2.3.109 Problems 10801 to 10900

Table 2.761: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

10801

2274

\begin{align*} y_{1}^{\prime }&=4 y_{1}-8 y_{2}-4 y_{3} \\ y_{2}^{\prime }&=-3 y_{1}-y_{2}-4 y_{3} \\ y_{3}^{\prime }&=y_{1}-y_{2}+9 y_{3} \\ \end{align*}
With initial conditions
\begin{align*} y_{1} \left (0\right ) &= -4 \\ y_{2} \left (0\right ) &= 1 \\ y_{3} \left (0\right ) &= -3 \\ \end{align*}

0.774

10802

2731

\begin{align*} x_{1}^{\prime }&=-7 x_{1}+6 x_{3} \\ x_{2}^{\prime }&=5 x_{2} \\ x_{3}^{\prime }&=6 x_{1}+2 x_{3} \\ \end{align*}

0.774

10803

6403

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

0.774

10804

6516

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

0.774

10805

10057

\begin{align*} x^{\prime }&=9 x+4 y \\ y^{\prime }&=-6 x-y \\ z^{\prime }&=6 x+4 y+3 z \\ \end{align*}

0.774

10806

14792

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

0.774

10807

19600

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

0.774

10808

21762

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

0.774

10809

22853

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

0.774

10810

22921

\begin{align*} 2 x^{\prime }-6 x+3 y^{\prime }-2 y&=0 \\ 7 x^{\prime }+4 x+7 y^{\prime }+20 y&=0 \\ \end{align*}

0.774

10811

989

\begin{align*} x_{1}^{\prime }&=5 x_{1}+5 x_{2}+2 x_{3} \\ x_{2}^{\prime }&=-6 x_{1}-6 x_{2}-5 x_{3} \\ x_{3}^{\prime }&=6 x_{1}+6 x_{2}+5 x_{3} \\ \end{align*}

0.775

10812

2205

\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+7 y^{\prime \prime }-6 y^{\prime }+2 y&={\mathrm e}^{x} \left (12 x -2 \cos \left (x \right )+2 \sin \left (x \right )\right ) \\ \end{align*}

0.775

10813

6405

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

0.775

10814

6434

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

0.775

10815

6480

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

0.775

10816

12406

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

0.775

10817

12660

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

0.775

10818

16943

\begin{align*} x^{\prime }&=8 x+2 y+7 \,{\mathrm e}^{2 t} \\ y^{\prime }&=4 x+y-7 \,{\mathrm e}^{2 t} \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= -1 \\ y \left (0\right ) &= 1 \\ \end{align*}

0.775

10819

1962

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

0.776

10820

1965

\begin{align*} 6 x^{2} y^{\prime \prime }+x \left (10-x \right ) y^{\prime }-\left (2+x \right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.776

10821

2250

\begin{align*} y_{1}^{\prime }&=-2 y_{1}+2 y_{2}-6 y_{3} \\ y_{2}^{\prime }&=2 y_{1}+6 y_{2}+2 y_{3} \\ y_{3}^{\prime }&=-2 y_{1}-2 y_{2}+2 y_{3} \\ \end{align*}

0.776

10822

2626

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

0.776

10823

9570

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (25 x^{2}-\frac {4}{9}\right ) y&=0 \\ \end{align*}

0.776

10824

9901

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

0.776

10825

14620

\begin{align*} 5 y+2 y^{\prime }+y^{\prime \prime }&=6 \sin \left (2 x \right )+7 \cos \left (2 x \right ) \\ \end{align*}

0.776

10826

17003

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

0.776

10827

19917

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

0.776

10828

16870

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

0.777

10829

16945

\begin{align*} x^{\prime }&=-y \\ y^{\prime }&=4 x+24 t \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 0 \\ \end{align*}

