2.3.91 Problems 9001 to 9100

Table 2.713: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

9001

17404

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

0.453

9002

19422

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

0.453

9003

23537

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

0.453

9004

25130

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

0.453

9005

877

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

0.454

9006

1907

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

0.454

9007

2402

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

0.454

9008

3590

\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x -8 y&=0 \\ \end{align*}

0.454

9009

4026

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

0.454

9010

4049

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

0.454

9011

5936

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

0.454

9012

7100

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

0.454

9013

7102

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

0.454

9014

7188

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

0.454

9015

8022

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

0.454

9016

8615

\begin{align*} 16 \left (x +1\right )^{2} y^{\prime \prime }+3 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.454

9017

8942

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

0.454

9018

12547

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

0.454

9019

14294

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

0.454

9020

14672

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

0.454

9021

14990

\begin{align*} x^{\prime }&=8 x+14 y \\ y^{\prime }&=7 x+y \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 1 \\ \end{align*}

0.454

9022

15326

\begin{align*} c v^{\prime \prime }+\frac {v^{\prime }}{r}+\frac {v}{L}&=\delta \left (-1+t \right )-\delta \left (t \right ) \\ \end{align*}
Using Laplace transform method.

0.454

9023

16099

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

0.454

9024

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*}

0.454

9025

17406

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

0.454

9026

17789

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

0.454

9027

17829

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

0.454

9028

18155

\begin{align*} y^{\prime \prime }+25 y&=\cos \left (5 x \right ) \\ \end{align*}

0.454

9029

18247

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

0.454

9030

20929

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

0.454

9031

21517

\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=x^{2}+2 x \\ \end{align*}

0.454

9032

23933

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

0.454

9033

24826

\begin{align*} 5 {y^{\prime }}^{2}+3 y^{\prime } x -y&=0 \\ \end{align*}

0.454

9034

1337

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

0.455

9035

1406

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

0.455

9036

1415

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

0.455

9037

1896

\begin{align*} \left (x^{2}+3 x +3\right ) y^{\prime \prime }+\left (6+4 x \right ) y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 7 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}
Series expansion around \(x=0\).

0.455

9038

3758

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

0.455

9039

12587

\begin{align*} y^{\prime \prime }&=\frac {\left (5 x -4\right ) y^{\prime }}{x \left (x -1\right )}-\frac {\left (9 x -6\right ) y}{x^{2} \left (x -1\right )} \\ \end{align*}

0.455

9040

14122

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

0.455

9041

14362

\begin{align*} x^{\prime }&=x-2 \operatorname {Heaviside}\left (-1+t \right ) \\ x \left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

0.455

9042

15990

\begin{align*} x^{\prime }&=5 x+4 y \\ y^{\prime }&=9 x \\ \end{align*}

0.455

9043

16105

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

0.455

9044

17405

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

0.455

9045

18727

\begin{align*} y^{\prime \prime }+y^{\prime }+16 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.455

9046

20144

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

0.455

9047

20206

\begin{align*} x^{\prime }-7 x+y&=0 \\ y^{\prime }-2 x-5 y&=0 \\ \end{align*}

0.455

9048

20645

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

0.455

9049

21102

\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*}

0.455

9050

25125

\begin{align*} y^{\prime \prime }+6 y^{\prime }+13 y&={\mathrm e}^{-3 t} \cos \left (2 t \right ) \\ \end{align*}

0.455

9051

1806

\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=\frac {4}{1+{\mathrm e}^{-x}} \\ \end{align*}

0.456

9052

3921

\begin{align*} x_{1}^{\prime }&=5 x_{1}+9 x_{2} \\ x_{2}^{\prime }&=-2 x_{1}-x_{2} \\ \end{align*}

0.456

9053

8935

\begin{align*} y^{\prime \prime \prime }-8 y&={\mathrm e}^{i x} \\ \end{align*}

0.456

9054

14057

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

0.456

9055

15072

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

0.456

9056

18853

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

0.456

9057

483

\begin{align*} y^{\prime \prime } x +2 y^{\prime }+9 y x&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.457

9058

1920

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

0.457

9059

3836

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

0.457

9060

3864

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

0.457

9061

4376

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

0.457

9062

5625

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

0.457

9063

5802

\begin{align*} 16 y+8 y^{\prime }+y^{\prime \prime }&=4 \,{\mathrm e}^{x}-{\mathrm e}^{2 x} \\ \end{align*}

0.457

9064

7092

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

0.457

9065

7771

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

0.457

9066

10081

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

0.457

9067

10153

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

0.457

9068

10662

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

0.457

9069

10726

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

0.457

9070

12648

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

0.457

9071

12941

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

0.457

9072

15041

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

0.457

9073

15408

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

0.457

9074

15984

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

0.457

9075

16645

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

0.457

9076

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 \(x=0\).

0.457

9077

17695

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

0.457

9078

18384

\begin{align*} y^{\prime \prime }-{\mathrm e}^{x} y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.457

9079

19555

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

0.457

9080

20062

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

0.457

9081

20606

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

0.457

9082

20938

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

0.457

9083

21527

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

0.457

9084

21736

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

0.457

9085

21854

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

0.457

9086

24851

\begin{align*} 4 x^{5} {y^{\prime }}^{2}+12 x^{4} y y^{\prime }+9&=0 \\ \end{align*}

0.457

9087

1093

\begin{align*} y^{\prime \prime }+{\mathrm e}^{-x} y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.458

9088

1290

\begin{align*} 5 u^{\prime \prime }+2 u^{\prime }+7 u&=0 \\ u \left (0\right ) &= 2 \\ u^{\prime }\left (0\right ) &= 1 \\ \end{align*}

0.458

9089

1817

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

0.458

9090

2370

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

0.458

9091

3753

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

0.458

9092

12609

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

0.458

9093

12643

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

0.458

9094

13059

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

0.458

9095

14804

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

N/A

N/A

N/A

0.458

9096

16041

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

0.458

9097

16620

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

0.458

9098

17827

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

0.458

9099

19482

\begin{align*} y^{\prime \prime }+8 y^{\prime }-9 y&=0 \\ y \left (1\right ) &= 2 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}

0.458

9100

20188

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

0.458