2.3.81 Problems 8001 to 8100

Table 2.705: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

8001

15474

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

0.516

8002

18032

\begin{align*} 8 {y^{\prime }}^{3}-12 {y^{\prime }}^{2}&=-27 x +27 y \\ \end{align*}

0.516

8003

19590

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

0.516

8004

20994

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

0.516

8005

21548

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

0.516

8006

21659

\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }+3 y^{\prime } x +y x&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 6 \\ \end{align*}
Series expansion around \(x=0\).

0.516

8007

22913

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

0.516

8008

23398

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

0.516

8009

23514

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

0.516

8010

23802

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

0.516

8011

25817

\begin{align*} 1+{\mathrm e}^{3 x} y^{\prime }&=0 \\ \end{align*}

0.516

8012

25949

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

0.516

8013

26028

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

0.516

8014

1401

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

0.517

8015

1405

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

0.517

8016

1432

\begin{align*} x_{1}^{\prime }&=4 x_{1}-2 x_{2}+\frac {1}{t^{3}} \\ x_{2}^{\prime }&=8 x_{1}-4 x_{2}-\frac {1}{t^{2}} \\ \end{align*}

0.517

8017

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 \(x=0\).

0.517

8018

2775

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

0.517

8019

4590

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

0.517

8020

5479

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

0.517

8021

5811

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

0.517

8022

9469

\begin{align*} x^{\prime }&=7 x+6 y \\ y^{\prime }&=2 x+6 y \\ \end{align*}

0.517

8023

10183

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

0.517

8024

12277

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

0.517

8025

14813

\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}
Using Laplace transform method.

0.517

8026

15443

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

0.517

8027

16136

\begin{align*} y^{\prime \prime }+4 y&=\cos \left (2 t \right ) \\ y \left (0\right ) &= -2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.517

8028

16865

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

0.517

8029

19179

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

0.517

8030

20949

\begin{align*} y^{\prime }&=y^{2}-6 y-16 \\ \end{align*}

0.517

8031

21587

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

0.517

8032

21601

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

0.517

8033

22197

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

0.517

8034

25127

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

0.517

8035

7837

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

0.518

8036

16347

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

0.518

8037

16363

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

0.518

8038

18157

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

0.518

8039

22179

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

0.518

8040

24740

\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=15 \sqrt {1+{\mathrm e}^{-x}} \\ \end{align*}

0.518

8041

25575

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

0.518

8042

1870

\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*}
Series expansion around \(x=2\).

0.519

8043

2675

\begin{align*} y^{\prime \prime }+y^{\prime }+y&=t^{3} \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.519

8044

3350

\begin{align*} 2 y^{\prime \prime } x +5 y^{\prime }+y x&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.519

8045

5788

\begin{align*} -4 y-3 y^{\prime }+y^{\prime \prime }&=10 \cos \left (2 x \right ) \\ \end{align*}

0.519

8046

9072

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

0.519

8047

9980

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

0.519

8048

10488

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

0.519

8049

12477

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

0.519

8050

15467

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

0.519

8051

15573

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

0.519

8052

16832

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

0.519

8053

17771

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

0.519

8054

18092

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

0.519

8055

18120

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

0.519

8056

20075

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

0.519

8057

25091

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

0.519

8058

26134

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

0.519

8059

1717

\begin{align*} 27 x y^{2}+8 y^{3}+\left (18 x^{2} y+12 x y^{2}\right ) y^{\prime }&=0 \\ \end{align*}

0.520

8060

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*}

0.520

8061

3372

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

0.520

8062

3749

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

0.520

8063

5750

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

0.520

8064

6206

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

0.520

8065

7366

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

0.520

8066

7843

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

0.520

8067

9589

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

0.520

8068

9832

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

0.520

8069

13292

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

0.520

8070

15667

\begin{align*} y^{\prime \prime }+9 y&=27 x +18 \\ y \left (0\right ) &= 23 \\ y^{\prime }\left (0\right ) &= 21 \\ \end{align*}

0.520

8071

16167

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

0.520

8072

18825

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

0.520

8073

18853

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

0.520

8074

21000

\begin{align*} u^{\prime \prime }+2 a u^{\prime }+\omega ^{2} u&=c \cos \left (\omega t \right ) \\ \end{align*}

0.520

8075

22100

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

0.520

8076

22822

\begin{align*} y^{\prime }&=y x \\ y \left (0\right ) &= 5 \\ \end{align*}
Series expansion around \(x=0\).

0.520

8077

1892

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

0.521

8078

3726

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

0.521

8079

4003

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

0.521

8080

4469

\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=36 x \,{\mathrm e}^{2 x} \\ \end{align*}

0.521

8081

6116

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

0.521

8082

8614

\begin{align*} \left (x -1\right )^{2} y^{\prime \prime }-\left (x -1\right ) y^{\prime }-35 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.521

8083

16885

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

0.521

8084

19697

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

0.521

8085

21695

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

0.521

8086

23011

\begin{align*} 38 x^{\prime \prime }+10 x^{\prime }-3 x&=0 \\ x \left (0\right ) &= 5 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.521

8087

23035

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

0.521

8088

25159

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

0.521

8089

593

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

0.522

8090

1410

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

0.522

8091

2403

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

0.522

8092

3374

\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 \left (x +1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.522

8093

4005

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

0.522

8094

5717

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

0.522

8095

8077

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

0.522

8096

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*}

0.522

8097

10241

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

0.522

8098

15246

\begin{align*} y^{\prime \prime }-7 y^{\prime }+6 y&=\delta \left (t -1\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.522

8099

15466

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

0.522

8100

16031

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

0.522