2.3.129 Problems 12801 to 12900

Table 2.789: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

12801

1968

\begin{align*} 2 x^{2} \left (3 x +2\right ) y^{\prime \prime }+x \left (4+11 x \right ) y^{\prime }-\left (1-x \right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.760

12802

3235

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

0.760

12803

3353

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

0.760

12804

5873

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

0.760

12805

7164

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

0.760

12806

8983

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

0.760

12807

9039

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

0.760

12808

14263

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

0.760

12809

14547

\begin{align*} 8 x^{2} y^{3}-2 y^{4}+\left (5 x^{3} y^{2}-8 x y^{3}\right ) y^{\prime }&=0 \\ \end{align*}

0.760

12810

19652

\begin{align*} x^{\prime }&=-x-2 y \\ y^{\prime }&=4 x-5 y \\ \end{align*}

0.760

12811

19970

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

0.760

12812

21893

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

0.760

12813

22324

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

0.760

12814

1386

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

0.761

12815

2741

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

0.761

12816

6314

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

0.761

12817

8255

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

0.761

12818

12984

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

0.761

12819

17716

\begin{align*} y^{\prime \prime }+\left (\frac {16}{3 x}-1\right ) y^{\prime }-\frac {16 y}{3 x^{2}}&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.761

12820

19649

\begin{align*} x^{\prime }&=x-2 y \\ y^{\prime }&=4 x+5 y \\ \end{align*}

0.761

12821

20622

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

0.761

12822

2730

\begin{align*} x_{1}^{\prime }&=7 x_{1}-x_{2}+6 x_{3} \\ x_{2}^{\prime }&=-10 x_{1}+4 x_{2}-12 x_{3} \\ x_{3}^{\prime }&=-2 x_{1}+x_{2}-x_{3} \\ \end{align*}

0.762

12823

10321

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

0.762

12824

14831

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

0.762

12825

23289

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

0.762

12826

1026

\begin{align*} x_{1}^{\prime }&=x_{1}-4 x_{2}-2 x_{4} \\ x_{2}^{\prime }&=x_{2} \\ x_{3}^{\prime }&=6 x_{1}-12 x_{2}-x_{3}-6 x_{4} \\ x_{4}^{\prime }&=-4 x_{2}-x_{4} \\ \end{align*}

0.763

12827

1420

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

0.763

12828

1804

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

0.763

12829

8926

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

0.763

12830

18363

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

0.763

12831

20471

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

0.763

12832

20659

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

0.763

12833

21149

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

0.763

12834

5437

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

0.764

12835

8740

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

0.764

12836

14810

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

0.764

12837

22297

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

0.764

12838

24919

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

0.764

12839

3137

\begin{align*} 4 y+y^{\prime \prime }&=12 \cos \left (x \right )^{2} \\ y \left (\frac {\pi }{2}\right ) &= 0 \\ y^{\prime }\left (\frac {\pi }{2}\right ) &= \frac {\pi }{2} \\ \end{align*}

0.765

12840

14157

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

0.765

12841

14280

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

0.765

12842

16517

\begin{align*} 4 y^{\prime \prime }+y&=0 \\ \end{align*}

0.765

12843

19163

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

0.765

12844

19167

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

0.765

12845

23331

\begin{align*} y^{\prime \prime }+25 y&=0 \\ \end{align*}

0.765

12846

1824

\begin{align*} 4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}+3\right ) y&=x^{{7}/{2}} \\ \end{align*}

0.766

12847

2011

\begin{align*} 16 x^{2} y^{\prime \prime }+4 x \left (2 x^{2}+x +6\right ) y^{\prime }+\left (18 x^{2}+5 x +1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.766

12848

2373

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

0.766

12849

2761

\begin{align*} x_{1}^{\prime }&=2 x_{1}-5 x_{2}+\sin \left (t \right ) \\ x_{2}^{\prime }&=x_{1}-2 x_{2}+\tan \left (t \right ) \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= 0 \\ x_{2} \left (0\right ) &= 0 \\ \end{align*}

