2.3.129 Problems 12801 to 12900

Table 2.831: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

12801

19130

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

1.129

12802

21002

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

1.130

12803

26945

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

1.130

12804

1260

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

1.131

12805

9428

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

Series expansion around \(x=0\).

1.131

12806

646

\begin{align*} x_{1}^{\prime }&=3 x_{1}+x_{3} \\ x_{2}^{\prime }&=9 x_{1}-x_{2}+2 x_{3} \\ x_{3}^{\prime }&=-9 x_{1}+4 x_{2}-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 ) &= 17 \\ \end{align*}

1.132

12807

1741

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

1.132

12808

5779

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

1.132

12809

12328

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

1.132

12810

16346

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

1.132

12811

17496

\begin{align*} y^{\prime \prime }-8 y^{\prime }+17 y&={\mathrm e}^{4 t} \sec \left (t \right ) \\ \end{align*}

1.132

12812

18247

\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&=1+8 \cos \left (x \right )+{\mathrm e}^{2 x} \\ \end{align*}

1.132

12813

18839

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

1.132

12814

19047

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

1.132

12815

12359

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

1.133

12816

16157

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

1.133

12817

26973

\begin{align*} y^{\prime \prime }-4 y^{\prime }&=8 x^{2}+2 \,{\mathrm e}^{3 x} \\ \end{align*}

1.133

12818

4586

\begin{align*} x_{1}^{\prime }&=2 x_{1}-x_{3}+24 t \\ x_{2}^{\prime }&=x_{1}-x_{2} \\ x_{3}^{\prime }&=3 x_{1}-x_{2}-x_{3} \\ \end{align*}

1.134

12819

5815

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

1.134

12820

9877

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

Series expansion around \(x=0\).

1.134

12821

12541

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

1.134

12822

15845

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

1.134

12823

6737

\begin{align*} y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=24 x \sin \left (x \right ) \\ \end{align*}

1.135

12824

7655

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

Series expansion around \(x=0\).

1.135

12825

9749

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

1.135

12826

12617

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

1.135

12827

26361

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

1.135

12828

27006

\begin{align*} x^{2} y^{\prime \prime }+5 x y^{\prime }-21 y&=0 \\ y \left (2\right ) &= 1 \\ y^{\prime }\left (2\right ) &= 0 \\ \end{align*}

1.135

12829

5771

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

1.136

12830

7687

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

1.136

12831

8219

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

1.136

12832

2082

\begin{align*} x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (1-10 x \right ) y^{\prime }-\left (9-10 x \right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.137

12833

15276

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

1.137

12834

15287

\begin{align*} x^{\prime }&=7 x+y-1-6 \,{\mathrm e}^{t} \\ y^{\prime }&=-4 x+3 y+4 \,{\mathrm e}^{t}-3 \\ \end{align*}

With initial conditions

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

1.137

12835

21681

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

Series expansion around \(x=0\).

1.137

12836

6383

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

1.138

12837

8562

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

Series expansion around \(x=0\).

1.138

12838

10441

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

1.138

12839

22940

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

With initial conditions

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

1.138

12840

24468

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

1.138

12841

1610

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

1.139

12842

2177

\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+2 y^{\prime }-2 y&={\mathrm e}^{2 x} \left (\left (-x^{2}+5 x +27\right ) \cos \left (x \right )+\left (9 x^{2}+13 x +2\right ) \sin \left (x \right )\right ) \\ \end{align*}

1.139

12843

6078

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

1.139

12844

8085

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

Series expansion around \(x=0\).

1.139

12845

9878

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

Series expansion around \(x=0\).

