| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 1001 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=47 x_{1} \left (t \right )-8 x_{2} \left (t \right )+5 x_{3} \left (t \right )-5 x_{4} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=-10 x_{1} \left (t \right )+32 x_{2} \left (t \right )+18 x_{3} \left (t \right )-2 x_{4} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=139 x_{1} \left (t \right )-40 x_{2} \left (t \right )-167 x_{3} \left (t \right )-121 x_{4} \left (t \right )\\ \frac {d}{d t}x_{4} \left (t \right )&=-232 x_{1} \left (t \right )+64 x_{2} \left (t \right )+360 x_{3} \left (t \right )+248 x_{4} \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.102 |
|
| 1002 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=139 x_{1} \left (t \right )-14 x_{2} \left (t \right )-52 x_{3} \left (t \right )-14 x_{4} \left (t \right )+28 x_{5} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=-22 x_{1} \left (t \right )+5 x_{2} \left (t \right )+7 x_{3} \left (t \right )+8 x_{4} \left (t \right )-7 x_{5} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=370 x_{1} \left (t \right )-38 x_{2} \left (t \right )-139 x_{3} \left (t \right )-38 x_{4} \left (t \right )+76 x_{5} \left (t \right )\\ \frac {d}{d t}x_{4} \left (t \right )&=152 x_{1} \left (t \right )-16 x_{2} \left (t \right )-59 x_{3} \left (t \right )-13 x_{4} \left (t \right )+35 x_{5} \left (t \right )\\ \frac {d}{d t}x_{5} \left (t \right )&=95 x_{1} \left (t \right )-10 x_{2} \left (t \right )-38 x_{3} \left (t \right )-7 x_{4} \left (t \right )+23 x_{5} \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.102 |
|
| 1003 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=9 x_{1} \left (t \right )+13 x_{2} \left (t \right )-13 x_{6} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=-14 x_{1} \left (t \right )+19 x_{2} \left (t \right )-10 x_{3} \left (t \right )-20 x_{4} \left (t \right )+10 x_{5} \left (t \right )+4 x_{6} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=-30 x_{1} \left (t \right )+12 x_{2} \left (t \right )-7 x_{3} \left (t \right )-30 x_{4} \left (t \right )+12 x_{5} \left (t \right )+18 x_{6} \left (t \right )\\ \frac {d}{d t}x_{4} \left (t \right )&=-12 x_{1} \left (t \right )+10 x_{2} \left (t \right )-10 x_{3} \left (t \right )-9 x_{4} \left (t \right )+10 x_{5} \left (t \right )+2 x_{6} \left (t \right )\\ \frac {d}{d t}x_{5} \left (t \right )&=6 x_{1} \left (t \right )+9 x_{2} \left (t \right )+6 x_{4} \left (t \right )+5 x_{5} \left (t \right )-15 x_{6} \left (t \right )\\ \frac {d}{d t}x_{6} \left (t \right )&=-14 x_{1} \left (t \right )+23 x_{2} \left (t \right )-10 x_{3} \left (t \right )-20 x_{4} \left (t \right )+10 x_{5} \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.102 |
|
| 1004 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=9 x_{1} \left (t \right )+4 x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=-6 x_{1} \left (t \right )-x_{2} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=6 x_{1} \left (t \right )+4 x_{2} \left (t \right )+3 x_{3} \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.102 |
|
| 1005 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=x_{1} \left (t \right )-3 x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=3 x_{1} \left (t \right )+7 x_{2} \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.102 |
|
| 1006 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=x_{2} \left (t \right )+2 x_{3} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=-5 x_{1} \left (t \right )-3 x_{2} \left (t \right )-7 x_{3} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=x_{1} \left (t \right )\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.102 |
|
| 1007 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=x_{3} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=x_{4} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=-2 x_{1} \left (t \right )+2 x_{2} \left (t \right )-3 x_{3} \left (t \right )+x_{4} \left (t \right )\\ \frac {d}{d t}x_{4} \left (t \right )&=2 x_{1} \left (t \right )-2 x_{2} \left (t \right )+x_{3} \left (t \right )-3 x_{4} \left (t \right )\\ \end {array} \]
|
✗ |
✗ |
✓ |
✗ |
0.102 |
|
| 1008 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=-2 x_{1} \left (t \right )+x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=-x_{1} \left (t \right )-4 x_{2} \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
0.102 |
|
| 1009 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=3 x_{1} \left (t \right )-x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=x_{1} \left (t \right )+x_{2} \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.103 |
|
| 1010 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=x_{1} \left (t \right )-2 x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=2 x_{1} \left (t \right )+5 x_{2} \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.103 |
|
| 1011 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=3 x_{1} \left (t \right )-x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=x_{1} \left (t \right )+5 x_{2} \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.103 |
|
| 1012 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=7 x_{1} \left (t \right )+x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=-4 x_{1} \left (t \right )+3 x_{2} \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
0.103 |
|
| 1013 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=x_{1} \left (t \right )-4 x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=4 x_{1} \left (t \right )+9 x_{2} \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.103 |
|
| 1014 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=2 x_{1} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=-7 x_{1} \left (t \right )+9 x_{2} \left (t \right )+7 x_{3} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=2 x_{3} \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.103 |
|
| 1015 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=25 x_{1} \left (t \right )+12 x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=-18 x_{1} \left (t \right )-5 x_{2} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=6 x_{1} \left (t \right )+6 x_{2} \left (t \right )+13 x_{3} \left (t \right )\\ \end {array} \]
