2.3.129 Problems 12801 to 12900

Table 2.801: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

12801

24935

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

1.093

12802

25741

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

1.093

12803

16876

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

1.094

12804

21619

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

1.094

12805

1437

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

1.095

12806

2394

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

1.095

12807

3217

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

1.095

12808

10422

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

1.095

12809

12417

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

1.095

12810

15271

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

1.095

12811

16705

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

1.095

12812

22851

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

1.095

12813

6061

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

1.096

12814

10193

\begin{align*} \left (x +3\right ) x^{2} y^{\prime \prime }+5 x \left (x +1\right ) y^{\prime }-\left (1-4 x \right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

1.096

12815

10361

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

1.097

12816

8790

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

1.098

12817

9407

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

1.098

12818

17708

\begin{align*} \left (x^{2}-25\right )^{2} y^{\prime \prime }-\left (x +5\right ) y^{\prime }+10 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

1.098

12819

18449

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

1.098

12820

23626

\begin{align*} x^{\prime }&=7 x+4 y-4 z \\ y^{\prime }&=4 x-8 y-z \\ z^{\prime }&=-4 x-y-8 z \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 3 \\ y \left (0\right ) &= 5 \\ z \left (0\right ) &= -1 \\ \end{align*}

1.098

12821

3962

\begin{align*} y^{\prime \prime }-y&=\operatorname {Heaviside}\left (t -1\right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

1.099

12822

6478

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

1.099

12823

9734

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

1.100

12824

10392

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

1.100

12825

15656

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

1.100

12826

1805

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

1.101

12827

6069

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

1.101

12828

6388

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

1.101

12829

7123

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

1.101

12830

7953

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

1.101

12831

17680

\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +7 y&=0 \\ \end{align*}
Series expansion around \(x=1\).

1.101

12832

1106

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

1.102

12833

8002

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

1.102

12834

13014

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

1.102

12835

14650

\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&=8 \sin \left (3 x \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}

1.102

12836

16423

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

1.102

12837

10177

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

1.103

12838

13881

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

1.103

12839

14786

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

1.103

12840

21974

\begin{align*} y^{\prime }&=5 \\ \end{align*}

1.103

12841

9211

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

1.104

12842

9539

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

1.104

12843

15887

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

1.104

12844

18633

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

1.104

12845

12470

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

1.105

12846

12977

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

1.105

12847

15371

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

1.105

12848

22220

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

1.105

12849

215

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

1.106

12850

7216

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

1.106

12851

9680

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

1.106

12852

12885

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

1.106

12853

15590

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

1.106

12854

22309

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

1.106

12855

23660

\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=3 \,{\mathrm e}^{2 t} t -4 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

1.106

12856

8041

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

1.107

12857

9868

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

1.107

12858

13687

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

1.107

12859

13884

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

1.107

12860

23654

\begin{align*} y^{\prime \prime }+7 y^{\prime }+10 y&=3 \,{\mathrm e}^{-2 t}-6 \,{\mathrm e}^{-5 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

1.108

12861

23690

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

1.108

12862

1350

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

1.109

12863

6848

\begin{align*} 1+\frac {y^{2}}{x^{2}}-\frac {2 y y^{\prime }}{x}&=0 \\ \end{align*}

1.109

12864

10187

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

1.109

12865

25755

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

1.109

12866

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*}

1.110

12867

6823

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

1.110

12868

17511

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

1.110

12869

24263

\begin{align*} L i^{\prime }+R i&=e \\ i \left (0\right ) &= 0 \\ \end{align*}

1.110

12870

6060

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

1.111

12871

7170

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

1.111

12872

9863

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

1.111

12873

1516

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

1.112

12874

3224

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

1.112

12875

9549

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

1.112

12876

19159

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

1.112

12877

8308

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

1.113

12878

9591

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

1.113

12879

9921

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

1.113

12880

14979

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

1.113

12881

25454

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

1.113

12882

25658

\begin{align*} y^{\prime }+20 y&=24 \\ \end{align*}

1.113

12883

1338

\begin{align*} y^{\prime \prime }+9 y&=9 \sec \left (3 t \right )^{2} \\ \end{align*}

1.114

12884

4123

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

1.114

12885

8996

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

1.114

12886

12583

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

1.114

12887

22855

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

1.114

12888

23643

\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&=24 \cosh \left (t \right ) \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= -3 \\ \end{align*}
Using Laplace transform method.

1.114

12889

23649

\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=\cos \left (t \right )+57 \sin \left (t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 7 \\ \end{align*}
Using Laplace transform method.

1.114

12890

5661

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

1.115

12891

9812

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

1.115

12892

9937

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

1.115

12893

18274

\begin{align*} y^{\prime \prime }-y^{\prime }&=-5 \,{\mathrm e}^{-x} \left (\cos \left (x \right )+\sin \left (x \right )\right ) \\ y \left (0\right ) &= -4 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}

1.115

12894

19009

\begin{align*} x_{1}^{\prime }&=-7 x_{1}+6 x_{2}-6 x_{3} \\ x_{2}^{\prime }&=-9 x_{1}+5 x_{2}-9 x_{3} \\ x_{3}^{\prime }&=-x_{2}-x_{3} \\ \end{align*}

1.115

12895

19431

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

1.115

12896

21123

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

1.115

12897

23603

\begin{align*} x^{\prime }&=3 x-2 y \\ y^{\prime }&=17 x-7 y \\ \end{align*}

1.115

12898

2272

\begin{align*} y_{1}^{\prime }&=-7 y_{1}-4 y_{2}+4 y_{3} \\ y_{2}^{\prime }&=y_{1}+y_{3} \\ y_{3}^{\prime }&=-9 y_{1}-5 y_{2}+6 y_{3} \\ \end{align*}
With initial conditions
\begin{align*} y_{1} \left (0\right ) &= -6 \\ y_{2} \left (0\right ) &= 9 \\ y_{3} \left (0\right ) &= -1 \\ \end{align*}

1.116

12899

3245

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

1.116

12900

4433

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

1.116