2.3.121 Problems 12001 to 12100

Table 2.773: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

12001

8039

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

0.674

12002

9430

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

0.674

12003

9542

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

0.674

12004

9556

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

0.674

12005

9956

\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 \(x=0\).

0.674

12006

10186

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

0.674

12007

12916

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

0.674

12008

15889

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

0.674

12009

16915

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

0.674

12010

23966

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

0.674

12011

25654

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

0.674

12012

995

\begin{align*} x_{1}^{\prime }&=-40 x_{1}-12 x_{2}+54 x_{3} \\ x_{2}^{\prime }&=35 x_{1}+13 x_{2}-46 x_{3} \\ x_{3}^{\prime }&=-25 x_{1}-7 x_{2}+34 x_{3} \\ \end{align*}

0.675

12013

1347

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

0.675

12014

2199

\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y&=4 \,{\mathrm e}^{-x} \left (1-6 x \right )-2 \cos \left (x \right ) x +2 \left (x +1\right ) \sin \left (x \right ) \\ \end{align*}

0.675

12015

3298

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

0.675

12016

6213

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

0.675

12017

6934

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

0.675

12018

16081

\begin{align*} y^{\prime \prime }+7 y^{\prime }+10 y&={\mathrm e}^{-2 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.675

12019

20172

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

0.675

12020

21967

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

0.675

12021

22066

\begin{align*} y^{\prime }-7 y&=14 x \\ \end{align*}

0.675

12022

22322

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

0.675

12023

23545

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

0.675

12024

23745

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

0.675

12025

25380

\begin{align*} y_{1}^{\prime }&=-y_{1}-4 y_{2}+4 \\ y_{2}^{\prime }&=y_{1}-y_{2}+1 \\ \end{align*}
With initial conditions
\begin{align*} y_{1} \left (0\right ) &= 2 \\ y_{2} \left (0\right ) &= -1 \\ \end{align*}

0.675

12026

23

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

0.676

12027

3374

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

0.676

12028

6130

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

0.676

12029

12669

\begin{align*} y^{\prime \prime }&=-\frac {27 x y}{16 \left (x^{3}-1\right )^{2}} \\ \end{align*}

0.676

12030

14944

\begin{align*} x^{\prime \prime }+4 x&=289 t \,{\mathrm e}^{t} \sin \left (2 t \right ) \\ \end{align*}

0.676

12031

21495

\begin{align*} y^{\prime \prime }-2 y^{\prime }+10 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

0.676

12032

1414

\begin{align*} x_{1}^{\prime }&=-\frac {x_{1}}{4}+x_{2} \\ x_{2}^{\prime }&=-x_{1}-\frac {x_{2}}{4} \\ x_{3}^{\prime }&=\frac {x_{3}}{10} \\ \end{align*}

0.677

12033

2450

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

0.677

12034

5446

\begin{align*} 9 {y^{\prime }}^{2}+3 x y^{4} y^{\prime }+y^{5}&=0 \\ \end{align*}

0.677

12035

7898

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

0.677

12036

7911

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

0.677

12037

8247

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

0.677

12038

9429

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

0.677

12039

9681

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

0.677

12040

10088

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

0.677

12041

12540

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

0.677

12042

22939

\begin{align*} x^{\prime }&=-12 x-7 y \\ y^{\prime }&=19 x+11 y \\ \end{align*}

0.677

12043

23748

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

0.677

12044

23954

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

0.677

12045

24885

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

0.677

12046

24926

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

0.677

12047

917

\begin{align*} x^{\prime \prime }+4 x^{\prime }+5 x&=10 \cos \left (3 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.678

12048

920

\begin{align*} x^{\prime \prime }+2 x^{\prime }+26 x&=600 \cos \left (10 t \right ) \\ x \left (0\right ) &= 10 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.678

12049

1747

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

0.678

12050

2273

\begin{align*} y_{1}^{\prime }&=-y_{1}-4 y_{2}-y_{3} \\ y_{2}^{\prime }&=3 y_{1}+6 y_{2}+y_{3} \\ y_{3}^{\prime }&=-3 y_{1}-2 y_{2}+3 y_{3} \\ \end{align*}
With initial conditions
\begin{align*} y_{1} \left (0\right ) &= -2 \\ y_{2} \left (0\right ) &= 1 \\ y_{3} \left (0\right ) &= 3 \\ \end{align*}