|
✗ |
✗ |
✓ |
✗ |
0.104 |
|
| 1016 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=-19 x_{1} \left (t \right )+12 x_{2} \left (t \right )+84 x_{3} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=5 x_{2} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=-8 x_{1} \left (t \right )+4 x_{2} \left (t \right )+33 x_{3} \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.104 |
|
| 1017 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }\left (t \right )&=-13 x_{1} \left (t \right )+40 x_{2} \left (t \right )-48 x_{3} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=-8 x_{1} \left (t \right )+23 x_{2} \left (t \right )-24 x_{3} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=3 x_{3} \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.104 |
|
| 1018 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=-3 x_{1} \left (t \right )-4 x_{3} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=-x_{1} \left (t \right )-x_{2} \left (t \right )-x_{3} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=x_{1} \left (t \right )+x_{3} \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
0.104 |
|
| 1019 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=-x_{1} \left (t \right )+x_{3} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=-x_{2} \left (t \right )+x_{3} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=x_{1} \left (t \right )-x_{2} \left (t \right )-x_{3} \left (t \right )\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.104 |
|
| 1020 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=-x_{1} \left (t \right )+x_{3} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=x_{2} \left (t \right )-4 x_{3} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=x_{2} \left (t \right )-3 x_{3} \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.104 |
|
| 1021 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=x_{3} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=-5 x_{1} \left (t \right )-x_{2} \left (t \right )-5 x_{3} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=4 x_{1} \left (t \right )+x_{2} \left (t \right )-2 x_{3} \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.104 |
|
| 1022 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=-2 x_{1} \left (t \right )-9 x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=x_{1} \left (t \right )+4 x_{2} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=x_{1} \left (t \right )+3 x_{2} \left (t \right )+x_{3} \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.104 |
|
| 1023 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=x_{1} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=-2 x_{1} \left (t \right )-2 x_{2} \left (t \right )-3 x_{3} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=2 x_{1} \left (t \right )+3 x_{2} \left (t \right )+4 x_{3} \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.104 |
|
| 1024 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=x_{1} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=18 x_{1} \left (t \right )+7 x_{2} \left (t \right )+4 x_{3} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=-27 x_{1} \left (t \right )-9 x_{2} \left (t \right )-5 x_{3} \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.105 |
|
| 1025 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=x_{1} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=x_{1} \left (t \right )+3 x_{2} \left (t \right )+x_{3} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=-2 x_{1} \left (t \right )-4 x_{2} \left (t \right )-x_{3} \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.105 |
|
| 1026 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=x_{1} \left (t \right )-4 x_{2} \left (t \right )-2 x_{4} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=x_{2} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=6 x_{1} \left (t \right )-12 x_{2} \left (t \right )-x_{3} \left (t \right )-6 x_{4} \left (t \right )\\ \frac {d}{d t}x_{4} \left (t \right )&=-4 x_{2} \left (t \right )-x_{4} \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.105 |
|
| 1027 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=2 x_{1} \left (t \right )+x_{2} \left (t \right )+x_{4} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=2 x_{2} \left (t \right )+x_{3} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=2 x_{3} \left (t \right )+x_{4} \left (t \right )\\ \frac {d}{d t}x_{4} \left (t \right )&=2 x_{4} \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.105 |
|
| 1028 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=-x_{1} \left (t \right )-4 x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=x_{1} \left (t \right )+3 x_{2} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=x_{1} \left (t \right )+2 x_{2} \left (t \right )+x_{3} \left (t \right )\\ \frac {d}{d t}x_{4} \left (t \right )&=x_{2} \left (t \right )+x_{4} \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.105 |
|
| 1029 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=x_{1} \left (t \right )+3 x_{2} \left (t \right )+7 x_{3} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=-x_{2} \left (t \right )-4 x_{3} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=x_{2} \left (t \right )+3 x_{3} \left (t \right )\\ \frac {d}{d t}x_{4} \left (t \right )&=-6 x_{2} \left (t \right )-14 x_{3} \left (t \right )+x_{4} \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.105 |
|
| 1030 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=39 x_{1} \left (t \right )+8 x_{2} \left (t \right )-16 x_{3} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=-36 x_{1} \left (t \right )-5 x_{2} \left (t \right )+16 x_{3} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=72 x_{1} \left (t \right )+16 x_{2} \left (t \right )-29 x_{3} \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
0.105 |
|
| 1031 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=28 x_{1} \left (t \right )+50 x_{2} \left (t \right )+100 x_{3} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=15 x_{1} \left (t \right )+33 x_{2} \left (t \right )+60 x_{3} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=-15 x_{1} \left (t \right )-30 x_{2} \left (t \right )-57 x_{3} \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
