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

3292

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

0.525

7002

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*}

0.525

7003

10939

\begin{align*} \left (2 x^{2}-8 x +11\right ) y^{\prime \prime }-16 \left (x -2\right ) y^{\prime }+36 y&=0 \\ \end{align*}

0.525

7004

13189

\(\left [\begin {array}{ccc} 6 & -5 & 2 \\ 4 & -3 & 2 \\ 2 & -2 & 3 \end {array}\right ]\)

N/A

N/A

N/A

0.525

7005

15315

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

0.525

7006

16935

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

With initial conditions

\begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= -21 \\ \end{align*}

0.525

7007

17437

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

0.525

7008

20150

\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 \(x=0\).

0.525

7009

21111

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

0.525

7010

22250

\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=3 \,{\mathrm e}^{-2 t} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

Using Laplace transform method.

0.525

7011

23499

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

0.525

7012

24623

\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=18 x \,{\mathrm e}^{-x} \\ \end{align*}

0.525

7013

26565

\begin{align*} 5 y+4 y^{\prime }+y^{\prime \prime }&=10 \,{\mathrm e}^{-2 x} \cos \left (x \right ) \\ \end{align*}

0.525

7014

27114

\(\left [\begin {array}{ccc} 5 & 0 & 0 \\ 1 & 0 & 3 \\ 0 & 0 & -2 \end {array}\right ]\)

N/A

N/A

N/A

0.525

7015

1018

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

0.526

7016

3267

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

0.526

7017

3817

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

With initial conditions

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

0.526

7018

5478

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

0.526

7019

7292

\begin{align*} y^{\prime \prime }+2 y^{\prime }+17 y&=60 \,{\mathrm e}^{-4 x} \sin \left (5 x \right ) \\ \end{align*}

0.526

7020

8584

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

Series expansion around \(x=0\).

0.526

7021

8636

\begin{align*} y^{\prime \prime }+3 y^{\prime }-4 y&=6 \,{\mathrm e}^{2 t -3} \\ y \left (\frac {3}{2}\right ) &= 4 \\ y^{\prime }\left (\frac {3}{2}\right ) &= 5 \\ \end{align*}

Using Laplace transform method.

0.526

7022

9170

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

0.526

7023

15687

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+21 y^{\prime }-26 y&=36 \,{\mathrm e}^{2 x} \sin \left (3 x \right ) \\ \end{align*}

0.526

7024

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*}

0.526

7025

16076

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

0.526

7026

16669

\begin{align*} y^{\left (5\right )}+18 y^{\prime \prime \prime }+81 y^{\prime }&=x^{2} {\mathrm e}^{3 x} \sin \left (3 x \right ) \\ \end{align*}

0.526

7027

19840

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

0.526

7028

20236

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

0.526

7029

21706

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

Using Laplace transform method.

0.526

7030

23700

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

Series expansion around \(x=1\).

0.526

7031

23792

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

0.526

7032

24020

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

0.526

7033

24051

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

Using Laplace transform method.

0.526

7034

24647

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

0.526

7035

24676

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

0.526

7036

24802

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

0.526

7037

25234

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

0.526

7038

27659

\begin{align*} y^{\prime \prime }-6 y^{\prime }+8 y&=5 x \,{\mathrm e}^{2 x}+2 \,{\mathrm e}^{4 x} \sin \left (x \right ) \\ \end{align*}

0.526

7039

9

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

0.527

7040

2826

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

0.527

7041

3818

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

With initial conditions

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

0.527

7042

5474

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

0.527

7043

5885

\begin{align*} 3 y-8 y^{\prime }+4 y^{\prime \prime }&=0 \\ \end{align*}

0.527

7044

11688

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

0.527

7045

12843

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

0.527

7046

15225

\begin{align*} 3 y^{\prime \prime }+5 y^{\prime }-2 y&=7 \,{\mathrm e}^{-2 t} \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

0.527

7047

15993

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

0.527

7048

16090

\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=2 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.527

7049

16442

\begin{align*} y^{\prime \prime }&=2 y^{\prime }-5 y+30 \,{\mathrm e}^{3 x} \\ \end{align*}

0.527

7050

17691

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

Series expansion around \(x=0\).

0.527

7051

21492

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

0.527

7052

21707

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

Using Laplace transform method.

0.527

7053

21897

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

0.527

7054

23495

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

0.527

7055

23933

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

0.527

7056

26550

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

0.527

7057

3892

\begin{align*} x_{1}^{\prime }&=-6 x_{1}+x_{2} \\ x_{2}^{\prime }&=6 x_{1}-5 x_{2} \\ \end{align*}

0.528

7058

7695

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

0.528

7059

7812

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

0.528

7060

9493

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

Series expansion around \(x=0\).

0.528

7061

15416

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

0.528

7062

16836

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

Series expansion around \(x=0\).

0.528

7063

19502

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

0.528

7064

21721

\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.

0.528

7065

3990

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

Series expansion around \(x=0\).

0.529

7066

3991

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

Series expansion around \(x=0\).

0.529

7067

4592

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

Series expansion around \(x=0\).

0.529

7068

6634

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

0.529

7069

7204

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

0.529

7070

9177

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

0.529

7071

15400

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

0.529

7072

17807

\begin{align*} \frac {x^{\prime \prime }}{32}+2 x^{\prime }+x&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.529

7073

18463

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

Using Laplace transform method.

0.529

7074

20453

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

0.529

7075

21224

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

With initial conditions

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

0.529

7076

25133

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

0.529

7077

629

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

With initial conditions

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

0.530

7078

7206

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

0.530

7079

8565

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

Series expansion around \(x=0\).

0.530

7080

9230

\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=0 \\ y \left (1\right ) &= {\mathrm e}^{2} \\ y^{\prime }\left (1\right ) &= 3 \,{\mathrm e}^{2} \\ \end{align*}

0.530

7081

9331

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

0.530

7082

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.

0.530

7083

9633

\begin{align*} y^{\prime \prime }+9 y&=\cos \left (3 t \right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}

Using Laplace transform method.

0.530

7084

10446

\begin{align*} 4 x^{2} y^{\prime \prime }+4 x^{5} y^{\prime }+\left (x^{8}+6 x^{4}+4\right ) y&=0 \\ \end{align*}

0.530

7085

11685

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

0.530

7086

12451

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

0.530

7087

14378

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

0.530

7088

16075

\begin{align*} y^{\prime \prime }+7 y^{\prime }+10 y&={\mathrm e}^{-2 t} \\ \end{align*}

0.530

7089

16986

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

0.530

7090

16987

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

0.530

7091

18085

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

0.530

7092

23473

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

0.530

7093

1915

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

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

0.531

7094

9321

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

0.531

7095

9495

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

Series expansion around \(x=0\).

0.531

7096

12370

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

0.531

7097

17014

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

With initial conditions

\begin{align*} x \left (0\right ) &= 4 \\ y \left (0\right ) &= 0 \\ \end{align*}

0.531

7098

17026

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

0.531

7099

24465

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

0.531

7100

25132

\begin{align*} y^{\prime \prime }+2 y^{\prime }-15 y&=16 \,{\mathrm e}^{t} \\ \end{align*}

0.531