2.3.139 Problems 13801 to 13900

Table 2.809: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

13801

19432

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

0.911

13802

21734

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

0.911

13803

24884

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

0.911

13804

25357

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

0.911

13805

25682

\begin{align*} x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y&=0 \\ \end{align*}

0.911

13806

10444

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

0.912

13807

15285

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

0.912

13808

16699

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

0.913

13809

22271

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

0.913

13810

25094

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

0.913

13811

575

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

0.914

13812

13749

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

0.914

13813

17105

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

0.914

13814

2291

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

0.915

13815

8508

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

0.915

13816

17523

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

0.915

13817

21474

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

0.915

13818

21563

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

0.915

13819

25460

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

0.915

13820

25562

\begin{align*} y^{\prime \prime }+\omega _{n}^{2} y&={\mathrm e}^{i \omega t} \\ \end{align*}

0.915

13821

3309

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

0.916

13822

9243

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

0.916

13823

22877

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

0.916

13824

2772

\begin{align*} x_{1}^{\prime }&=3 x_{1}+2 x_{2}+4 x_{3}+2 \,{\mathrm e}^{8 t} \\ x_{2}^{\prime }&=2 x_{1}+2 x_{3}+{\mathrm e}^{8 t} \\ x_{3}^{\prime }&=4 x_{1}+2 x_{2}+3 x_{3}+2 \,{\mathrm e}^{8 t} \\ \end{align*}

0.917

13825

5745

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

0.917

13826

10274

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

0.917

13827

14827

\begin{align*} y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} -4 t +8 \pi & 0<t <2 \pi \\ 0 & 2<t \end {array}\right . \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.917

13828

18192

\begin{align*} y^{\prime \prime }+8 y^{\prime }&=8 x \\ \end{align*}

0.917

13829

18807

\begin{align*} 2 x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\ \end{align*}

0.917

13830

22251

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

0.918

13831

4566

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

0.919

13832

17302

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

0.919

13833

4600

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

0.920

13834

5067

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

0.920

13835

16552

\begin{align*} x^{2} y^{\prime \prime }-5 y^{\prime } x +8 y&=0 \\ \end{align*}

0.920

13836

17415

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

0.920

13837

19456

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

0.920

13838

21000

\begin{align*} u^{\prime \prime }+2 a u^{\prime }+\omega ^{2} u&=c \cos \left (\omega t \right ) \\ \end{align*}

0.920

13839

24718

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

0.920

13840

2687

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

0.921

13841

5362

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

0.921

13842

5971

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

0.921

13843

9903

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

0.921

13844

11691

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

0.921

13845

14705

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

0.921

13846

16418

\begin{align*} y^{\prime \prime }&=y^{\prime } \\ y \left (0\right ) &= 8 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}

0.921

13847

18148

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

0.921

13848

18812

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

0.921

13849

18928

\begin{align*} y^{\prime \prime }+y^{\prime }+\frac {5 y}{4}&=t -\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right ) \left (t -\frac {\pi }{2}\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.921

13850

21584

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

0.921

13851

21655

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

0.921

13852

7850

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

0.922

13853

13750

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

0.922

13854

14840

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

0.922

13855

19775

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

0.922

13856

7275

\begin{align*} y^{\prime \prime }-4 y^{\prime }&=10 \\ \end{align*}

0.923

13857

18229

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

0.923

13858

22771

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

0.923

13859

5488

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

0.924

13860

6070

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

0.924

13861

6594

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

0.924

13862

8033

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

0.924

13863

8981

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

0.924

13864

9986

\begin{align*} x^{\prime }&=6 x-7 y+10 \\ y^{\prime }&=x-2 y-2 \,{\mathrm e}^{t} \\ \end{align*}

0.924

13865

12406

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

0.924

13866

16171

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

0.924

13867

19894

\begin{align*} v^{\prime \prime }+\frac {2 v^{\prime }}{r}&=0 \\ \end{align*}

0.924

13868

21160

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

0.924

13869

23616

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

0.924

13870

597

\begin{align*} -x^{\prime }+2 y^{\prime }&=x+3 y+{\mathrm e}^{t} \\ 3 x^{\prime }-4 y^{\prime }&=x-15 y+{\mathrm e}^{-t} \\ \end{align*}

0.925

13871

5674

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

0.925

13872

6365

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

0.925

13873

7153

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

0.925

13874

7296

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

0.925

13875

18806

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

0.925

13876

18841

\begin{align*} y^{\prime \prime }+4 y&=t^{2} \sin \left (2 t \right )+\left (6 t +7\right ) \cos \left (2 t \right ) \\ \end{align*}

0.925

13877

1007

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

0.926

13878

15843

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

0.926

13879

19045

\begin{align*} x_{1}^{\prime }&=-\frac {x_{1}}{2}+\frac {x_{2}}{2}-\frac {x_{3}}{2}+1 \\ x_{2}^{\prime }&=-x_{1}-2 x_{2}+x_{3}+t \\ x_{3}^{\prime }&=\frac {x_{1}}{2}+\frac {x_{2}}{2}-\frac {3 x_{3}}{2}+11 \,{\mathrm e}^{-3 t} \\ \end{align*}

0.926

13880

22629

\begin{align*} 4 y^{\prime \prime }-25 y&=0 \\ \end{align*}

0.926

13881

23569

\begin{align*} x_{1}^{\prime }&=-10 x_{1}+x_{2}+7 x_{3} \\ x_{2}^{\prime }&=-9 x_{1}+4 x_{2}+5 x_{3} \\ x_{3}^{\prime }&=-17 x_{1}+x_{2}+12 x_{3} \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= 5 \\ x_{2} \left (0\right ) &= 2 \\ x_{3} \left (0\right ) &= -2 \\ \end{align*}

0.926

13882

9756

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

0.927

13883

13009

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

0.927

13884

23052

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

0.927

13885

23235

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

0.927

13886

23267

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

0.927

13887

2812

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

0.928

13888

8729

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

0.928

13889

12871

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

0.928

13890

14904

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

0.928

13891

16382

\begin{align*} y^{\prime \prime } x +4 y^{\prime }&=18 x^{2} \\ \end{align*}

0.928

13892

17175

\begin{align*} y+y^{\prime }&=\left \{\begin {array}{cc} 4 & 0\le t <2 \\ 0 & 2\le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ \end{align*}

0.928

13893

23183

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

0.928

13894

101

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

0.929

13895

2636

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

0.929

13896

3382

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

0.929

13897

21688

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

0.929

13898

2411

\begin{align*} m y^{\prime \prime }+c y^{\prime }+k y&=F_{0} \cos \left (\omega t \right ) \\ \end{align*}

0.930

13899

13724

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

0.930

13900

18104

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

0.930