2.3.119 Problems 11801 to 11900

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

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

11801

18120

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

0.954

11802

21592

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

0.954

11803

23051

\begin{align*} y^{\prime \prime }-4 y^{\prime }&=7 \\ \end{align*}

0.954

11804

27783

\begin{align*} y^{\prime \prime }-y^{\prime }-y&=\frac {2 \sin \left (x \right )}{5-4 \cos \left (x \right )} \\ \end{align*}

Series expansion around \(x=0\).

0.954

11805

8277

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

0.955

11806

8945

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

0.955

11807

16839

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

Series expansion around \(x=0\).

0.955

11808

17710

\begin{align*} 5 x y^{\prime \prime }+8 y^{\prime }-y x&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.955

11809

18644

\begin{align*} x^{\prime }&=-2 x+y-11 \\ y^{\prime }&=-5 x+4 y-35 \\ \end{align*}

0.955

11810

18682

\begin{align*} x^{\prime }&=4 x+a y \\ y^{\prime }&=8 x-6 y \\ \end{align*}

0.955

11811

22276

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

With initial conditions

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

0.955

11812

24628

\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=4 x -6 \,{\mathrm e}^{-2 x}+3 \,{\mathrm e}^{x} \\ \end{align*}

0.955

11813

9189

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

0.956

11814

14618

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

0.956

11815

14645

\begin{align*} y^{\prime \prime }+7 y^{\prime }+10 y&=4 x \,{\mathrm e}^{-3 x} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}

0.956

11816

15008

\begin{align*} x^{\prime }&=7 x-5 y \\ y^{\prime }&=10 x-3 y \\ \end{align*}

0.956

11817

15334

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

0.956

11818

2588

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

0.957

11819

10033

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

0.957

11820

14672

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

0.957

11821

19666

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

0.957

11822

20364

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

0.957

11823

22744

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

0.957

11824

26628

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

0.957

11825

1516

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

Using Laplace transform method.

0.958

11826

1997

\begin{align*} 4 x^{2} \left (x^{2}+2 x +3\right ) y^{\prime \prime }-x \left (-15 x^{2}-14 x +3\right ) y^{\prime }+\left (7 x^{2}+3\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.958

11827

5408

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

0.958

11828

7324

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

0.958

11829

9852

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

Series expansion around \(x=0\).

0.958

11830

12639

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

0.958

11831

19704

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

0.958

11832

8557

\begin{align*} 4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (16 x^{4}+3\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.959

11833

22937

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

With initial conditions

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

0.959

11834

24849

\begin{align*} 5 {y^{\prime }}^{2}+6 x y^{\prime }-2 y&=0 \\ \end{align*}

0.959

11835

2587

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

0.960

11836

2651

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

Series expansion around \(t=0\).

0.960

11837

3352

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

Series expansion around \(x=0\).

0.960

11838

6676

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

0.960

11839

9829

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

0.960

11840

17514

\begin{align*} y^{\prime \prime }+9 y&=\tan \left (3 t \right ) \\ \end{align*}

0.960

11841

1964

\begin{align*} x^{2} \left (4 x +3\right ) y^{\prime \prime }+x \left (5+18 x \right ) y^{\prime }-\left (1-12 x \right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.961

11842

5890

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

0.961

11843

6851

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

0.961

11844

8550

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

Series expansion around \(x=0\).

0.961

11845

11365

\begin{align*} y^{\prime }-\sqrt {\frac {a y^{2}+b y+c}{a \,x^{2}+b x +c}}&=0 \\ \end{align*}

0.961

11846

23052

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

0.961

11847

24551

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

0.961

11848

26182

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

0.961

11849

12663

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

0.962

11850

22186

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

Series expansion around \(x=-1\).

0.962

11851

166

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

0.963

11852

1943

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

Series expansion around \(x=0\).

0.963

11853

2446

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

Series expansion around \(t=0\).

0.963

11854

3512

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

Series expansion around \(z=0\).

0.963

11855

6331

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

0.963

11856

8598

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

Series expansion around \(x=0\).

0.963

11857

12575

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

0.963

11858

22205

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

Series expansion around \(x=0\).

0.963

11859

2078

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

Series expansion around \(x=0\).

0.964

11860

8007

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

0.964

11861

8384

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

0.964

11862

14676

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

0.964

11863

17775

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

0.964

11864

21757

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

0.964

11865

23622

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

0.964

11866

24635

\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=48 \,{\mathrm e}^{-x} \cos \left (4 x \right ) \\ \end{align*}

0.964

11867

24900

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

0.964

11868

1967

\begin{align*} x^{2} \left (4 x +3\right ) y^{\prime \prime }+x \left (11+4 x \right ) y^{\prime }-\left (4 x +3\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.965

11869

14204

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

0.965

11870

20584

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

0.965

11871

8202

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

0.966

11872

9841

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

Series expansion around \(x=0\).

0.966

11873

12475

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

0.966

11874

14728

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

Series expansion around \(x=0\).

0.966

11875

23367

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

0.966

11876

27221

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

0.966

11877

2763

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

With initial conditions

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

0.967

11878

4072

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

Series expansion around \(x=0\).

0.967

11879

8994

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

Series expansion around \(x=0\).

0.967

11880

16913

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

Series expansion around \(x=3\).

0.967

11881

24888

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

0.967

11882

837

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

0.968

11883

6509

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

0.968

11884

11791

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

0.968

11885

18202

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

0.968

11886

3361

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

Series expansion around \(x=0\).

0.969

11887

3630

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

0.969

11888

7949

\begin{align*} 16 y^{3} {y^{\prime }}^{2}-4 x y^{\prime }+y&=0 \\ \end{align*}

0.969

11889

8589

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

Series expansion around \(x=0\).

0.969

11890

9388

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

Series expansion around \(x=0\).

0.969

11891

12518

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

0.969

11892

16991

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

0.969

11893

24864

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

0.969

11894

1493

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

Using Laplace transform method.

0.970

11895

2730

\begin{align*} x_{1}^{\prime }&=7 x_{1}-x_{2}+6 x_{3} \\ x_{2}^{\prime }&=-10 x_{1}+4 x_{2}-12 x_{3} \\ x_{3}^{\prime }&=-2 x_{1}+x_{2}-x_{3} \\ \end{align*}

0.970

11896

3684

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

0.970

11897

4548

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

0.970

11898

5734

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

0.970

11899

20526

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

0.970

11900

22745

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

0.970