2.3.11 Problems 1001 to 1100

Table 2.605: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

1001

9293

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=47 x_{1} \left (t \right )-8 x_{2} \left (t \right )+5 x_{3} \left (t \right )-5 x_{4} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=-10 x_{1} \left (t \right )+32 x_{2} \left (t \right )+18 x_{3} \left (t \right )-2 x_{4} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=139 x_{1} \left (t \right )-40 x_{2} \left (t \right )-167 x_{3} \left (t \right )-121 x_{4} \left (t \right )\\ \frac {d}{d t}x_{4} \left (t \right )&=-232 x_{1} \left (t \right )+64 x_{2} \left (t \right )+360 x_{3} \left (t \right )+248 x_{4} \left (t \right )\\ \end {array} \]

0.102

1002

9294

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=139 x_{1} \left (t \right )-14 x_{2} \left (t \right )-52 x_{3} \left (t \right )-14 x_{4} \left (t \right )+28 x_{5} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=-22 x_{1} \left (t \right )+5 x_{2} \left (t \right )+7 x_{3} \left (t \right )+8 x_{4} \left (t \right )-7 x_{5} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=370 x_{1} \left (t \right )-38 x_{2} \left (t \right )-139 x_{3} \left (t \right )-38 x_{4} \left (t \right )+76 x_{5} \left (t \right )\\ \frac {d}{d t}x_{4} \left (t \right )&=152 x_{1} \left (t \right )-16 x_{2} \left (t \right )-59 x_{3} \left (t \right )-13 x_{4} \left (t \right )+35 x_{5} \left (t \right )\\ \frac {d}{d t}x_{5} \left (t \right )&=95 x_{1} \left (t \right )-10 x_{2} \left (t \right )-38 x_{3} \left (t \right )-7 x_{4} \left (t \right )+23 x_{5} \left (t \right )\\ \end {array} \]

0.102

1003

9306

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=9 x_{1} \left (t \right )+13 x_{2} \left (t \right )-13 x_{6} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=-14 x_{1} \left (t \right )+19 x_{2} \left (t \right )-10 x_{3} \left (t \right )-20 x_{4} \left (t \right )+10 x_{5} \left (t \right )+4 x_{6} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=-30 x_{1} \left (t \right )+12 x_{2} \left (t \right )-7 x_{3} \left (t \right )-30 x_{4} \left (t \right )+12 x_{5} \left (t \right )+18 x_{6} \left (t \right )\\ \frac {d}{d t}x_{4} \left (t \right )&=-12 x_{1} \left (t \right )+10 x_{2} \left (t \right )-10 x_{3} \left (t \right )-9 x_{4} \left (t \right )+10 x_{5} \left (t \right )+2 x_{6} \left (t \right )\\ \frac {d}{d t}x_{5} \left (t \right )&=6 x_{1} \left (t \right )+9 x_{2} \left (t \right )+6 x_{4} \left (t \right )+5 x_{5} \left (t \right )-15 x_{6} \left (t \right )\\ \frac {d}{d t}x_{6} \left (t \right )&=-14 x_{1} \left (t \right )+23 x_{2} \left (t \right )-10 x_{3} \left (t \right )-20 x_{4} \left (t \right )+10 x_{5} \left (t \right )\\ \end {array} \]

0.102

1004

10902

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=9 x_{1} \left (t \right )+4 x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=-6 x_{1} \left (t \right )-x_{2} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=6 x_{1} \left (t \right )+4 x_{2} \left (t \right )+3 x_{3} \left (t \right )\\ \end {array} \]

0.102

1005

11247

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=x_{1} \left (t \right )-3 x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=3 x_{1} \left (t \right )+7 x_{2} \left (t \right )\\ \end {array} \]

0.102

1006

14166

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=x_{2} \left (t \right )+2 x_{3} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=-5 x_{1} \left (t \right )-3 x_{2} \left (t \right )-7 x_{3} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=x_{1} \left (t \right )\\ \end {array} \]

