2.3.61 Problems 6001 to 6100

Table 2.653: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

6001

19882

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

0.486

6002

21632

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

0.486

6003

24908

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

0.486

6004

1938

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

0.487

6005

5277

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

0.487

6006

10061

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

0.487

6007

15322

\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=f \left (t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.487

6008

16953

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

0.487

6009

19266

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

0.487

6010

19664

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

0.487

6011

20026

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

0.487

6012

21898

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

0.487

6013

22924

\begin{align*} x^{\prime }-x+2 y^{\prime }+7 y&=3 t -15 \\ 2 x^{\prime }+y^{\prime }+x+5 y&=9 t -7 \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= -3 \\ \end{align*}

0.487

6014

24706

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

0.487

6015

24781

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

0.487

6016

1028

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

0.488

6017

4661

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

0.488

6018

6515

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

0.488

6019

16044

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

0.488

6020

20937

\begin{align*} x^{\prime }&=12 x-15 y \\ y^{\prime }&=4 x-4 y \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 0 \\ \end{align*}

0.488

6021

5643

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

0.489

6022

16395

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

0.489

6023

20704

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

0.489

6024

21216

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

0.489

6025

1864

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

0.490

6026

2046

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

0.490

6027

2467

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

0.490

6028

3828

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

0.490

6029

4169

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

0.490

6030

6924

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

0.490

6031

7661

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

0.490

6032

16838

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

0.490

6033

17828

\begin{align*} x^{\prime }&=8 x-y \\ y^{\prime }&=x+6 y \\ \end{align*}

0.490

6034

18677

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

0.490

6035

20739

\begin{align*} {y^{\prime }}^{3}-4 y y^{\prime } x +8 y^{2}&=0 \\ \end{align*}

0.490

6036

24050

\begin{align*} y^{\prime \prime \prime \prime }-12 y^{\prime \prime \prime }+54 y^{\prime \prime }-108 y^{\prime }+81 y&=x^{2} {\mathrm e}^{3 x} \\ \end{align*}
Using Laplace transform method.

0.490

6037

24947

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

0.490

6038

25369

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

0.490

6039

349

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

0.491

6040

507

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

0.491

6041

1016

\begin{align*} x_{1}^{\prime }&=-19 x_{1}+12 x_{2}+84 x_{3} \\ x_{2}^{\prime }&=5 x_{2} \\ x_{3}^{\prime }&=-8 x_{1}+4 x_{2}+33 x_{3} \\ \end{align*}

0.492

6042

1017

\begin{align*} x_{1}^{\prime }&=-13 x_{1}+40 x_{2}-48 x_{3} \\ x_{2}^{\prime }&=-8 x_{1}+23 x_{2}-24 x_{3} \\ x_{3}^{\prime }&=3 x_{3} \\ \end{align*}

0.492

6043

5414

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

0.492

6044

10420

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

0.492

6045

13028

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

0.492

6046

13071

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

0.492

6047

23712

\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +12 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.492

6048

469

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

0.493

6049

1392

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

0.493

6050

2421

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

0.493

6051

11734

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

0.493

6052

17632

\begin{align*} x^{3} y^{\prime \prime \prime \prime }+6 x^{2} y^{\prime \prime \prime }+7 y^{\prime \prime } x +y^{\prime }&=0 \\ \end{align*}

0.493

6053

19598

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

0.493

6054

23435

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

0.493

6055

1022

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

0.494

6056

1639

\begin{align*} y^{\prime }-4 y&=\frac {48 x}{y^{2}} \\ y \left (0\right ) &= 1 \\ \end{align*}

0.494

6057

2659

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

0.494

6058

2701

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

0.494

6059

13051

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

0.494

6060

2020

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

0.495

6061

12877

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

0.495

6062

17685

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

0.495

6063

1889

\begin{align*} \left (-x^{6}+1\right ) y^{\prime \prime }-12 x^{5} y^{\prime }-30 x^{4} y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.496

6064

6460

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

0.496

6065

6498

\begin{align*} x y y^{\prime \prime }&=y \left (\operatorname {a2} +\operatorname {a3} y^{2}\right )+x \left (\operatorname {a0} +\operatorname {a1} y^{4}\right )-y y^{\prime }+x {y^{\prime }}^{2} \\ \end{align*}

0.496

6066

14051

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

0.496

6067

453

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

0.497

6068

605

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

0.497

6069

1843

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

0.497

6070

4460

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

0.497

6071

6644

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

0.497

6072

8615

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

0.497

6073

11666

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

0.497

6074

18672

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

0.497

6075

20034

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

0.497

6076

20368

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

0.497

6077

24049

\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+4 y^{\prime \prime }&=16 \,{\mathrm e}^{2 x} \\ \end{align*}
Using Laplace transform method.

0.497

6078

1409

\begin{align*} x_{1}^{\prime }&=x_{1}-5 x_{2} \\ x_{2}^{\prime }&=x_{1}-3 x_{2} \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 1 \\ \end{align*}

0.498

6079

1865

\begin{align*} \left (2 x^{2}+1\right ) y^{\prime \prime }-9 y^{\prime } x -6 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}
Series expansion around \(x=0\).

0.498

6080

7455

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

0.498

6081

9379

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

0.498

6082

9469

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

0.498

6083

9993

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

0.498

6084

10197

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

0.498

6085

20413

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

0.498

6086

21410

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

0.498

6087

22945

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

0.498

6088

23594

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

0.498

6089

24989

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

0.498

6090

6327

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

0.499

6091

6368

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

0.499

6092

6524

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

0.499

6093

10184

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

0.499

6094

19652

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

0.499

6095

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 \(x=0\).

0.499

6096

23715

\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +9 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.499

6097

471

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

0.500

6098

3509

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

0.500

6099

4217

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

0.500

6100

4588

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

0.500