2.3.71 Problems 7001 to 7100

Table 2.715: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

7001

18262

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

0.876

7002

20157

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

0.876

7003

23996

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

0.876

7004

386

\begin{align*} x^{\prime \prime }+25 x&=90 \cos \left (4 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 90 \\ \end{align*}

0.877

7005

505

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

Series expansion around \(x=0\).

0.877

7006

1420

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

0.877

7007

1845

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

Series expansion around \(x=2\).

0.877

7008

3508

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

Series expansion around \(z=0\).

0.877

7009

12877

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

0.877

7010

14379

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

0.877

7011

14860

\begin{align*} x^{\prime }&=x+7 y \\ y^{\prime }&=3 x+5 y \\ \end{align*}

0.877

7012

15111

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

With initial conditions

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

0.877

7013

25256

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

0.877

7014

602

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

0.878

7015

3205

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

0.878

7016

3368

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

Series expansion around \(x=0\).

0.878

7017

3758

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

0.878

7018

3768

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

0.878

7019

3897

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

0.878

7020

5481

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

0.878

7021

6251

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

0.878

7022

12610

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

0.878

7023

14098

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

0.878

7024

17279

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

0.878

7025

18384

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

Series expansion around \(x=0\).

0.878

7026

18682

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

0.878

7027

19260

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

0.878

7028

22098

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

0.878

7029

23824

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

0.878

7030

150

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

0.879

7031

3350

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

Series expansion around \(x=0\).

0.879

7032

9309

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

0.879

7033

14788

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

With initial conditions

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

0.879

7034

19439

\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

0.879

7035

19516

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

0.879

7036

23357

\begin{align*} y^{\prime \prime }+9 y^{\prime }+4 y&=0 \\ \end{align*}

0.879

7037

25264

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

0.879

7038

11

\begin{align*} x^{\prime \prime }&=50 \\ x \left (0\right ) &= 20 \\ x^{\prime }\left (0\right ) &= 10 \\ \end{align*}

0.880

7039

3249

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

0.880

7040

3870

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

0.880

7041

23975

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

0.880

7042

1026

\begin{align*} x_{1}^{\prime }&=x_{1}-4 x_{2}-2 x_{4} \\ x_{2}^{\prime }&=x_{2} \\ x_{3}^{\prime }&=6 x_{1}-12 x_{2}-x_{3}-6 x_{4} \\ x_{4}^{\prime }&=-4 x_{2}-x_{4} \\ \end{align*}

0.881

7043

2457

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

Series expansion around \(t=0\).

0.881

7044

3376

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

Series expansion around \(x=0\).

0.881

7045

3485

\begin{align*} f^{\prime \prime }+2 f^{\prime }+5 f&={\mathrm e}^{-t} \cos \left (3 t \right ) \\ f \left (0\right ) &= 0 \\ f^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.881

7046

3760

\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=\frac {4 \,{\mathrm e}^{-2 x}}{x^{2}+1}+2 x^{2}-1 \\ \end{align*}

0.881

7047

4431

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

0.881

7048

8019

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

0.881

7049

8850

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

With initial conditions

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

0.881

7050

12646

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

0.881

7051

13162

\(\left [\begin {array}{cccc} 1 & 0 & 1 & 0 \\ 0 & 1 & 1 & 0 \\ 0 & 0 & 2 & 0 \\ 0 & 0 & 0 & 2 \end {array}\right ]\)

N/A

N/A

N/A

0.881

7052

14935

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

0.881

7053

17490

\begin{align*} y^{\prime \prime }+6 y^{\prime }+25 y&={\mathrm e}^{-3 t} \left (\sec \left (4 t \right )+\csc \left (4 t \right )\right ) \\ \end{align*}

0.881

7054

19508

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

0.881

7055

21931

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ \end{align*}

0.881

7056

23831

\begin{align*} y^{\prime }&={\mathrm e}^{t} t \\ \end{align*}

0.881

7057

25253

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

0.881

7058

2392

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

0.882

7059

2693

\begin{align*} y^{\prime \prime }+4 y^{\prime }+5 y&=\delta \left (t -1\right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

0.882

7060

7969

\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{5 x} \\ \end{align*}

0.882

7061

22229

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

Using Laplace transform method.

0.882

7062

3372

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

Series expansion around \(x=0\).

0.883

7063

19520

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

0.883

7064

2591

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

0.884

7065

3840

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

0.884

7066

4684

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

0.884

7067

5023

\begin{align*} y^{\prime } \sqrt {a_{4} x^{4}+a_{3} x^{3}+a_{2} x^{2}+a_{1} x +a_{0}}&=0 \\ \end{align*}

0.884

7068

6876

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

0.884

7069

19438

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

0.884

7070

886

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

0.885

7071

2274

\begin{align*} y_{1}^{\prime }&=4 y_{1}-8 y_{2}-4 y_{3} \\ y_{2}^{\prime }&=-3 y_{1}-y_{2}-4 y_{3} \\ y_{3}^{\prime }&=y_{1}-y_{2}+9 y_{3} \\ \end{align*}

With initial conditions

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

0.885

7072

7366

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

Series expansion around \(x=0\).

0.885

7073

7887

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

0.885

7074

14105

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

0.885

7075

14386

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

0.885

7076

18868

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

0.885

7077

19187

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

0.885

7078

21127

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

0.885

7079

21800

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

0.885

7080

1040

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

0.886

7081

15429

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

0.886

7082

19657

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

0.886

7083

25535

\begin{align*} 2 y^{\prime \prime }+8 y^{\prime }+6 y&=0 \\ \end{align*}

0.886

7084

600

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

0.887

7085

9330

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

0.887

7086

19425

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

0.887

7087

25250

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

0.887

7088

3369

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

Series expansion around \(x=0\).

0.888

7089

7761

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

0.888

7090

8027

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

0.888

7091

8071

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

Series expansion around \(x=0\).

0.888

7092

9667

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

0.888

7093

19495

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

0.888

7094

21580

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

0.888

7095

25260

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

0.888

7096

501

\begin{align*} 5 y^{\prime \prime } x +\left (30+3 x \right ) y^{\prime }+3 y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.889

7097

7814

\begin{align*} y^{\prime \prime }-60 y^{\prime }-900 y&=5 \,{\mathrm e}^{10 x} \\ \end{align*}

0.889

7098

16513

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

0.889

7099

18082

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

0.889

7100

18236

\begin{align*} 2 y^{\prime \prime }-3 y^{\prime }-2 y&=5 \,{\mathrm e}^{x} \cosh \left (x \right ) \\ \end{align*}

0.889