2.3.109 Problems 10801 to 10900

Table 2.791: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

10801

24606

\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=7+{\mathrm e}^{x}+{\mathrm e}^{2 x} \\ \end{align*}

0.828

10802

1345

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

0.829

10803

1632

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

0.829

10804

1985

\begin{align*} 6 x^{2} y^{\prime \prime }+x \left (6 x^{2}+1\right ) y^{\prime }+\left (9 x^{2}+1\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.829

10805

3723

\begin{align*} y^{\prime \prime }+9 y&=5 \cos \left (2 x \right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}

0.829

10806

6436

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

0.829

10807

8477

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

Series expansion around \(x=1\).

0.829

10808

9511

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

Series expansion around \(x=0\).

0.829

10809

10944

\begin{align*} \left (2 x^{5}+1\right ) y^{\prime \prime }+14 x^{4} y^{\prime }+10 x^{3} y&=0 \\ \end{align*}

0.829

10810

14939

\begin{align*} x^{\prime \prime }+2 x^{\prime }+10 x&={\mathrm e}^{-t} \\ \end{align*}

0.829

10811

14940

\begin{align*} x^{\prime \prime }+2 x^{\prime }+10 x&={\mathrm e}^{-t} \cos \left (3 t \right ) \\ \end{align*}

0.829

10812

15777

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

0.829

10813

16872

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

Series expansion around \(x=1\).

0.829

10814

17835

\begin{align*} x^{\prime \prime }+16 x&=t \sin \left (t \right ) \\ \end{align*}

0.829

10815

24757

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

0.829

10816

24764

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

0.829

10817

26029

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

Series expansion around \(x=0\).

0.829

10818

26962

\begin{align*} y^{\prime \prime }+9 y&=12 \sec \left (3 x \right ) \\ \end{align*}

0.829

10819

1987

\begin{align*} 9 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+3 x \left (13 x^{2}+3\right ) y^{\prime }-\left (-25 x^{2}+1\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.830

10820

4502

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

0.830

10821

9796

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

0.830

10822

14737

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

Series expansion around \(x=0\).

0.830

10823

15806

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

0.830

10824

20898

\begin{align*} \frac {y^{\prime \prime }}{x}+\frac {3 \left (x -4\right ) y^{\prime }}{6+x}+\frac {x^{2} \left (x -2\right ) y}{x -1}&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.830

10825

616

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

With initial conditions

\begin{align*} x_{1} \left (0\right ) &= 0 \\ x_{2} \left (0\right ) &= 0 \\ x_{3} \left (0\right ) &= 4 \\ \end{align*}

0.831

10826

7355

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

0.831

10827

12493

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

0.831

10828

20537

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

0.831

10829

23676

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

Series expansion around \(x=0\).

0.831

10830

27691

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

0.831

10831

2181

\begin{align*} y^{\prime \prime \prime }-7 y^{\prime \prime }+20 y^{\prime }-24 y&=-{\mathrm e}^{2 x} \left (\left (13-8 x \right ) \cos \left (2 x \right )-\left (8-4 x \right ) \sin \left (2 x \right )\right ) \\ \end{align*}

0.832

10832

3851

\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*}

With initial conditions

\begin{align*} x_{1} \left (0\right ) &= -4 \\ x_{2} \left (0\right ) &= 4 \\ x_{3} \left (0\right ) &= 4 \\ \end{align*}

0.832

10833

14805

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

N/A

N/A

N/A

0.832

10834

18269

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

0.832

10835

18327

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

0.832

10836

18433

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

0.832

10837

18853

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

0.832

10838

20735

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

0.832

10839

21778

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

0.832

10840

23921

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

0.832

10841

24068

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

0.832

10842

25973

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

0.832

10843

26981

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

0.832

10844

2270

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

With initial conditions

\begin{align*} y_{1} \left (0\right ) &= 6 \\ y_{2} \left (0\right ) &= 5 \\ y_{3} \left (0\right ) &= -7 \\ \end{align*}

0.833

10845

4157

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

0.833

10846

5406

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

0.833

10847

7083

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

0.833

10848

9372

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

Series expansion around \(x=0\).

