2.3.91 Problems 9001 to 9100

Table 2.755: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

9001

8055

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

0.661

9002

8137

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

Series expansion around \(x=0\).

0.661

9003

9474

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

0.661

9004

17232

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

0.661

9005

18428

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

0.661

9006

20367

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

0.661

9007

20774

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

0.661

9008

24016

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

0.661

9009

14083

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

0.662

9010

14640

\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-3 y^{\prime \prime }&=18 x^{2}+16 x \,{\mathrm e}^{x}+4 \,{\mathrm e}^{3 x}-9 \\ \end{align*}

0.662

9011

17773

\begin{align*} y^{\prime \prime }-8 y^{\prime }+16 y&=\frac {{\mathrm e}^{4 t}}{t^{3}} \\ \end{align*}

0.662

9012

18387

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

Series expansion around \(x=0\).

0.662

9013

18649

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

0.662

9014

18656

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

0.662

9015

21153

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

0.662

9016

25325

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

Series expansion around \(t=0\).

0.662

9017

27007

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

0.662

9018

27179

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

With initial conditions

\begin{align*} x_{1} \left (0\right ) &= 13 \\ x_{2} \left (0\right ) &= 12 \\ \end{align*}

0.662

9019

27707

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

0.662

9020

882

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

0.663

9021

3143

\begin{align*} 8 y^{\prime \prime }-y&=x \,{\mathrm e}^{-\frac {x}{2}} \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}

0.663

9022

12958

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

0.663

9023

14379

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

0.663

9024

14405

\begin{align*} x^{\prime }&=9 y \\ y^{\prime }&=-x \\ \end{align*}

0.663

9025

18201

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

0.663

9026

18458

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

Using Laplace transform method.

0.663

9027

3378

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

Series expansion around \(x=0\).

0.664

9028

8006

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

0.664

9029

9132

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

0.664

9030

12980

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

0.664

9031

13015

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

0.664

9032

14398

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

0.664

9033

16177

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

0.664

9034

16886

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

Series expansion around \(x=0\).

0.664

9035

20641

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

0.664

9036

27029

\begin{align*} y^{\prime \prime }+10 y^{\prime }+24 y&=f \left (t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

0.664

9037

981

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

0.665

9038

982

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

0.665

9039

3373

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

Series expansion around \(x=0\).

0.665

9040

3846

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

0.665

9041

7122

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

0.665

9042

8062

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

0.665

9043

9045

\begin{align*} y_{1}^{\prime }&=y_{2} \\ y_{2}^{\prime }&=6 y_{1}+y_{2} \\ \end{align*}

With initial conditions

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

0.665

9044

9071

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

0.665

9045

10213

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

Series expansion around \(x=0\).

0.665

9046

16012

\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*}

0.665

9047

16085

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

0.665

9048

19043

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

0.665

9049

20532

\begin{align*} x^{5} y^{\prime \prime }+3 x^{3} y^{\prime }+\left (3-6 x \right ) x^{2} y&=x^{4}+2 x -5 \\ \end{align*}

0.665

9050

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*}

0.665

9051

23725

\begin{align*} x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }+\frac {y}{16}&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.665

9052

9587

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

Series expansion around \(x=0\).

0.666

9053

10211

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

Series expansion around \(x=0\).

0.666

9054

10218

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

Series expansion around \(x=0\).

0.666

9055

16192

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

0.666

9056

18815

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

0.666

9057

22913

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

0.666

9058

24760

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

0.666

9059

26656

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

0.666

9060

2831

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

0.667

9061

4107

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

0.667

9062

7915

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

0.667

9063

9516

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

Series expansion around \(x=0\).

0.667

9064

9700

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

0.667

9065

9803

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

0.667

9066

18204

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

0.667

9067

18637

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

0.667

9068

18905

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

Using Laplace transform method.

0.667

9069

23497

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

0.667

9070

24107

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

Series expansion around \(x=0\).

0.667

9071

24636

\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=18 \cos \left (3 x \right ) {\mathrm e}^{-2 x} \\ \end{align*}

0.667

9072

25125

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

0.667

9073

27377

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

0.667

9074

154

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

0.668

9075

1004

\begin{align*} x_{1}^{\prime }&=9 x_{1}+4 x_{2} \\ x_{2}^{\prime }&=-6 x_{1}-x_{2} \\ x_{3}^{\prime }&=6 x_{1}+4 x_{2}+3 x_{3} \\ \end{align*}

0.668

9076

2586

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

0.668

9077

2609

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=t^{{3}/{2}} {\mathrm e}^{3 t} \\ \end{align*}

0.668

9078

3218

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

0.668

9079

5767

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

0.668

9080

10191

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

Series expansion around \(x=1\).

0.668

9081

18660

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

With initial conditions

\begin{align*} x \left (0\right ) &= 2 \\ y \left (0\right ) &= 5 \\ \end{align*}

0.668

9082

19064

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

0.668

9083

19366

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

0.668

9084

19620

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

Series expansion around \(x=0\).

0.668

9085

21470

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

0.668

9086

22198

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

Series expansion around \(x=1\).

0.668

9087

22657

\begin{align*} 4 y^{\prime \prime }-8 y^{\prime }+7 y&=0 \\ \end{align*}

0.668

9088

23498

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

0.668

9089

23624

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

With initial conditions

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

0.668

9090

25939

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

0.668

9091

27716

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

0.668

9092

3999

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

Series expansion around \(x=0\).

0.669

9093

9005

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

Series expansion around \(x=0\).

0.669

9094

9251

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

0.669

9095

14386

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

0.669

9096

14920

\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=0 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 8 \\ \end{align*}

0.669

9097

18962

\begin{align*} \frac {7 y^{\prime \prime }}{5}+y&=\operatorname {Heaviside}\left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

0.669

9098

24714

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

0.669

9099

25547

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

0.669

9100

25984

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

0.669