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

4001

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

Series expansion around \(x=0\).

0.549

9002

6120

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

0.549

9003

6297

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

0.549

9004

7656

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

Series expansion around \(x=0\).

0.549

9005

8536

\begin{align*} 4 x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}-25\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.549

9006

8601

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

Series expansion around \(x=0\).

0.549

9007

9271

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

0.549

9008

9421

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

Series expansion around \(x=0\).

0.549

9009

10440

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

0.549

9010

16034

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

With initial conditions

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

0.549

9011

16168

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

0.549

9012

19452

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

0.549

9013

19778

\begin{align*} v^{\prime \prime }+\frac {2 v^{\prime }}{r}&=0 \\ \end{align*}

0.549

9014

21551

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

0.549

9015

25197

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

0.549

9016

26008

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

Series expansion around \(x=0\).

0.549

9017

27018

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

Using Laplace transform method.

0.549

9018

1739

\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 7 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*}

0.550

9019

2644

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

Series expansion around \(t=0\).

0.550

9020

2828

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

0.550

9021

4602

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

Series expansion around \(x=0\).

0.550

9022

6229

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

0.550

9023

7994

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

0.550

9024

11734

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

0.550

9025

16689

\begin{align*} y^{\prime \prime }-7 y^{\prime }+10 y&=6 \,{\mathrm e}^{3 x} \\ \end{align*}

0.550

9026

16846

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

Series expansion around \(x=0\).

0.550

9027

18446

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

With initial conditions

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

0.550

9028

18678

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

0.550

9029

23707

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

Series expansion around \(x=0\).

0.550

9030

25548

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

0.550

9031

26964

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

0.550

9032

27092

\(\left [\begin {array}{cc} 1 & -6 \\ 2 & 2 \end {array}\right ]\)

N/A

N/A

N/A

0.550

9033

1389

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

Series expansion around \(x=0\).

0.551

9034

1885

\begin{align*} \left (2 x^{5}+1\right ) y^{\prime \prime }+14 x^{4} y^{\prime }+10 x^{3} y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.551

9035

9071

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

0.551

9036

15770

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

0.551

9037

16523

\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&=0 \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= 31 \\ \end{align*}

0.551

9038

18004

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

0.551

9039

18666

\begin{align*} x^{\prime }&=2 x-\frac {5 y}{2} \\ y^{\prime }&=\frac {9 x}{5}-y \\ \end{align*}

0.551

9040

20454

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

0.551

9041

23579

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

With initial conditions

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

0.551

9042

24768

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

0.551

9043

24814

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

0.551

9044

25417

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

0.551

9045

26840

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

Using Laplace transform method.

0.551

9046

314

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

0.552

9047

979

\begin{align*} x_{1}^{\prime }&=7 x_{1}-5 x_{2} \\ x_{2}^{\prime }&=4 x_{1}+3 x_{2} \\ \end{align*}

0.552

9048

2646

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

Series expansion around \(t=0\).

0.552

9049

4523

\begin{align*} y^{\prime \prime }+4 y&=8 \operatorname {Heaviside}\left (t -\pi \right ) \sin \left (2 t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}

Using Laplace transform method.

0.552

9050

6096

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

0.552

9051

6613

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

0.552

9052

8737

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

0.552

9053

10455

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

Series expansion around \(x=0\).

0.552

9054

14225

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

0.552

9055

14678

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

0.552

9056

17393

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

0.552

9057

22734

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

0.552

9058

22884

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

0.552

9059

23078

\begin{align*} y^{\prime \prime }+y^{\prime }+y&=2 x^{3}+7 x^{2}-x \\ \end{align*}

0.552

9060

23514

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

0.552

9061

26116

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

0.552

9062

26706

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

Series expansion around \(x=0\).

0.552

9063

977

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

0.553

9064

1395

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

Series expansion around \(x=0\).

0.553

9065

1635

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

0.553

9066

1888

\begin{align*} \left (x^{8}+1\right ) y^{\prime \prime }-16 x^{7} y^{\prime }+72 x^{6} y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.553

9067

7657

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

Series expansion around \(x=0\).

0.553

9068

13164

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

N/A

N/A

N/A

0.553

9069

14675

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

0.553

9070

16144

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

Using Laplace transform method.

0.553

9071

18025

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

0.553

9072

20762

\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*}

0.553

9073

23074

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

0.553

9074

23439

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

Series expansion around \(x=0\).

0.553

9075

23444

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

Series expansion around \(x=0\).

0.553

9076

26933

\begin{align*} y^{\prime \prime }-6 y^{\prime }+13 y&=-{\mathrm e}^{x} \\ \end{align*}

0.553

9077

26934

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

0.553

9078

338

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

0.554

9079

473

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

Series expansion around \(x=0\).

0.554

9080

882

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

0.554

9081

1891

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

Series expansion around \(x=0\).

0.554

9082

1933

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

Series expansion around \(x=0\).

0.554

9083

2019

\begin{align*} x^{2} \left (9+4 x \right ) y^{\prime \prime }+3 y^{\prime } x +\left (x +1\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.554

9084

9778

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

0.554

9085

14680

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=\frac {{\mathrm e}^{-3 x}}{x^{3}} \\ \end{align*}

0.554

9086

16062

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

0.554

9087

17392

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

0.554

9088

245

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

0.555

9089

1317

\begin{align*} 4 y^{\prime \prime }+12 y^{\prime }+9 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -4 \\ \end{align*}

0.555

9090

7280

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=12 \,{\mathrm e}^{-x} \\ \end{align*}

0.555

9091

8603

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

Series expansion around \(x=0\).

0.555

9092

9479

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

0.555

9093

12546

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

0.555

9094

14103

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

0.555

9095

20847

\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=10 \\ \end{align*}

0.555

9096

21584

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

0.555

9097

23457

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

0.555

9098

24729

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

0.555

9099

27038

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

Using Laplace transform method.

0.555

9100

474

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

Series expansion around \(x=0\).

0.556