0.102

1007

20146

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=x_{3} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=x_{4} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=-2 x_{1} \left (t \right )+2 x_{2} \left (t \right )-3 x_{3} \left (t \right )+x_{4} \left (t \right )\\ \frac {d}{d t}x_{4} \left (t \right )&=2 x_{1} \left (t \right )-2 x_{2} \left (t \right )+x_{3} \left (t \right )-3 x_{4} \left (t \right )\\ \end {array} \]

0.102

1008

27703

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=-2 x_{1} \left (t \right )+x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=-x_{1} \left (t \right )-4 x_{2} \left (t \right )\\ \end {array} \]

0.102

1009

6623

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=3 x_{1} \left (t \right )-x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=x_{1} \left (t \right )+x_{2} \left (t \right )\\ \end {array} \]

0.103

1010

6642

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=x_{1} \left (t \right )-2 x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=2 x_{1} \left (t \right )+5 x_{2} \left (t \right )\\ \end {array} \]

0.103

1011

6667

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=3 x_{1} \left (t \right )-x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=x_{1} \left (t \right )+5 x_{2} \left (t \right )\\ \end {array} \]

0.103

1012

10913

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=7 x_{1} \left (t \right )+x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=-4 x_{1} \left (t \right )+3 x_{2} \left (t \right )\\ \end {array} \]

0.103

1013

15069

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=x_{1} \left (t \right )-4 x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=4 x_{1} \left (t \right )+9 x_{2} \left (t \right )\\ \end {array} \]

0.103

1014

25916

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=2 x_{1} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=-7 x_{1} \left (t \right )+9 x_{2} \left (t \right )+7 x_{3} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=2 x_{3} \left (t \right )\\ \end {array} \]

0.103

1015

3370

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=25 x_{1} \left (t \right )+12 x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=-18 x_{1} \left (t \right )-5 x_{2} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=6 x_{1} \left (t \right )+6 x_{2} \left (t \right )+13 x_{3} \left (t \right )\\ \end {array} \]

0.104

1016

3795

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=-19 x_{1} \left (t \right )+12 x_{2} \left (t \right )+84 x_{3} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=5 x_{2} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=-8 x_{1} \left (t \right )+4 x_{2} \left (t \right )+33 x_{3} \left (t \right )\\ \end {array} \]

0.104

1017

7617

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }\left (t \right )&=-13 x_{1} \left (t \right )+40 x_{2} \left (t \right )-48 x_{3} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=-8 x_{1} \left (t \right )+23 x_{2} \left (t \right )-24 x_{3} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=3 x_{3} \left (t \right )\\ \end {array} \]

0.104

1018

11179

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=-3 x_{1} \left (t \right )-4 x_{3} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=-x_{1} \left (t \right )-x_{2} \left (t \right )-x_{3} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=x_{1} \left (t \right )+x_{3} \left (t \right )\\ \end {array} \]

0.104

1019

15141

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=-x_{1} \left (t \right )+x_{3} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=-x_{2} \left (t \right )+x_{3} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=x_{1} \left (t \right )-x_{2} \left (t \right )-x_{3} \left (t \right )\\ \end {array} \]

0.104

1020

20665

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=-x_{1} \left (t \right )+x_{3} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=x_{2} \left (t \right )-4 x_{3} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=x_{2} \left (t \right )-3 x_{3} \left (t \right )\\ \end {array} \]

0.104

1021

24055

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=x_{3} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=-5 x_{1} \left (t \right )-x_{2} \left (t \right )-5 x_{3} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=4 x_{1} \left (t \right )+x_{2} \left (t \right )-2 x_{3} \left (t \right )\\ \end {array} \]

0.104

1022

25914

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=-2 x_{1} \left (t \right )-9 x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=x_{1} \left (t \right )+4 x_{2} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=x_{1} \left (t \right )+3 x_{2} \left (t \right )+x_{3} \left (t \right )\\ \end {array} \]

0.104

1023

26497

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=x_{1} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=-2 x_{1} \left (t \right )-2 x_{2} \left (t \right )-3 x_{3} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=2 x_{1} \left (t \right )+3 x_{2} \left (t \right )+4 x_{3} \left (t \right )\\ \end {array} \]

