2.3.89 Problems 8801 to 8900

Table 2.751: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

8801

21095

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

0.646

8802

25221

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

0.646

8803

25280

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

0.646

8804

26415

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

0.646

8805

878

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

0.647

8806

1029

\begin{align*} x_{1}^{\prime }&=x_{1}+3 x_{2}+7 x_{3} \\ x_{2}^{\prime }&=-x_{2}-4 x_{3} \\ x_{3}^{\prime }&=x_{2}+3 x_{3} \\ x_{4}^{\prime }&=-6 x_{2}-14 x_{3}+x_{4} \\ \end{align*}

0.647

8807

1343

\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=g \left (t \right ) \\ \end{align*}

0.647

8808

1344

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

0.647

8809

3836

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

0.647

8810

7760

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

0.647

8811

8904

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

0.647

8812

12393

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

0.647

8813

12455

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

0.647

8814

14599

\begin{align*} y^{\prime \prime }+7 y^{\prime }+10 y&=0 \\ y \left (0\right ) &= -4 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}

0.647

8815

15013

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

0.647

8816

15514

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

0.647

8817

15662

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

0.647

8818

16901

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

Series expansion around \(x=0\).

0.647

8819

18906

\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=18 \,{\mathrm e}^{-t} \\ y \left (0\right ) &= 7 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*}

Using Laplace transform method.

0.647

8820

617

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

With initial conditions

\begin{align*} x_{1} \left (0\right ) &= 10 \\ x_{2} \left (0\right ) &= 12 \\ x_{3} \left (0\right ) &= -1 \\ \end{align*}

0.648

8821

1808

\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=14 x^{{3}/{2}} {\mathrm e}^{x} \\ \end{align*}

0.648

8822

2756

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

With initial conditions

\begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 1 \\ x_{3} \left (0\right ) &= 1 \\ x_{4} \left (0\right ) &= 1 \\ \end{align*}

0.648

8823

7894

\begin{align*} 1-\sqrt {a^{2}-x^{2}}\, y^{\prime }&=0 \\ \end{align*}

0.648

8824

8135

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

Series expansion around \(x=0\).

0.648

8825

9419

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

Series expansion around \(x=0\).

0.648

8826

9672

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

0.648

8827

10339

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

Using Laplace transform method.

0.648

8828

13155

\(\left [\begin {array}{ccc} 1 & 0 & 0 \\ -6 & 8 & 2 \\ 12 & -15 & -3 \end {array}\right ]\)

N/A

N/A

N/A

0.648

8829

14600

\begin{align*} y^{\prime \prime }-6 y^{\prime }+8 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 6 \\ \end{align*}

0.648

8830

15427

\begin{align*} 12 y-7 y^{\prime }+y^{\prime \prime }&=x \\ \end{align*}

0.648

8831

16916

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

Series expansion around \(x=0\).

0.648

8832

16927

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

Series expansion around \(x=0\).

0.648

8833

17004

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

0.648

8834

19242

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

0.648

8835

23532

\begin{align*} y^{\prime \prime }-12 y^{\prime }+36 y&={\mathrm e}^{6 x} \ln \left (x \right ) \\ \end{align*}

0.648

8836

23733

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

Series expansion around \(x=0\).

0.648

8837

24565

\begin{align*} x^{\prime \prime }+4 x^{\prime }+5 x&=10 \\ x \left (0\right ) &= 4 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.648

8838

24892

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

0.648

8839

25091

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

0.648

8840

25130

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

0.648

8841

25272

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

0.648

8842

26649

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

0.648

8843

2462

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

Series expansion around \(t=0\).