0.833

10849

10456

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

0.833

10850

11775

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

0.833

10851

14607

\begin{align*} y^{\prime \prime }+6 y^{\prime }+58 y&=0 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}

0.833

10852

17298

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

0.833

10853

17724

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

Series expansion around \(x=0\).

0.833

10854

21216

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

0.833

10855

27152

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

With initial conditions

\begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 7 \\ x_{3} \left (0\right ) &= 3 \\ \end{align*}

0.833

10856

474

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

Series expansion around \(x=0\).

0.834

10857

4406

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

0.834

10858

9679

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

0.834

10859

22733

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

0.834

10860

24703

\begin{align*} y^{\prime \prime }+16 y&=8 x +8 \sin \left (4 x \right ) \\ \end{align*}

0.834

10861

25600

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

0.834

10862

1353

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

0.835

10863

1494

\begin{align*} y^{\prime \prime }+y&=\left \{\begin {array}{cc} t & 0\le t <1 \\ 2-t & 1\le t <2 \\ 0 & 2\le t <\infty \end {array}\right . \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

0.835

10864

1495

\begin{align*} y^{\prime \prime }+y&=\left \{\begin {array}{cc} 1 & 0\le t <3 \pi \\ 0 & 3 \pi \le t <\infty \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

Using Laplace transform method.

0.835

10865

1979

\begin{align*} 2 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+5 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-40 x^{2}+2\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.835

10866

2048

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

Series expansion around \(x=0\).

0.835

10867

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*}

0.835

10868

4052

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

Series expansion around \(x=0\).

0.835

10869

5731

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

0.835

10870

6724

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

0.835

10871

19731

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

0.835

10872

20505

\begin{align*} y+3 x y^{\prime }+9 x^{2} y^{\prime \prime }+6 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime }&=4 x \\ \end{align*}

0.835

10873

21155

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

0.835

10874

22769

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

0.835

10875

23621

\begin{align*} x^{\prime }&=-10 x+y+7 z \\ y^{\prime }&=-9 x+4 y+5 z \\ z^{\prime }&=-17 x+y+12 z \\ \end{align*}

0.835

10876

26128

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

0.835

10877

509

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

Series expansion around \(x=0\).

0.836

10878

846

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

0.836

10879

1813

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

0.836

10880

2017

\begin{align*} 25 x^{2} y^{\prime \prime }+x \left (15+x \right ) y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.836

10881

5804

\begin{align*} 20 y-9 y^{\prime }+y^{\prime \prime }&=x^{2} {\mathrm e}^{3 x} \\ \end{align*}

0.836

10882

6728

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

0.836

10883

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*}

0.836

10884

17337

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

0.836

10885

18455

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

0.836

10886

19426

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

0.836

10887

20946

\begin{align*} x^{\prime }&=5 x+3 y+1 \\ y^{\prime }&=-6 x-4 y+{\mathrm e}^{t} \\ \end{align*}

With initial conditions

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

0.836

10888

27525

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

0.836

10889

1986

\begin{align*} x^{2} \left (x^{2}+8\right ) y^{\prime \prime }+7 x \left (x^{2}+2\right ) y^{\prime }-\left (-9 x^{2}+2\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.837

10890

2018

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

Series expansion around \(x=0\).

0.837

10891

4156

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

0.837

10892

5392

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

0.837

10893

14134

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

0.837

10894

14634

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

0.837

10895

19263

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

0.837

10896

22912

\begin{align*} x^{\prime }+6 x+3 y^{\prime }+2 y&=0 \\ x^{\prime }+5 x+2 y^{\prime }+3 y&=0 \\ \end{align*}

With initial conditions

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

0.837

10897

24100

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

Series expansion around \(x=0\).

0.837

10898

12434

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

0.838

10899

13202

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

0.838

10900

20669

\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }-\left (4 x^{2}-3 x -5\right ) y^{\prime }+\left (4 x^{2}-6 x -5\right ) y&={\mathrm e}^{2 x} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}

0.838