0.766

12850

2806

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

0.766

12851

5493

\begin{align*} 16 x {y^{\prime }}^{2}+8 y^{\prime } y+y^{6}&=0 \\ \end{align*}

0.766

12852

8110

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

0.766

12853

9323

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

0.766

12854

9677

\begin{align*} x^{\prime }&=2 x-7 y \\ y^{\prime }&=5 x+10 y+4 z \\ z^{\prime }&=5 y+2 z \\ \end{align*}

0.766

12855

19892

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

0.766

12856

22660

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

0.766

12857

22807

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

0.766

12858

3979

\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&=\delta \left (t -\frac {\pi }{4}\right ) \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.767

12859

15716

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

0.767

12860

16057

\begin{align*} x^{\prime }&=\pi ^{2} x+\frac {187 y}{5} \\ y^{\prime }&=\sqrt {555}\, x+\frac {400617 y}{5000} \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 0 \\ \end{align*}

0.767

12861

17584

\begin{align*} y^{\prime \prime \prime }+10 y^{\prime \prime }+34 y^{\prime }+40 y&=t \,{\mathrm e}^{-4 t}+2 \,{\mathrm e}^{-3 t} \cos \left (t \right ) \\ \end{align*}

0.767

12862

21630

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

0.767

12863

22656

\begin{align*} 4 y^{\prime \prime }+9 y&=0 \\ \end{align*}

0.767

12864

24519

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

0.767

12865

3132

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

0.768

12866

10317

\begin{align*} {y^{\prime }}^{2}&=\frac {1}{y^{4} x^{3}} \\ \end{align*}

0.768

12867

12357

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

0.768

12868

17610

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

0.768

12869

18251

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

0.768

12870

21778

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

0.768

12871

2663

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

0.769

12872

5533

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

0.769

12873

5926

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

0.769

12874

18244

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

0.769

12875

2007

\begin{align*} 9 x^{2} y^{\prime \prime }+3 x \left (-2 x^{2}+3 x +5\right ) y^{\prime }+\left (-14 x^{2}+12 x +1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.770

12876

2247

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

0.770

12877

3205

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

0.770

12878

5954

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

0.770

12879

6458

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

0.770

12880

12531

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

0.770

12881

13109

\begin{align*} x^{\prime }&=-3 x+48 y-28 z \\ y^{\prime }&=-4 x+40 y-22 z \\ z^{\prime }&=-6 x+57 y-31 z \\ \end{align*}

0.770

12882

15308

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

0.770

12883

15539

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

0.770

12884

15978

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

0.770

12885

16917

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

0.770

12886

19042

\begin{align*} x_{1}^{\prime }&=2 x_{1}-5 x_{2}-\cos \left (t \right ) \\ x_{2}^{\prime }&=x_{1}-2 x_{2}+\sin \left (t \right ) \\ \end{align*}

0.770

12887

19587

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

0.770

12888

10613

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

0.771

12889

16556

\begin{align*} x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y&=0 \\ \end{align*}

0.771

12890

22943

\begin{align*} x^{\prime }+2 x-y&=100 \sin \left (t \right ) \\ y^{\prime }-4 x-y&=36 t \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= -8 \\ y \left (0\right ) &= -21 \\ \end{align*}

0.771

12891

1125

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

0.772

12892

1835

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

0.772

12893

2628

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

0.772

12894

8591

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

0.772

12895

8993

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

0.772

12896

9334

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

0.772

12897

10392

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

0.772

12898

19056

\begin{align*} x_{1}^{\prime }&=x_{1}-x_{2}-2 x_{3}+3 x_{4} \\ x_{2}^{\prime }&=2 x_{1}-\frac {3 x_{2}}{2}-x_{3}+\frac {7 x_{4}}{2} \\ x_{3}^{\prime }&=-x_{1}+\frac {x_{2}}{2}-\frac {3 x_{4}}{2} \\ x_{4}^{\prime }&=-2 x_{1}+\frac {3 x_{2}}{2}+3 x_{3}-\frac {7 x_{4}}{2} \\ \end{align*}

0.772

12899

20872

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

0.772

12900

70

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

0.773