0.649

8844

3177

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

0.649

8845

3728

\begin{align*} y^{\prime \prime }-4 y^{\prime }+6 y&=7 \,{\mathrm e}^{2 x} \\ \end{align*}

0.649

8846

7337

\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=10 \,{\mathrm e}^{x}+6 \cos \left (x \right ) {\mathrm e}^{-x} \\ \end{align*}

0.649

8847

9984

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

With initial conditions

\begin{align*} x \left (0\right ) &= 3 \\ y \left (0\right ) &= 0 \\ \end{align*}

0.649

8848

21760

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

0.649

8849

24007

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

0.649

8850

25602

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

0.649

8851

26953

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

0.649

8852

27156

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

0.649

8853

7135

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

0.650

8854

11728

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

0.650

8855

13170

\(\left [\begin {array}{ccc} 32 & -67 & 47 \\ 7 & -14 & 13 \\ -7 & 15 & -6 \end {array}\right ]\)

N/A

N/A

N/A

0.650

8856

14170

\begin{align*} \left (x^{3}-x \right ) y^{\prime \prime \prime }+\left (8 x^{2}-3\right ) y^{\prime \prime }+14 x y^{\prime }+4 y&=0 \\ \end{align*}

0.650

8857

18662

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

With initial conditions

\begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 3 \\ \end{align*}

0.650

8858

18963

\begin{align*} \frac {8 y^{\prime \prime }}{5}+y&=\operatorname {Heaviside}\left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

0.650

8859

21581

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

0.650

8860

26596

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=x^{2}-x +3 \\ y \left (0\right ) &= {\frac {4}{3}} \\ y^{\prime }\left (0\right ) &= {\frac {1}{27}} \\ \end{align*}

0.650

8861

27557

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

0.650

8862

2786

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

With initial conditions

\begin{align*} x_{1} \left (0\right ) &= 0 \\ x_{2} \left (0\right ) &= 1 \\ x_{3} \left (0\right ) &= 1 \\ \end{align*}

0.651

8863

2838

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

0.651

8864

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.

0.651

8865

9507

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

Series expansion around \(x=0\).

0.651

8866

12895

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

0.651

8867

14297

\begin{align*} x^{\prime \prime }+x^{\prime }+x&=12 \\ \end{align*}

0.651

8868

14428

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

0.651

8869

16431

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

0.651

8870

16553

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

0.651

8871

16614

\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=-4 \cos \left (x \right )+7 \sin \left (x \right ) \\ y \left (0\right ) &= 8 \\ y^{\prime }\left (0\right ) &= -5 \\ \end{align*}

0.651

8872

16851

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

Series expansion around \(x=0\).

0.651

8873

16887

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

Series expansion around \(x=0\).

0.651

8874

19178

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

0.651

8875

22153

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

0.651

8876

23524

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

0.651

8877

24013

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

0.651

8878

24744

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

0.651

8879

25944

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

0.651

8880

1917

\begin{align*} \left (2 x^{2}+3 x +1\right ) y^{\prime \prime }+\left (6+8 x \right ) y^{\prime }+4 y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.652

8881

2421

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

Series expansion around \(t=0\).

0.652

8882

3122

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

0.652

8883

9738

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

0.652

8884

17460

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

0.652

8885

18659

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

With initial conditions

\begin{align*} x \left (0\right ) &= 3 \\ y \left (0\right ) &= 1 \\ \end{align*}

0.652

8886

19457

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

0.652

8887

23085

\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&={\mathrm e}^{2 x} \sin \left (3 x \right ) \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= -{\frac {25}{6}} \\ \end{align*}

0.652

8888

24075

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

0.652

8889

1426

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

With initial conditions

\begin{align*} x_{1} \left (0\right ) &= -1 \\ x_{2} \left (0\right ) &= 2 \\ x_{3} \left (0\right ) &= -30 \\ \end{align*}

0.653

8890

1934

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

Series expansion around \(x=1\).

0.653

8891

7648

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

Series expansion around \(x=2\).

0.653

8892

8758

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

0.653

8893

16739

\begin{align*} y^{\prime \prime }-12 y^{\prime }+36 y&=25 \sin \left (3 x \right ) \\ \end{align*}

0.653

8894

16870

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

Series expansion around \(x=0\).

0.653

8895

23291

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

0.653

8896

23618

\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*}

0.653

8897

23741

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

Series expansion around \(x=0\).

0.653

8898

25818

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

0.653

8899

344

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

0.654

8900

908

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

0.654