0.104

1024

942

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=x_{1} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=18 x_{1} \left (t \right )+7 x_{2} \left (t \right )+4 x_{3} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=-27 x_{1} \left (t \right )-9 x_{2} \left (t \right )-5 x_{3} \left (t \right )\\ \end {array} \]

0.105

1025

3704

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=x_{1} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=x_{1} \left (t \right )+3 x_{2} \left (t \right )+x_{3} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=-2 x_{1} \left (t \right )-4 x_{2} \left (t \right )-x_{3} \left (t \right )\\ \end {array} \]

0.105

1026

4474

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=x_{1} \left (t \right )-4 x_{2} \left (t \right )-2 x_{4} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=x_{2} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=6 x_{1} \left (t \right )-12 x_{2} \left (t \right )-x_{3} \left (t \right )-6 x_{4} \left (t \right )\\ \frac {d}{d t}x_{4} \left (t \right )&=-4 x_{2} \left (t \right )-x_{4} \left (t \right )\\ \end {array} \]

0.105

1027

6668

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=2 x_{1} \left (t \right )+x_{2} \left (t \right )+x_{4} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=2 x_{2} \left (t \right )+x_{3} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=2 x_{3} \left (t \right )+x_{4} \left (t \right )\\ \frac {d}{d t}x_{4} \left (t \right )&=2 x_{4} \left (t \right )\\ \end {array} \]

0.105

1028

7990

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=-x_{1} \left (t \right )-4 x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=x_{1} \left (t \right )+3 x_{2} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=x_{1} \left (t \right )+2 x_{2} \left (t \right )+x_{3} \left (t \right )\\ \frac {d}{d t}x_{4} \left (t \right )&=x_{2} \left (t \right )+x_{4} \left (t \right )\\ \end {array} \]

0.105

1029

10835

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=x_{1} \left (t \right )+3 x_{2} \left (t \right )+7 x_{3} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=-x_{2} \left (t \right )-4 x_{3} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=x_{2} \left (t \right )+3 x_{3} \left (t \right )\\ \frac {d}{d t}x_{4} \left (t \right )&=-6 x_{2} \left (t \right )-14 x_{3} \left (t \right )+x_{4} \left (t \right )\\ \end {array} \]

0.105

1030

10924

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=39 x_{1} \left (t \right )+8 x_{2} \left (t \right )-16 x_{3} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=-36 x_{1} \left (t \right )-5 x_{2} \left (t \right )+16 x_{3} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=72 x_{1} \left (t \right )+16 x_{2} \left (t \right )-29 x_{3} \left (t \right )\\ \end {array} \]

0.105

1031

11225

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=28 x_{1} \left (t \right )+50 x_{2} \left (t \right )+100 x_{3} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=15 x_{1} \left (t \right )+33 x_{2} \left (t \right )+60 x_{3} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=-15 x_{1} \left (t \right )-30 x_{2} \left (t \right )-57 x_{3} \left (t \right )\\ \end {array} \]

0.105

1032

14864

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }\left (t \right )&=-2 x_{1} \left (t \right )+17 x_{2} \left (t \right )+4 x_{3} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=-x_{1} \left (t \right )+6 x_{2} \left (t \right )+x_{3} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=x_{2} \left (t \right )+2 x_{3} \left (t \right )\\ \end {array} \]

0.105

1033

15426

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=5 x_{1} \left (t \right )-x_{2} \left (t \right )+x_{3} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=x_{1} \left (t \right )+3 x_{2} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=-3 x_{1} \left (t \right )+2 x_{2} \left (t \right )+x_{3} \left (t \right )\\ \end {array} \]

0.105

1034

16444

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=-3 x_{1} \left (t \right )+5 x_{2} \left (t \right )-5 x_{3} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=3 x_{1} \left (t \right )-x_{2} \left (t \right )+3 x_{3} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=8 x_{1} \left (t \right )-8 x_{2} \left (t \right )+10 x_{3} \left (t \right )\\ \end {array} \]