0.777

10830

4071

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

0.778

10831

5889

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

0.778

10832

6541

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

0.778

10833

9027

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

0.778

10834

9426

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

0.778

10835

15000

\begin{align*} x^{\prime }&=8 x+14 y \\ y^{\prime }&=7 x+y \\ \end{align*}

0.778

10836

17358

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

0.778

10837

21703

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

0.778

10838

23985

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

0.778

10839

25340

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

0.778

10840

3222

\begin{align*} 4 x^{2} y^{\prime \prime }-16 y^{\prime } x +25 y&=0 \\ \end{align*}

0.779

10841

8519

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

0.779

10842

8588

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

0.779

10843

10153

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

0.779

10844

11733

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

0.779

10845

11778

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

0.779

10846

14404

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

0.779

10847

18438

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

0.779

10848

21119

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

0.779

10849

23509

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

0.779

10850

23571

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

0.779

10851

3393

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

0.780

10852

3483

\begin{align*} x^{\prime \prime }+\omega _{0}^{2} x&=a \cos \left (\omega t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.780

10853

6043

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

0.780

10854

18031

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

0.780

10855

19156

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

0.780

10856

21699

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

0.780

10857

21944

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

0.780

10858

25345

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

0.780

10859

6333

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

0.781

10860

8586

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

0.781

10861

21567

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

0.781

10862

23790

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

0.781

10863

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*}

0.781

10864

1386

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

0.782

10865

2786

\begin{align*} x_{1}^{\prime }&=x_{1} \\ x_{2}^{\prime }&=2 x_{1}+x_{2}-2 x_{3} \\ x_{3}^{\prime }&=3 x_{1}+2 x_{2}+x_{3}+{\mathrm e}^{t} \cos \left (2 t \right ) \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= 0 \\ x_{2} \left (0\right ) &= 1 \\ x_{3} \left (0\right ) &= 1 \\ \end{align*}

0.782

10866

6542

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

0.782

10867

6719

\begin{align*} 10 x^{2} y^{\prime }+8 x^{3} y^{\prime \prime }+x^{2} \left (x^{2}+1\right ) y^{\prime \prime \prime }&=-1+3 x^{2}+2 \ln \left (x \right ) x^{2} \\ \end{align*}

0.782

10868

8394

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

0.782

10869

9877

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

0.782

10870

13932

\begin{align*} b \,{\mathrm e}^{2 a x} y+a y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}

0.782

10871

14390

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

0.782

10872

26182

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

0.782

10873

1346

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

0.783

10874

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 \(x=0\).

0.783

10875

2664

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

0.783

10876

2717

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

0.783

10877

3830

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

0.783

10878

4487

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

0.783

10879

13171

\(\left [\begin {array}{cccc} 22 & -9 & -8 & -8 \\ 10 & -7 & -14 & 2 \\ 10 & 0 & 8 & -10 \\ 29 & -9 & -3 & -15 \end {array}\right ]\)

N/A

N/A

N/A

0.783

10880

15549

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

0.783

10881

16949

\begin{align*} x^{\prime }&=2 x-5 y \\ y^{\prime }&=3 x-7 y \\ \end{align*}

0.783

10882

19032

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

0.783

10883

19149

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

0.783

10884

20145

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

0.783

10885

4540

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

0.784

10886

7178

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

0.784

10887

8049

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

0.784

10888

8327

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

0.784

10889

9374

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

0.784

10890

9893

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

0.784

10891

14307

\begin{align*} x^{\prime \prime }+7 x&=t \,{\mathrm e}^{3 t} \\ \end{align*}

0.784

10892

20530

\begin{align*} x^{5} y^{\left (6\right )}+x^{4} y^{\left (5\right )}+y^{\prime } x +y&=\ln \left (x \right ) \\ \end{align*}

0.784

10893

2249

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

0.785

10894

8171

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

0.785

10895

11385

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

0.785

10896

14609

\begin{align*} 5 y+2 y^{\prime }+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 6 \\ \end{align*}

0.785

10897

14805

\(\left [\begin {array}{ccc} 1 & 3 & -6 \\ 0 & 2 & 2 \\ 0 & -1 & 5 \end {array}\right ]\)

N/A

N/A

N/A

0.785

10898

15765

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

0.785

10899

19043

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

0.785

10900

21330

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

0.785