2.3.79 Problems 7801 to 7900

Table 2.731: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

7801

17688

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

Series expansion around \(x=0\).

0.578

7802

20187

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

0.578

7803

21530

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

0.578

7804

25117

\begin{align*} y^{\prime \prime }+4 y^{\prime }+5 y&={\mathrm e}^{-3 t} \\ \end{align*}

0.578

7805

591

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

0.579

7806

1390

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

Series expansion around \(x=4\).

0.579

7807

1639

\begin{align*} y^{\prime }-4 y&=\frac {48 x}{y^{2}} \\ y \left (0\right ) &= 1 \\ \end{align*}

0.579

7808

2375

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

0.579

7809

2617

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

Series expansion around \(t=-1\).

0.579

7810

4001

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

Series expansion around \(x=0\).

0.579

7811

4559

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

With initial conditions

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

0.579

7812

5495

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

0.579

7813

7110

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

0.579

7814

8577

\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+30 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= {\frac {15}{8}} \\ \end{align*}

Series expansion around \(x=0\).

0.579

7815

9475

\begin{align*} x^{\prime }&=5 x+3 y \\ y^{\prime }&=-6 x-4 y \\ \end{align*}

0.579

7816

9697

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

With initial conditions

\begin{align*} x \left (0\right ) &= -1 \\ y \left (0\right ) &= 6 \\ \end{align*}

0.579

7817

10414

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

0.579

7818

10522

\begin{align*} \left (2 x^{2}+4 x +5\right ) y^{\prime \prime }-20 \left (x +1\right ) y^{\prime }+60 y&=0 \\ \end{align*}

0.579

7819

13067

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

0.579

7820

15011

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

0.579

7821

16079

\begin{align*} y^{\prime \prime }+7 y^{\prime }+12 y&=3 \,{\mathrm e}^{-t} \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

0.579

7822

16107

\begin{align*} y^{\prime \prime }+6 y^{\prime }+8 y&=2 t +{\mathrm e}^{t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.579

7823

17447

\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=-78 \cos \left (3 t \right ) \\ \end{align*}

0.579

7824

20392

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

0.579

7825

21486

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

0.579

7826

25687

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

0.579

7827

25936

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

0.579

7828

2722

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

0.580

7829

16017

\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*}

0.580

7830

24666

\begin{align*} 4 y^{\prime \prime }+y&=33 \sin \left (3 x \right ) \\ \end{align*}

0.580

7831

24704

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

0.580

7832

26759

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

0.580

7833

4650

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

0.581

7834

4841

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

0.581

7835

7759

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

0.581

7836

9032

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

0.581

7837

9168

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

0.581

7838

9805

\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=12 x^{2} \\ \end{align*}

0.581

7839

10138

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

0.581

7840

11675

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

0.581

7841

20660

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

0.581

7842

21586

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

0.581

7843

24432

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

0.581

7844

24728

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

0.581

7845

25110

\begin{align*} y^{\prime \prime }-10 y^{\prime }+25 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

0.581

7846

26505

\begin{align*} y^{\prime \prime }-8 y^{\prime }+16 y&=\left (1-x \right ) {\mathrm e}^{4 x} \\ \end{align*}

0.581

7847

1869

\begin{align*} \left (2 x^{2}-4 x +1\right ) y^{\prime \prime }+10 \left (x -1\right ) y^{\prime }+6 y&=0 \\ \end{align*}

Series expansion around \(x=1\).

0.582

7848

1936

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

Series expansion around \(x=0\).

0.582

7849

2179

\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+4 y^{\prime }+12 y&=8 \cos \left (2 x \right )-16 \sin \left (2 x \right ) \\ \end{align*}

0.582

7850

2380

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

0.582

7851

2825

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

0.582

7852

4127

\begin{align*} y^{\prime \prime }-6 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 7 \\ \end{align*}

0.582

7853

8493

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

Series expansion around \(x=0\).

