2.3.59 Problems 5801 to 5900

Table 2.649: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

5801

2466

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

0.464

5802

9521

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

0.464

5803

14209

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

0.464

5804

18629

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

0.464

5805

19024

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

0.464

5806

20580

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

0.464

5807

21233

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

0.464

5808

22175

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

0.464

5809

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 \(x=-2\).

0.464

5810

25687

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

0.464

5811

1888

\begin{align*} \left (x^{8}+1\right ) y^{\prime \prime }-16 x^{7} y^{\prime }+72 x^{6} y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.465

5812

2832

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

0.465

5813

7636

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

0.465

5814

9632

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

0.465

5815

9843

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

0.465

5816

14751

\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +\left (x^{2}+\frac {8}{9}\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.465

5817

20935

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

0.465

5818

3996

\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }-6 y^{\prime } x +12 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.466

5819

6872

\begin{align*} u^{\prime }-u^{2}&=\frac {2}{x^{{8}/{3}}} \\ \end{align*}

0.466

5820

6952

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

0.466

5821

7406

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

0.466

5822

7699

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

0.466

5823

9466

\begin{align*} x^{\prime }&=4 x-3 y \\ y^{\prime }&=8 x-6 y \\ \end{align*}

0.466

5824

11852

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

0.466

5825

22860

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

0.466

5826

1868

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

0.467

5827

3895

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

0.467

5828

6416

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

0.467

5829

6511

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

0.467

5830

6548

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

0.467

5831

8803

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

0.467

5832

9473

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

0.467

5833

16018

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

0.467

5834

16413

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

0.467

5835

18674

\begin{align*} x^{\prime }&=-\frac {4 x}{5}+2 y \\ y^{\prime }&=-x+\frac {6 y}{5} \\ \end{align*}

0.467

5836

20421

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

0.467

5837

20929

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

0.467

5838

25611

\begin{align*} y^{\prime \prime \prime \prime }-y&=t^{3} \cos \left (5 t \right ) \\ \end{align*}

0.467

5839

1879

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

0.468

5840

1923

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

0.468

5841

4841

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

0.468

5842

7830

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

0.468

5843

7834

\begin{align*} q^{\prime \prime }+9 q^{\prime }+14 q&=\frac {\sin \left (t \right )}{2} \\ q \left (0\right ) &= 0 \\ q^{\prime }\left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

0.468

5844

9445

\begin{align*} L i^{\prime }+R i&=E_{0} \operatorname {Heaviside}\left (t \right ) \\ i \left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.468

5845

14045

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

0.468

5846

24085

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

0.468

5847

4476

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

0.469

5848

14069

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

0.469

5849

16834

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

0.469

5850

16865

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

0.469

5851

23708

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

0.469

5852

1024

\begin{align*} x_{1}^{\prime }&=x_{1} \\ x_{2}^{\prime }&=18 x_{1}+7 x_{2}+4 x_{3} \\ x_{3}^{\prime }&=-27 x_{1}-9 x_{2}-5 x_{3} \\ \end{align*}

0.470

5853

2051

\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*}
Series expansion around \(x=0\).

0.470

5854

2779

\begin{align*} x_{1}^{\prime }&=4 x_{1}+5 x_{2}+4 \,{\mathrm e}^{t} \cos \left (t \right ) \\ x_{2}^{\prime }&=-2 x_{1}-2 x_{2} \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 1 \\ \end{align*}

0.470

5855

7889

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

0.470

5856

10514

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

0.470

5857

10518

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

0.470

5858

10785

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

0.470

5859

18412

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

0.470

5860

20504

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

0.470

5861

20893

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

0.470

5862

20921

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

0.470

5863

2825

\begin{align*} x_{1}^{\prime }&=-x_{2} \\ x_{2}^{\prime }&=8 x_{1}-6 x_{2} \\ \end{align*}

0.471

5864

7890

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

0.471

5865

14753

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

0.471

5866

16819

\begin{align*} y^{\prime \prime \prime \prime }-16 y&=\delta \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.471

5867

16987

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

0.471

5868

21856

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

0.471

5869

23607

\begin{align*} x^{\prime }&=3 x-2 y \\ y^{\prime }&=12 x-7 y \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 3 \\ \end{align*}

0.471

5870

1925

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

0.472

5871

9604

\begin{align*} y^{\prime \prime }-4 y^{\prime }&=6 \,{\mathrm e}^{3 t}-3 \,{\mathrm e}^{-t} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}
Using Laplace transform method.

0.472

5872

15269

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

0.472

5873

16855

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

0.472

5874

25157

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

0.472

5875

1924

\begin{align*} y^{\prime \prime }+5 y^{\prime } x -\left (-x^{2}+3\right ) y&=0 \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*}
Series expansion around \(x=0\).

0.473

5876

1926

\begin{align*} y^{\prime \prime }+3 y^{\prime } x +\left (4 x^{2}+2\right ) y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 6 \\ \end{align*}
Series expansion around \(x=0\).

0.473

5877

3868

\begin{align*} x_{1}^{\prime }&=-2 x_{1}-x_{2} \\ x_{2}^{\prime }&=x_{1}-4 x_{2} \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= 0 \\ x_{2} \left (0\right ) &= -1 \\ \end{align*}

0.473

5878

14749

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

0.473

5879

22941

\begin{align*} x^{\prime }+3 x+4 y&=8 \,{\mathrm e}^{t} \\ -x+y^{\prime }-y&=0 \\ \end{align*}

0.473

5880

506

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

0.474

5881

1004

\begin{align*} x_{1}^{\prime }&=9 x_{1}+4 x_{2} \\ x_{2}^{\prime }&=-6 x_{1}-x_{2} \\ x_{3}^{\prime }&=6 x_{1}+4 x_{2}+3 x_{3} \\ \end{align*}

0.474

5882

1034

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

0.474

5883

1857

\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-8 y^{\prime } x -12 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.474

5884

3344

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

0.474

5885

10358

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

0.474

5886

13029

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

0.474

5887

14350

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

0.474

5888

14981

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

0.474

5889

17759

\begin{align*} y^{\prime \prime \prime }-12 y^{\prime }-16 y&={\mathrm e}^{4 t}-{\mathrm e}^{-2 t} \\ \end{align*}

0.474

5890

19764

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

0.474

5891

22858

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

0.474

5892

25805

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

0.474

5893

444

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

0.475

5894

1006

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

0.475

5895

6856

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

0.475

5896

18702

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

0.475

5897

21229

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

0.475

5898

22862

\begin{align*} U^{\prime \prime }+\frac {2 U^{\prime }}{r}+a U&=0 \\ \end{align*}
Series expansion around \(r=0\).

0.475

5899

2642

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

0.476

5900

7842

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

0.476