0.678

12051

3177

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

0.678

12052

3369

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

0.678

12053

3643

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

0.678

12054

6141

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

0.678

12055

8045

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

0.678

12056

9684

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

0.678

12057

10585

\begin{align*} 4 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+12 x^{2} \left (x +1\right ) y^{\prime }+\left (3 x^{2}+3 x +1\right ) y&=0 \\ \end{align*}

0.678

12058

14891

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

0.678

12059

16591

\begin{align*} 9 y+6 y^{\prime }+y^{\prime \prime }&=169 \sin \left (2 x \right ) \\ y \left (0\right ) &= -10 \\ y^{\prime }\left (0\right ) &= 9 \\ \end{align*}

0.678

12060

16736

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

0.678

12061

18157

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

0.678

12062

18268

\begin{align*} 9 y+6 y^{\prime }+y^{\prime \prime }&=10 \sin \left (x \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.678

12063

19053

\begin{align*} x_{1}^{\prime }&=-7 x_{1}+9 x_{2}-6 x_{3} \\ x_{2}^{\prime }&=-8 x_{1}+11 x_{2}-7 x_{3} \\ x_{3}^{\prime }&=-2 x_{1}+3 x_{2}-x_{3} \\ \end{align*}

0.678

12064

23282

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

0.678

12065

24284

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

0.678

12066

15735

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

0.679

12067

15887

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

0.679

12068

18681

\begin{align*} x^{\prime }&=a x+10 y \\ y^{\prime }&=-x-4 y \\ \end{align*}

0.679

12069

2591

\begin{align*} y^{\prime \prime }+p \left (t \right ) y^{\prime }+q \left (t \right ) y&=t +1 \\ \end{align*}

0.680

12070

3350

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

0.680

12071

9382

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

0.680

12072

12672

\begin{align*} y^{\prime \prime }&=-a \,x^{2 a -1} x^{-2 a} y^{\prime }-b^{2} x^{-2 a} y \\ \end{align*}

0.680

12073

14760

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

0.680

12074

20032

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

0.680

12075

23731

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

0.680

12076

23793

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

0.680

12077

24

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

0.681

12078

387

\begin{align*} m x^{\prime \prime }+k x&=F_{0} \cos \left (\omega t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.681

12079

2246

\begin{align*} y_{1}^{\prime }&=-6 y_{1}-4 y_{2}-8 y_{3} \\ y_{2}^{\prime }&=-4 y_{1}-4 y_{3} \\ y_{3}^{\prime }&=-8 y_{1}-4 y_{2}-6 y_{3} \\ \end{align*}

0.681

12080

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 \(x=0\).

0.681

12081

3822

\begin{align*} x_{1}^{\prime }&=x_{1}+x_{2}+{\mathrm e}^{2 t} \\ x_{2}^{\prime }&=3 x_{1}-x_{2}+5 \,{\mathrm e}^{2 t} \\ \end{align*}

0.681

12082

6419

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

0.681

12083

8352

\begin{align*} s^{\prime }&=k s \\ \end{align*}

0.681

12084

8617

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

0.681

12085

9491

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

0.681

12086

9544

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

0.681

12087

9555

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

0.681

12088

9985

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

0.681

12089

10558

\begin{align*} x^{2} \left (2+x \right ) y^{\prime \prime }+5 x \left (1-x \right ) y^{\prime }-\left (2-8 x \right ) y&=0 \\ \end{align*}

0.681

12090

14539

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

0.681

12091

19247

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

0.681

12092

21113

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

0.681

12093

21232

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

0.681

12094

23737

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

0.681

12095

2101

\begin{align*} 4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 y^{\prime } x -\left (-x^{2}+35\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.682

12096

6500

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

0.682

12097

7946

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

0.682

12098

19657

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

0.682

12099

3297

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

0.683

12100

5447

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

0.683