0.105

1035

20613

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=-15 x_{1} \left (t \right )-7 x_{2} \left (t \right )+4 x_{3} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=34 x_{1} \left (t \right )+16 x_{2} \left (t \right )-11 x_{3} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=17 x_{1} \left (t \right )+7 x_{2} \left (t \right )+5 x_{3} \left (t \right )\\ \end {array} \]

0.105

1036

24015

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=-x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right )-2 x_{4} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=7 x_{1} \left (t \right )-4 x_{2} \left (t \right )-6 x_{3} \left (t \right )+11 x_{4} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=5 x_{1} \left (t \right )-x_{2} \left (t \right )+x_{3} \left (t \right )+3 x_{4} \left (t \right )\\ \frac {d}{d t}x_{4} \left (t \right )&=6 x_{1} \left (t \right )-2 x_{2} \left (t \right )-2 x_{3} \left (t \right )+6 x_{4} \left (t \right )\\ \end {array} \]

0.105

1037

24574

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=2 x_{1} \left (t \right )+x_{2} \left (t \right )-2 x_{3} \left (t \right )+x_{4} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=3 x_{2} \left (t \right )-5 x_{3} \left (t \right )+3 x_{4} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=-13 x_{2} \left (t \right )+22 x_{3} \left (t \right )-12 x_{4} \left (t \right )\\ \frac {d}{d t}x_{4} \left (t \right )&=-27 x_{2} \left (t \right )+45 x_{3} \left (t \right )-25 x_{4} \left (t \right )\\ \end {array} \]

0.105

1038

25928

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=35 x_{1} \left (t \right )-12 x_{2} \left (t \right )+4 x_{3} \left (t \right )+30 x_{4} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=22 x_{1} \left (t \right )-8 x_{2} \left (t \right )+3 x_{3} \left (t \right )+19 x_{4} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=-10 x_{1} \left (t \right )+3 x_{2} \left (t \right )-9 x_{4} \left (t \right )\\ \frac {d}{d t}x_{4} \left (t \right )&=-27 x_{1} \left (t \right )+9 x_{2} \left (t \right )-3 x_{3} \left (t \right )-23 x_{4} \left (t \right )\\ \end {array} \]

0.105

1039

25929

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=11 x_{1} \left (t \right )-x_{2} \left (t \right )+26 x_{3} \left (t \right )+6 x_{4} \left (t \right )-3 x_{5} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=3 x_{2} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=-9 x_{1} \left (t \right )-24 x_{3} \left (t \right )-6 x_{4} \left (t \right )+3 x_{5} \left (t \right )\\ \frac {d}{d t}x_{4} \left (t \right )&=3 x_{1} \left (t \right )+9 x_{3} \left (t \right )+5 x_{4} \left (t \right )-x_{5} \left (t \right )\\ \frac {d}{d t}x_{5} \left (t \right )&=-48 x_{1} \left (t \right )-3 x_{2} \left (t \right )-138 x_{3} \left (t \right )-30 x_{4} \left (t \right )+18 x_{5} \left (t \right )\\ \end {array} \]

0.105

1040

26485

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=3 x_{1} \left (t \right )-4 x_{2} \left (t \right )+x_{3} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=4 x_{1} \left (t \right )+3 x_{2} \left (t \right )+x_{4} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=3 x_{3} \left (t \right )-4 x_{4} \left (t \right )\\ \frac {d}{d t}x_{4} \left (t \right )&=4 x_{3} \left (t \right )+3 x_{4} \left (t \right )\\ \end {array} \]

0.105

1041

253

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=2 x_{1} \left (t \right )-8 x_{3} \left (t \right )-3 x_{4} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=-18 x_{1} \left (t \right )-x_{2} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=-9 x_{1} \left (t \right )-3 x_{2} \left (t \right )-25 x_{3} \left (t \right )-9 x_{4} \left (t \right )\\ \frac {d}{d t}x_{4} \left (t \right )&=33 x_{1} \left (t \right )+10 x_{2} \left (t \right )+90 x_{3} \left (t \right )+32 x_{4} \left (t \right )\\ \end {array} \]

0.106

1042

295

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=y \end {array} \]

Series expansion around \(x=0\).