0.582

7854

9262

\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=64 x \,{\mathrm e}^{-x} \\ \end{align*}

0.582

7855

16166

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

0.582

7856

16174

\begin{align*} y^{\prime }&=40 x \,{\mathrm e}^{2 x} \\ y \left (0\right ) &= 4 \\ \end{align*}

0.582

7857

17607

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

0.582

7858

18228

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

0.582

7859

18280

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

0.582

7860

18688

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

0.582

7861

20188

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

0.582

7862

22233

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

Using Laplace transform method.

0.582

7863

23488

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

0.582

7864

23608

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

With initial conditions

\begin{align*} x \left (\pi \right ) &= 1 \\ y \left (\pi \right ) &= {\frac {4}{5}} \\ \end{align*}

0.582

7865

24580

\begin{align*} y^{\prime \prime }+9 y&=15 \cos \left (2 x \right ) \\ \end{align*}

0.582

7866

24883

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

0.582

7867

25366

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

With initial conditions

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

0.582

7868

25386

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

With initial conditions

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

0.582

7869

25806

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

0.582

7870

26037

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

Series expansion around \(x=0\).

0.582

7871

27127

\(\left [\begin {array}{ccc} 2 & -4 & 0 \\ -4 & 0 & 0 \\ 0 & 0 & 0 \end {array}\right ]\)

N/A

N/A

N/A

0.582

7872

27166

\begin{align*} x_{1}^{\prime }&=7 x_{1}-x_{2}+2 \,{\mathrm e}^{6 t} \\ x_{2}^{\prime }&=x_{1}+5 x_{2}+6 t \,{\mathrm e}^{6 t} \\ \end{align*}

0.582

7873

838

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

0.583

7874

1920

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

Series expansion around \(x=0\).

0.583

7875

2396

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

0.583

7876

7152

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

0.583

7877

8821

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

0.583

7878

9249

\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=20 \,{\mathrm e}^{-2 x} \\ \end{align*}

0.583

7879

10517

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

0.583

7880

14992

\(\left [\begin {array}{cc} 7 & -2 \\ 26 & -1 \end {array}\right ]\)

N/A

N/A

N/A

0.583

7881

16746

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=10 \,{\mathrm e}^{-3 x} \\ \end{align*}

0.583

7882

21743

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

0.583

7883

1908

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

Series expansion around \(x=-2\).

0.584

7884

7998

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

0.584

7885

8200

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

0.584

7886

9377

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

Series expansion around \(x=0\).

0.584

7887

10200

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

Series expansion around \(x=0\).

0.584

7888

14404

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

0.584

7889

15974

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

0.584

7890

16096

\begin{align*} y^{\prime \prime }+4 y&={\mathrm e}^{t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.584

7891

19885

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

0.584

7892

23995

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

0.584

7893

24677

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

0.584

7894

25286

\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&=\left \{\begin {array}{cc} {\mathrm e}^{t} & 0\le t <1 \\ {\mathrm e}^{2 t} & 1\le t <\infty \end {array}\right . \\ \end{align*}

Using Laplace transform method.

0.584

7895

26511

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

0.584

7896

1391

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

Series expansion around \(x=-4\).

0.585

7897

1877

\begin{align*} \left (2 x^{2}+4 x +5\right ) y^{\prime \prime }-20 \left (x +1\right ) y^{\prime }+60 y&=0 \\ y \left (-1\right ) &= 3 \\ y^{\prime }\left (-1\right ) &= -3 \\ \end{align*}

Series expansion around \(x=-1\).

0.585

7898

1914

\begin{align*} \left (7+x \right ) y^{\prime \prime }+\left (8+2 x \right ) y^{\prime }+\left (5+x \right ) y&=0 \\ y \left (-4\right ) &= 1 \\ y^{\prime }\left (-4\right ) &= 2 \\ \end{align*}

Series expansion around \(x=-4\).

0.585

7899

2422

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

Series expansion around \(t=0\).

0.585

7900

3321

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

0.585