2.3.119 Problems 11801 to 11900

Table 2.781: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

11801

1946

\begin{align*} x^{2} \left (x^{2}+3 x +3\right ) y^{\prime \prime }+x \left (7 x^{2}+8 x +5\right ) y^{\prime }-\left (-9 x^{2}-2 x +1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.908

11802

12853

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

0.908

11803

14400

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

0.908

11804

23809

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

0.908

11805

8208

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

0.909

11806

10343

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

0.909

11807

23694

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

0.909

11808

5821

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

0.910

11809

9267

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

0.910

11810

16012

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

0.910

11811

19858

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

0.910

11812

21635

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

0.910

11813

23821

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

0.910

11814

23983

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

0.910

11815

3965

\begin{align*} y^{\prime \prime }+y&=t -\operatorname {Heaviside}\left (t -1\right ) \left (t -1\right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

0.911

11816

4567

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

0.911

11817

7642

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

0.911

11818

9542

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

0.911

11819

16608

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

0.911

11820

18866

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

0.911

11821

22916

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

0.911

11822

6348

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

0.912

11823

14605

\begin{align*} 9 y^{\prime \prime }-6 y^{\prime }+y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}

0.912

11824

15166

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

0.912

11825

25335

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

0.912

11826

1851

\begin{align*} x^{2} \left (1+3 x \right ) y^{\prime \prime }+x \left (x^{2}+12 x +2\right ) y^{\prime }+2 x \left (x +3\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.913

11827

2026

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

0.913

11828

7769

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

0.913

11829

8508

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

0.913

11830

13723

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

0.913

11831

9408

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

0.914

11832

16040

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

0.914

11833

4140

\begin{align*} y^{\prime \prime }+2 n y^{\prime }+n^{2} y&=A \cos \left (p x \right ) \\ y \left (0\right ) &= 9 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.915

11834

5607

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

0.915

11835

23433

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

0.915

11836

23832

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

0.915

11837

23939

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

0.915

11838

8032

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

0.916

11839

9668

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

0.916

11840

17795

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

0.916

11841

2719

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

0.917

11842

9350

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

0.917

11843

16911

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

0.917

11844

20605

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

0.917

11845

21173

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

0.917

11846

22905

\begin{align*} x^{\prime }-3 x-6 y&=27 t^{2} \\ x^{\prime }+y^{\prime }-3 y&=5 \,{\mathrm e}^{t} \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 5 \\ y \left (0\right ) &= -1 \\ \end{align*}

0.917

11847

24808

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

0.917

11848

8216

\begin{align*} x^{\prime \prime }+x&=0 \\ x \left (\frac {\pi }{6}\right ) &= {\frac {1}{2}} \\ x^{\prime }\left (\frac {\pi }{6}\right ) &= 0 \\ \end{align*}

0.918

11849

9963

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

0.918

11850

20204

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

0.918

11851

23062

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

0.918

11852

2806

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

0.919

11853

4022

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

0.919

11854

7690

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

0.919

11855

8033

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

0.919

11856

14602

\begin{align*} 9 y+6 y^{\prime }+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -3 \\ \end{align*}

0.919

11857

19604

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

0.919

11858

23702

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

0.919

11859

2648

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

0.920

11860

7622

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

0.920

11861

8273

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

0.920

11862

9902

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

0.920

11863

10211

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

0.920

11864

21621

\begin{align*} \theta ^{\prime \prime }+4 \theta &=15 \cos \left (3 t \right ) \\ \theta \left (0\right ) &= 0 \\ \theta ^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.920

11865

21741

\begin{align*} x^{\prime }&=7 x-y+6 z \\ y^{\prime }&=-10 x+4 y-12 z \\ z^{\prime }&=-2 x+y-z \\ \end{align*}

0.920

11866

2742

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

0.921

11867

4010

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

0.921

11868

5414

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

0.921

11869

16905

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

0.921

11870

21614

\begin{align*} \left (x^{2}-x \right ) y^{\prime \prime }+\left (2 x^{2}+4 x -3\right ) y^{\prime }+8 y x&=1 \\ \end{align*}

0.921

11871

23988

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

0.921

11872

3221

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

0.922

11873

3586

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

0.922

11874

6952

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

0.922

11875

15750

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

0.922

11876

16393

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

0.922

11877

16396

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

0.922

11878

2407

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

0.923

11879

16441

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

0.923

11880

17446

\begin{align*} y^{\prime \prime }-9 y&=54 t \sin \left (2 t \right ) \\ \end{align*}

0.923

11881

22832

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

0.923

11882

2646

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

0.924

11883

4548

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

0.924

11884

6407

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

0.924

11885

9551

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

0.924

11886

9556

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

0.924

11887

10368

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

0.924

11888

15888

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

0.924

11889

20640

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

0.924

11890

2650

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

0.925

11891

13793

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

0.925

11892

15051

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

0.926

11893

2003

\begin{align*} x^{2} \left (2 x^{2}+x +1\right ) y^{\prime \prime }+x \left (7 x^{2}+6 x +3\right ) y^{\prime }+\left (-3 x^{2}+6 x +1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.927

11894

10043

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

0.927

11895

15661

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

0.927

11896

23625

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

0.927

11897

23704

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

0.927

11898

23823

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

0.927

11899

9208

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

0.928

11900

10218

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

0.928