859

11079

1972

\begin{align*} 8 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x \left (-13 x^{2}+1\right ) y^{\prime }+\left (-9 x^{2}+1\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.860

11080

8520

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

Series expansion around \(x=0\).

0.860

11081

14621

\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=10 \sin \left (4 x \right ) \\ \end{align*}

0.860

11082

22703

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

0.860

11083

22915

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

0.860

11084

26034

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

Series expansion around \(x=0\).

0.860

11085

27777

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

Series expansion around \(x=0\).

0.860

11086

2180

\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+2 y&={\mathrm e}^{x} \left (\left (20+4 x \right ) \cos \left (x \right )-\left (12+12 x \right ) \sin \left (x \right )\right ) \\ \end{align*}

0.861

11087

2665

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

Series expansion around \(t=0\).

0.861

11088

8011

\begin{align*} y^{\prime \prime }+y^{\prime }+y&={\mathrm e}^{3 x}+6 \,{\mathrm e}^{x}-3 \,{\mathrm e}^{-2 x}+5 \\ \end{align*}

0.861

11089

8971

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

Series expansion around \(x=0\).

0.861

11090

9839

\begin{align*} \left (x^{2}-9\right ) y^{\prime \prime }+3 x y^{\prime }-3 y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.861

11091

16266

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

0.861

11092

16880

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

Series expansion around \(x=0\).

0.861

11093

18915

\begin{align*} y_{1}^{\prime }&=2 y_{1}-64 y_{2} \\ y_{2}^{\prime }&=y_{1}-14 y_{2} \\ \end{align*}

With initial conditions

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

0.861

11094

23108

\begin{align*} m s^{\prime \prime }&=\frac {g \,t^{2}}{2} \\ \end{align*}

0.861

11095

157

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

0.862

11096

1958

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

Series expansion around \(x=0\).

0.862

11097

1977

\begin{align*} 2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }-x \left (-7 x^{2}+12\right ) y^{\prime }+\left (3 x^{2}+7\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.862

11098

2100

\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (11 x^{2}+5\right ) y^{\prime }+24 x^{2} y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.862

11099

10271

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

0.862

11100

14207

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

0.862