2.3.109 Problems 10801 to 10900

Table 2.749: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

10801

14408

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

0.572

10802

15106

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

0.572

10803

15236

\begin{align*} y^{\prime \prime }-2 y^{\prime }&=\left \{\begin {array}{cc} 4 & 0\le t <1 \\ 6 & 1\le t \end {array}\right . \\ y \left (0\right ) &= -6 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

0.572

10804

17464

\begin{align*} y^{\prime \prime }+6 y^{\prime }+25 y&=-1 \\ y \left (0\right ) &= -{\frac {1}{25}} \\ y^{\prime }\left (0\right ) &= 7 \\ \end{align*}

0.572

10805

19499

\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=14 \sin \left (2 x \right )-18 \cos \left (2 x \right ) \\ \end{align*}

0.572

10806

19656

\begin{align*} x^{\prime }&=4 x-3 y \\ y^{\prime }&=8 x-6 y \\ \end{align*}

0.572

10807

19880

\begin{align*} z^{\prime }+7 y-3 z&=0 \\ 7 y^{\prime }+63 y-36 z&=0 \\ \end{align*}

0.572

10808

25319

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=\delta \left (t -3\right ) \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= -3 \\ \end{align*}
Using Laplace transform method.

0.572

10809

25691

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

0.572

10810

499

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

0.573

10811

664

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

0.573

10812

3583

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

0.573

10813

4041

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

0.573

10814

6804

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

0.573

10815

8534

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

0.573

10816

9142

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

0.573

10817

9810

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

0.573

10818

10247

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

0.573

10819

15440

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

0.573

10820

15760

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

0.573

10821

15761

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

0.573

10822

17825

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

0.573

10823

19012

\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*}

0.573

10824

19554

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

0.573

10825

19626

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

0.573

10826

23529

\begin{align*} y^{\prime \prime }+10 y^{\prime }+25 y&=\frac {{\mathrm e}^{-5 x} \ln \left (x \right )}{x^{2}} \\ \end{align*}

0.573

10827

25808

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

0.573

10828

4037

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

0.574

10829

6119

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

0.574

10830

9388

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

0.574

10831

21223

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

0.574

10832

21966

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

0.574

10833

2278

\begin{align*} y_{1}^{\prime }&=-6 y_{1}-4 y_{2}-4 y_{3} \\ y_{2}^{\prime }&=2 y_{1}-y_{2}+y_{3} \\ y_{3}^{\prime }&=2 y_{1}+3 y_{2}+y_{3} \\ \end{align*}

0.575

10834

2405

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

0.575

10835

2706

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

0.575

10836

5645

\begin{align*} 8 {y^{\prime }}^{3}+12 {y^{\prime }}^{2}&=27 x +27 y \\ \end{align*}

0.575

10837

8505

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

0.575

10838

8516

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

0.575

10839

9784

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

0.575

10840

12911

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

0.575

10841

14974

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

0.575

10842

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 \(x=0\).

0.575

10843

17867

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

0.575

10844

18032

\begin{align*} 8 {y^{\prime }}^{3}-12 {y^{\prime }}^{2}&=27 y-27 x \\ \end{align*}

0.575

10845

18454

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

0.575

10846

20149

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

0.575

10847

20890

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

0.575

10848

23088

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

0.575

10849

25185

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

0.575

10850

25554

\begin{align*} y^{\prime \prime }+c y&={\mathrm e}^{i \omega t} \\ \end{align*}

0.575

10851

1358

\begin{align*} u^{\prime \prime }+\frac {u^{\prime }}{8}+4 u&=3 \cos \left (2 t \right ) \\ u \left (0\right ) &= 2 \\ u^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.576

10852

4018

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

0.576

10853

4088

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

0.576

10854

5999

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

0.576

10855

7620

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

0.576

10856

7664

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

0.576

10857

7807

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

0.576

10858

8331

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

0.576

10859

8537

\begin{align*} 16 x^{2} y^{\prime \prime }+16 y^{\prime } x +\left (16 x^{2}-1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.576

10860

10168

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

0.576

10861

16911

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

0.576

10862

16949

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

0.576

10863

18265

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

0.576

10864

19638

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

0.576

10865

1792

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

0.577

10866

2442

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

0.577

10867

4564

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

0.577

10868

5724

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

0.577

10869

6471

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

0.577

10870

9238

\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime } x -12 y&=0 \\ \end{align*}

0.577

10871

12368

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

0.577

10872

500

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

0.578

10873

1614

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

0.578

10874

3215

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

0.578

10875

6405

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

0.578

10876

8137

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

0.578

10877

8605

\begin{align*} 9 x^{2} y^{\prime \prime }+9 y^{\prime } x +\left (36 x^{4}-16\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.578

10878

9676

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

0.578

10879

18895

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

0.578

10880

21632

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

0.578

10881

25300

\begin{align*} y^{\prime \prime }+9 y&=\operatorname {Heaviside}\left (t -3\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.578

10882

1034

\begin{align*} x_{1}^{\prime }&=-3 x_{1}+5 x_{2}-5 x_{3} \\ x_{2}^{\prime }&=3 x_{1}-x_{2}+3 x_{3} \\ x_{3}^{\prime }&=8 x_{1}-8 x_{2}+10 x_{3} \\ \end{align*}

0.579

10883

1974

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

0.579

10884

1983

\begin{align*} 2 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (8 x^{2}+3\right ) y^{\prime }-\left (-4 x^{2}+3\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.579

10885

3167

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

0.579

10886

4179

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

0.579

10887

5529

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

0.579

10888

6120

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

0.579

10889

6128

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

0.579

10890

6558

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

0.579

10891

7674

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

0.579

10892

8479

\begin{align*} \left (x^{2}-2 x +10\right ) y^{\prime \prime }+y^{\prime } x -4 y&=0 \\ \end{align*}
Series expansion around \(x=1\).

0.579

10893

8501

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

0.579

10894

8520

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

0.579

10895

8647

\begin{align*} y^{\prime \prime }+4 y&=\delta \left (t -\pi \right ) \\ y \left (0\right ) &= 8 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.579

10896

9180

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

0.579

10897

9517

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

0.579

10898

10169

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

0.579

10899

12501

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

0.579

10900

14361

\begin{align*} x^{\prime \prime }+4 x&=\cos \left (2 t \right ) \operatorname {Heaviside}\left (2 \pi -t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.579