0.106

1043

341

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=4 y \end {array} \]

Series expansion around \(x=0\).

0.106

1044

859

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime }+3 y&=0 \end {array} \]

Series expansion around \(x=0\).

0.106

1045

4164

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+2 y x&=0 \end {array} \]

Series expansion around \(x=0\).

0.106

1046

6649

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=x^{2} y \end {array} \]

Series expansion around \(x=0\).

0.106

1047

10540

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x -2\right ) y^{\prime }+y&=0 \end {array} \]

Series expansion around \(x=0\).

0.106

1048

12816

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (2 x -1\right ) y^{\prime }+2 y&=0 \end {array} \]

Series expansion around \(x=0\).

0.106

1049

12819

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 \left (x +1\right ) y^{\prime }&=y \end {array} \]

Series expansion around \(x=0\).

0.106

1050

14173

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-1+x \right ) y^{\prime }+2 y&=0 \end {array} \]

Series expansion around \(x=0\).

0.106

1051

20337

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 \left (-1+x \right ) y^{\prime }&=3 y \end {array} \]

Series expansion around \(x=0\).

0.106

1052

25143

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=y \end {array} \]

Series expansion around \(x=0\).

0.106

1053

27760

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=4 y \end {array} \]

Series expansion around \(x=0\).

0.106

1054

319

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+9 y&=0 \end {array} \]

Series expansion around \(x=0\).

0.107

1055

10476

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=x \end {array} \]

Series expansion around \(x=0\).

0.107

1056

12821

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x +y&=0 \end {array} \]

Series expansion around \(x=0\).

0.107

1057

20064

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime } x&=y \end {array} \]

Series expansion around \(x=0\).

0.107

1058

27049

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime }+y&=0 \end {array} \]

Series expansion around \(x=0\).

0.107

1059

416

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime }&=2 y \end {array} \]

Series expansion around \(x=0\).

0.108

1060

472

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y+y^{\prime \prime }&=0\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=3\\ \end {array} \]

Series expansion around \(x=0\).

0.108

1061

1481

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y&=0\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]

Series expansion around \(x=0\).

0.108

1062

7169

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y-2 y^{\prime }+y^{\prime \prime }&=0\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]

Series expansion around \(x=0\).

0.108

1063

10782

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }-2 y&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-2\\ \end {array} \]

Series expansion around \(x=0\).

0.108

1064

10796

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x^{2} y^{\prime }+y&=0 \end {array} \]

Series expansion around \(x=0\).

0.108

1065

11102

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=1+y^{2}\\ y \left (0\right )&=0\\ \end {array} \]

0.108

1066

11140

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-1\right ) y^{\prime \prime }+4 y^{\prime } x +2 y&=0 \end {array} \]

Series expansion around \(x=0\).

0.108

1067

14595

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+2\right ) y^{\prime \prime }+4 y^{\prime } x +2 y&=0 \end {array} \]

Series expansion around \(x=0\).

0.108

1068

16526

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime } x +y&=0 \end {array} \]

Series expansion around \(x=0\).

0.108

1069

19541

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+1\right ) y^{\prime \prime }+6 y^{\prime } x +4 y&=0 \end {array} \]

Series expansion around \(x=0\).

0.108

1070

3103

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x&=0 \end {array} \]

Series expansion around \(x=0\).

0.109

1071

10498

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-1\right ) y^{\prime \prime }-6 y^{\prime } x +12 y&=0 \end {array} \]

Series expansion around \(x=0\).

0.109

1072

10501

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+3\right ) y^{\prime \prime }-7 y^{\prime } x +16 y&=0 \end {array} \]

Series expansion around \(x=0\).

0.109

1073

10713

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-x^{2}+2\right ) y^{\prime \prime }-y^{\prime } x +16 y&=0 \end {array} \]

Series expansion around \(x=0\).

0.109

1074

10901

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-1\right ) y^{\prime \prime }+8 y^{\prime } x +12 y&=0 \end {array} \]

Series expansion around \(x=0\).

