2.3.119 Problems 11801 to 11900

Table 2.769: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

11801

10265

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

0.655

11802

18442

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

0.655

11803

19260

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

0.655

11804

21138

\begin{align*} x^{\prime \prime }-4 x^{\prime }+13 x&=20 \,{\mathrm e}^{t} \\ \end{align*}

0.655

11805

21650

\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-6 y^{\prime } x -4 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.655

11806

23249

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

0.655

11807

23901

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

0.655

11808

248

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

0.656

11809

6061

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

0.656

11810

6888

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

0.656

11811

19031

\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*}

0.656

11812

23508

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

0.656

11813

24916

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

0.656

11814

464

\begin{align*} \left (2 x^{3}+6 x^{2}\right ) y^{\prime \prime }+21 y^{\prime } x +9 \left (x^{2}-1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.657

11815

1995

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

0.657

11816

3181

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

0.657

11817

9645

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

0.657

11818

21140

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

0.657

11819

21933

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

0.657

11820

23231

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

0.657

11821

23822

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

0.657

11822

272

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

0.658

11823

986

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

0.658

11824

2188

\begin{align*} y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+13 y^{\prime \prime }-19 y^{\prime }+10 y&={\mathrm e}^{x} \left (\sin \left (2 x \right )+\cos \left (2 x \right )\right ) \\ \end{align*}

0.658

11825

2219

\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime }+2 y&=30 \cos \left (x \right )-10 \sin \left (x \right ) \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -4 \\ y^{\prime \prime }\left (0\right ) &= 16 \\ \end{align*}

0.658

11826

3139

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

0.658

11827

6380

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

0.658

11828

6516

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

0.658

11829

7195

\begin{align*} 2 \left (1-x \right ) x y^{\prime \prime }+\left (1-11 x \right ) y^{\prime }-10 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.658

11830

8421

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

0.658

11831

8590

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

0.658

11832

9760

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

0.658

11833

17506

\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&={\mathrm e}^{-2 t} \sqrt {-t^{2}+1} \\ \end{align*}

0.658

11834

18093

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

0.658

11835

21228

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

0.658

11836

22285

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

0.658

11837

22353

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

0.658

11838

24964

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

0.658

11839

385

\begin{align*} x^{\prime \prime }+100 x&=225 \cos \left (5 t \right )+300 \sin \left (5 t \right ) \\ x \left (0\right ) &= 375 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.659

11840

1960

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

0.659

11841

3151

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

0.659

11842

6568

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

0.659

11843

12649

\begin{align*} y^{\prime \prime }&=\frac {18 y}{\left (2 x +1\right )^{2} \left (x^{2}+x +1\right )} \\ \end{align*}

0.659

11844

19130

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

0.659

11845

20809

\begin{align*} 4 x^{\prime }+9 y^{\prime }+11 x+31 y&={\mathrm e}^{t} \\ 3 x^{\prime }+7 y^{\prime }+8 x+24 y&={\mathrm e}^{2 t} \\ \end{align*}

0.659

11846

21695

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

0.659

11847

23727

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

0.659

11848

24575

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

0.659

11849

890

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

0.660

11850

2436

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

0.660

11851

7902

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

0.660

11852

10192

\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*}
Series expansion around \(x=0\).

0.660

11853

12703

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

0.660

11854

16674

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=27 \,{\mathrm e}^{6 x}+25 \sin \left (6 x \right ) \\ \end{align*}

0.660

11855

17479

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

0.660

11856

19065

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

0.660

11857

20017

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

0.660

11858

21690

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

0.660

11859

25533

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

0.660

11860

2446

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

0.661

11861

3214

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

0.661

11862

6199

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

0.661

11863

9391

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

0.661

11864

12451

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

0.661

11865

14787

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

0.661

11866

16141

\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=\delta \left (t -3\right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

0.661

11867

16384

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

0.661

11868

16399

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

0.661

11869

18874

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

0.661

11870

22159

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

0.661

11871

984

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

0.662

11872

1618

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

0.662

11873

8518

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

0.662

11874

8910

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

0.662

11875

13664

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

0.662

11876

17882

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

0.662

11877

20657

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

0.662

11878

20709

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

0.662

11879

21663

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

0.662

11880

25218

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

0.662

11881

1951

\begin{align*} 18 x^{2} \left (x +1\right ) y^{\prime \prime }+3 x \left (x^{2}+11 x +5\right ) y^{\prime }-\left (-5 x^{2}-2 x +1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.663

11882

16646

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

0.663

11883

16647

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

0.663

11884

17681

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

0.663

11885

21654

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

0.663

11886

23747

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

0.663

11887

23792

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

0.663

11888

25349

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

0.663

11889

666

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

0.664

11890

1749

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

0.664

11891

2449

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

0.664

11892

3750

\begin{align*} y^{\prime \prime }+9 y&=\frac {36}{4-\cos \left (3 x \right )^{2}} \\ \end{align*}

0.664

11893

5507

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

0.664

11894

5690

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

0.664

11895

5939

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

0.664

11896

6537

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

0.664

11897

8987

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

0.664

11898

12564

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

0.664

11899

12613

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

0.664

11900

18933

\begin{align*} y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y&=1-\operatorname {Heaviside}\left (t -\pi \right ) \\ 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 ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.664