1.139

12846

14646

\begin{align*} 16 y+8 y^{\prime }+y^{\prime \prime }&=8 \,{\mathrm e}^{-2 x} \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

1.139

12847

15028

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

1.139

12848

17478

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

1.139

12849

19131

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

1.139

12850

20032

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

1.139

12851

20501

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

1.139

12852

20560

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

1.139

12853

23474

\begin{align*} 3 x y^{\prime \prime \prime }+5 y^{\prime \prime }+6 y^{\prime }&=3 \cos \left (x \right ) \\ \end{align*}

1.139

12854

12387

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

1.140

12855

19195

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

1.140

12856

27176

\begin{align*} x_{1}^{\prime }&=6 x_{1}+5 x_{2}-4 \cos \left (3 t \right ) \\ x_{2}^{\prime }&=x_{1}+2 x_{2}+8 \\ \end{align*}

1.140

12857

1331

\begin{align*} 4 t^{2} y^{\prime \prime }-8 t y^{\prime }+9 y&=0 \\ \end{align*}

1.141

12858

2797

\begin{align*} x^{\prime }&=x+y+z-2 \,{\mathrm e}^{-t} \\ y^{\prime }&=2 x+y-z-2 \,{\mathrm e}^{-t} \\ z^{\prime }&=-3 x+2 y+4 z+3 \,{\mathrm e}^{-t} \\ \end{align*}

With initial conditions

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

1.141

12859

4188

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

Series expansion around \(x=0\).

1.141

12860

7128

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

1.141

12861

19001

\begin{align*} x_{1}^{\prime }&=x_{1}+8 x_{2}+5 x_{3}+3 x_{4} \\ x_{2}^{\prime }&=2 x_{1}+16 x_{2}+10 x_{3}+6 x_{4} \\ x_{3}^{\prime }&=5 x_{1}-14 x_{2}-11 x_{3}-3 x_{4} \\ x_{4}^{\prime }&=-x_{1}-8 x_{2}-5 x_{3}-3 x_{4} \\ \end{align*}

1.141

12862

25951

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

1.141

12863

4137

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

1.142

12864

8394

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

1.142

12865

11282

\begin{align*} y^{\prime \prime }&=\left (-\frac {3}{16 x^{2}}-\frac {2}{9 \left (x -1\right )^{2}}+\frac {3}{16 \left (x -1\right ) x}\right ) y \\ \end{align*}

1.142

12866

12933

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

1.142

12867

14724

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

1.142

12868

16011

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

With initial conditions

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

1.142

12869

6953

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

1.143

12870

22277

\begin{align*} x_{1}^{\prime }&=x_{2} \\ x_{2}^{\prime }&=6 x_{1}+9 \,{\mathrm e}^{-t} \\ \end{align*}

With initial conditions

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

1.143

12871

6376

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

1.144

12872

15404

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

1.144

12873

16764

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

Using Laplace transform method.

1.144

12874

17511

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

1.144

12875

21699

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

Series expansion around \(x=0\).

1.144

12876

1755

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

1.145

12877

2705

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

With initial conditions

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

1.145

12878

4041

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

Series expansion around \(x=0\).

1.145

12879

4585

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

1.145

12880

9409

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

Series expansion around \(x=1\).

1.145

12881

19847

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

1.145

12882

20910

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

Series expansion around \(x=0\).

1.145

12883

23100

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

1.145

12884

27383

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

1.145

12885

1125

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

1.146

12886

4574

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

1.146

12887

4601

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

Series expansion around \(x=0\).

1.146

12888

19429

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

1.146

12889

21773

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

1.146

12890

23379

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

1.146

12891

2102

\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-x^{2}+5\right ) y^{\prime }-\left (25 x^{2}+7\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.147

12892

8108

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

Series expansion around \(x=0\).

1.147

12893

14785

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

1.147

12894

16519

\begin{align*} y^{\prime \prime }+16 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

1.147

12895

20459

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

1.147

12896

9430

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

Series expansion around \(x=0\).

1.148

12897

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*}

1.148

12898

16950

\begin{align*} x^{\prime }&=2 x-5 y+4 \\ y^{\prime }&=3 x-7 y+5 \\ \end{align*}

1.148

12899

17493

\begin{align*} y^{\prime \prime }-6 y^{\prime }+34 y&={\mathrm e}^{3 t} \tan \left (5 t \right ) \\ \end{align*}

1.148

12900

18828

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

1.148