0.109

1075

11178

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 y^{\prime \prime }+y^{\prime } x -4 y&=0 \end {array} \]

Series expansion around \(x=0\).

0.109

1076

12535

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 5 y^{\prime \prime }-2 y^{\prime } x +10 y&=0 \end {array} \]

Series expansion around \(x=0\).

0.109

1077

16468

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-x^{2} y^{\prime }-3 y x&=0 \end {array} \]

Series expansion around \(x=0\).

0.109

1078

20579

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+x^{2} y^{\prime }+2 y x&=0 \end {array} \]

Series expansion around \(x=0\).

0.109

1079

22111

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y x&=0 \end {array} \]

Series expansion around \(x=0\).

0.109

1080

22314

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+x^{2} y&=0 \end {array} \]

Series expansion around \(x=0\).

0.109

1081

23342

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y&=0\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]

Series expansion around \(x=0\).

0.109

1082

7191

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime } x -2 y&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]

Series expansion around \(x=0\).

0.110

1083

10492

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\left (-1+x \right ) y^{\prime }+y&=0\\ y \left (1\right )&=2\\ y^{\prime }\left (1\right )&=0\\ \end {array} \]

Series expansion around \(x=1\).

0.110

1084

10496

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-x^{2}+2 x \right ) y^{\prime \prime }-6 \left (-1+x \right ) y^{\prime }-4 y&=0\\ y \left (1\right )&=0\\ y^{\prime }\left (1\right )&=1\\ \end {array} \]

Series expansion around \(x=1\).

0.110

1085

10848

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-6 x +10\right ) y^{\prime \prime }-4 \left (x -3\right ) y^{\prime }+6 y&=0\\ y \left (3\right )&=2\\ y^{\prime }\left (3\right )&=0\\ \end {array} \]

Series expansion around \(x=3\).

0.110

1086

19170

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (4 x^{2}+16 x +17\right ) y^{\prime \prime }&=8 y\\ y \left (-2\right )&=1\\ y^{\prime }\left (-2\right )&=0\\ \end {array} \]

Series expansion around \(x=-2\).

0.110

1087

19182

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+6 x \right ) y^{\prime \prime }+\left (3 x +9\right ) y^{\prime }-3 y&=0\\ y \left (-3\right )&=1\\ y^{\prime }\left (-3\right )&=0\\ \end {array} \]

Series expansion around \(x=-3\).

0.110

1088

22112

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\left (x +1\right ) y&=0 \end {array} \]

Series expansion around \(x=0\).

0.110

1089

25520

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-1\right ) y^{\prime \prime }+2 y^{\prime } x +2 y x&=0 \end {array} \]

Series expansion around \(x=0\).

0.110

1090

25689

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+x^{2} y^{\prime }+x^{2} y&=0 \end {array} \]

Series expansion around \(x=0\).

0.110

1091

5767

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{3}+1\right ) y^{\prime \prime }+x^{4} y&=0 \end {array} \]

Series expansion around \(x=0\).

0.111

1092

6740

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime } x +\left (2 x^{2}+1\right ) y&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-1\\ \end {array} \]

Series expansion around \(x=0\).

0.111

1093

10877

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+{\mathrm e}^{-x} y&=0 \end {array} \]

Series expansion around \(x=0\).

0.111

1094

11250

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \cos \left (x \right ) y^{\prime \prime }+y&=0 \end {array} \]

Series expansion around \(x=0\).

0.111

1095

11277

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +\sin \left (x \right ) y^{\prime }+y x&=0 \end {array} \]

Series expansion around \(x=0\).

0.111

1096

14171

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime } x +2 \alpha y&=0 \end {array} \]

Series expansion around \(x=0\).

0.111

1097

15425

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=y x \end {array} \]

Series expansion around \(x=0\).

0.111

1098

16465

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 y+y^{\prime }&={\mathrm e}^{-2 t}+t \end {array} \]

0.111

1099

16486

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -2 y+y^{\prime }&={\mathrm e}^{2 t} t^{2} \end {array} \]

0.111

1100

17992

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+y^{\prime }&=1+t \,{\mathrm e}^{-t} \end {array} \]

0.111