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

2699

\begin{align*} x^{\prime }&=6 x-3 y \\ y^{\prime }&=2 x+y \\ \end{align*}

0.519

7802

5393

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

0.519

7803

7884

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

0.519

7804

10145

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

0.519

7805

11218

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

0.519

7806

11714

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

0.519

7807

14147

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

0.519

7808

15085

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

0.519

7809

17117

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

0.519

7810

19141

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

0.519

7811

20057

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

0.519

7812

22238

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

Using Laplace transform method.

0.519

7813

24823

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

0.519

7814

25128

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

0.519

7815

25755

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

0.519

7816

27070

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

Series expansion around \(x=0\).

0.519

7817

1316

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

0.520

7818

1639

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

0.520

7819

1857

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

Series expansion around \(x=0\).

0.520

7820

4577

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

0.520

7821

5946

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

0.520

7822

6701

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

0.520

7823

8963

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

Series expansion around \(x=0\).

0.520

7824

9251

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

0.520

7825

9465

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

0.520

7826

9667

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

0.520

7827

11163

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

0.520

7828

14974

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

Series expansion around \(x=0\).

0.520

7829

15082

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (9 x^{2}-\frac {1}{25}\right ) y&=0 \\ \end{align*}

0.520

7830

16002

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

With initial conditions

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

0.520

7831

16779

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

Using Laplace transform method.

0.520

7832

16830

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

Series expansion around \(x=0\).

0.520

7833

16833

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

Series expansion around \(x=0\).

0.520

7834

21886

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

0.520

7835

23283

\begin{align*} 3 y^{\prime \prime }+48 y^{\prime }+192 y&=0 \\ \end{align*}

0.520

7836

25580

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

0.520

7837

26618

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

0.520

7838

485

\begin{align*} 4 x y^{\prime \prime }+8 y^{\prime }+x y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.521

7839

877

\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&=1+x \,{\mathrm e}^{x} \\ \end{align*}

0.521

7840

1846

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

Series expansion around \(x=0\).

0.521

7841

4378

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

0.521

7842

7767

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

0.521

7843

9343

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

0.521

7844

9453

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

Using Laplace transform method.

0.521

7845

10164

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

Series expansion around \(x=0\).

0.521

7846

14408

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

With initial conditions

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

0.521

7847

16648

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

0.521

7848

21242

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

0.521

7849

23765

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

0.521

7850

25094

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

0.521

7851

25218

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

0.521

7852

26986

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

0.521

7853

2151

\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }-3 y&={\mathrm e}^{x} \left (16 x^{3}+24 x^{2}+2 x -1\right ) \\ \end{align*}

0.522

7854

2241

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

0.522

7855

12552

\begin{align*} \left (3+4 x \right ) y+16 x^{2} y^{\prime \prime }&=0 \\ \end{align*}

0.522

7856

22617

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

0.522

7857

22732

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

0.522

7858

24526

\begin{align*} y^{\prime \prime \prime }+4 y^{\prime \prime }&=12 \\ \end{align*}

0.522

7859

24927

\begin{align*} y^{\prime \prime }&=6 \sin \left (3 t \right ) \\ \end{align*}

0.522

7860

25341

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

Series expansion around \(t=0\).

0.522

7861

26928

\begin{align*} y^{\prime \prime }-6 y^{\prime }+13 y&=0 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

0.522

7862

490

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

Series expansion around \(x=0\).

0.523

7863

635

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

0.523

7864

1863

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

Series expansion around \(x=0\).

0.523

7865

2225

\begin{align*} x^{4} y^{\prime \prime \prime \prime }-4 x^{3} y^{\prime \prime \prime }+12 x^{2} y^{\prime \prime }-24 x y^{\prime }+24 y&=x^{4} \\ \end{align*}

0.523

7866

6383

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

0.523

7867

8841

\begin{align*} x_{1}^{\prime }&=3 x_{1}-18 x_{2} \\ x_{2}^{\prime }&=2 x_{1}-9 x_{2} \\ \end{align*}

With initial conditions

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

0.523

7868

10043

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

0.523

7869

14683

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

0.523

7870

14762

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

Series expansion around \(x=0\).

0.523

7871

16007

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

With initial conditions

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

0.523

7872

16430

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

0.523

7873

16523

\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&=0 \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= 31 \\ \end{align*}

0.523

7874

19242

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

0.523

7875

19452

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

0.523

7876

19554

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

0.523

7877

19577

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

0.523

7878

19778

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

0.523

7879

23031

\begin{align*} z^{\prime \prime }+8 z^{\prime }+16 z&=0 \\ \end{align*}

0.523

7880

24529

\begin{align*} y^{\prime \prime \prime }+9 y^{\prime \prime }&=11 \\ \end{align*}

0.523

7881

24533

\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime }&=12 \\ \end{align*}

0.523

7882

24633

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

0.523

7883

25951

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

0.523

7884

26229

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

0.523

7885

914

\begin{align*} x^{\prime \prime }+3 x^{\prime }+5 x&=-4 \cos \left (5 t \right ) \\ \end{align*}

0.524

7886

7817

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

0.524

7887

8560

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

Series expansion around \(x=0\).

0.524

7888

14680

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

0.524

7889

14681

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

0.524

7890

15181

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

0.524

7891

16761

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

Using Laplace transform method.

0.524

7892

16936

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

With initial conditions

\begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 15 \\ \end{align*}

0.524

7893

16948

\begin{align*} x^{\prime }&=5 x+4 y \\ y^{\prime }&=8 x+y \\ \end{align*}

0.524

7894

21117

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

0.524

7895

21247

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

With initial conditions

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

0.524

7896

24524

\begin{align*} y^{\prime \prime \prime }-5 y^{\prime \prime }+4 y&=14 \\ \end{align*}

0.524

7897

25343

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

Series expansion around \(t=0\).

0.524

7898

26126

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

0.524

7899

873

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

0.525

7900

3819

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

0.525