0.105 |
|
| 1032 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }\left (t \right )&=-2 x_{1} \left (t \right )+17 x_{2} \left (t \right )+4 x_{3} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=-x_{1} \left (t \right )+6 x_{2} \left (t \right )+x_{3} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=x_{2} \left (t \right )+2 x_{3} \left (t \right )\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.105 |
|
| 1033 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=5 x_{1} \left (t \right )-x_{2} \left (t \right )+x_{3} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=x_{1} \left (t \right )+3 x_{2} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=-3 x_{1} \left (t \right )+2 x_{2} \left (t \right )+x_{3} \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.105 |
|
| 1034 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=-3 x_{1} \left (t \right )+5 x_{2} \left (t \right )-5 x_{3} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=3 x_{1} \left (t \right )-x_{2} \left (t \right )+3 x_{3} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=8 x_{1} \left (t \right )-8 x_{2} \left (t \right )+10 x_{3} \left (t \right )\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.105 |
|
| 1035 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=-15 x_{1} \left (t \right )-7 x_{2} \left (t \right )+4 x_{3} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=34 x_{1} \left (t \right )+16 x_{2} \left (t \right )-11 x_{3} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=17 x_{1} \left (t \right )+7 x_{2} \left (t \right )+5 x_{3} \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.105 |
|
| 1036 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=-x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right )-2 x_{4} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=7 x_{1} \left (t \right )-4 x_{2} \left (t \right )-6 x_{3} \left (t \right )+11 x_{4} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=5 x_{1} \left (t \right )-x_{2} \left (t \right )+x_{3} \left (t \right )+3 x_{4} \left (t \right )\\ \frac {d}{d t}x_{4} \left (t \right )&=6 x_{1} \left (t \right )-2 x_{2} \left (t \right )-2 x_{3} \left (t \right )+6 x_{4} \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.105 |
|
| 1037 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=2 x_{1} \left (t \right )+x_{2} \left (t \right )-2 x_{3} \left (t \right )+x_{4} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=3 x_{2} \left (t \right )-5 x_{3} \left (t \right )+3 x_{4} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=-13 x_{2} \left (t \right )+22 x_{3} \left (t \right )-12 x_{4} \left (t \right )\\ \frac {d}{d t}x_{4} \left (t \right )&=-27 x_{2} \left (t \right )+45 x_{3} \left (t \right )-25 x_{4} \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.105 |
|
| 1038 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=35 x_{1} \left (t \right )-12 x_{2} \left (t \right )+4 x_{3} \left (t \right )+30 x_{4} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=22 x_{1} \left (t \right )-8 x_{2} \left (t \right )+3 x_{3} \left (t \right )+19 x_{4} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=-10 x_{1} \left (t \right )+3 x_{2} \left (t \right )-9 x_{4} \left (t \right )\\ \frac {d}{d t}x_{4} \left (t \right )&=-27 x_{1} \left (t \right )+9 x_{2} \left (t \right )-3 x_{3} \left (t \right )-23 x_{4} \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.105 |
|
| 1039 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=11 x_{1} \left (t \right )-x_{2} \left (t \right )+26 x_{3} \left (t \right )+6 x_{4} \left (t \right )-3 x_{5} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=3 x_{2} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=-9 x_{1} \left (t \right )-24 x_{3} \left (t \right )-6 x_{4} \left (t \right )+3 x_{5} \left (t \right )\\ \frac {d}{d t}x_{4} \left (t \right )&=3 x_{1} \left (t \right )+9 x_{3} \left (t \right )+5 x_{4} \left (t \right )-x_{5} \left (t \right )\\ \frac {d}{d t}x_{5} \left (t \right )&=-48 x_{1} \left (t \right )-3 x_{2} \left (t \right )-138 x_{3} \left (t \right )-30 x_{4} \left (t \right )+18 x_{5} \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.105 |
|
| 1040 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=3 x_{1} \left (t \right )-4 x_{2} \left (t \right )+x_{3} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=4 x_{1} \left (t \right )+3 x_{2} \left (t \right )+x_{4} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=3 x_{3} \left (t \right )-4 x_{4} \left (t \right )\\ \frac {d}{d t}x_{4} \left (t \right )&=4 x_{3} \left (t \right )+3 x_{4} \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.105 |
|
| 1041 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x_{1} \left (t \right )&=2 x_{1} \left (t \right )-8 x_{3} \left (t \right )-3 x_{4} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=-18 x_{1} \left (t \right )-x_{2} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=-9 x_{1} \left (t \right )-3 x_{2} \left (t \right )-25 x_{3} \left (t \right )-9 x_{4} \left (t \right )\\ \frac {d}{d t}x_{4} \left (t \right )&=33 x_{1} \left (t \right )+10 x_{2} \left (t \right )+90 x_{3} \left (t \right )+32 x_{4} \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.106 |
|
| 1042 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=y \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.106 |
|
| 1043 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=4 y \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.106 |
|
| 1044 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime }+3 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.106 |
|
| 1045 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+2 y x&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.106 |
|
| 1046 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=x^{2} y \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.106 |
|
| 1047 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x -2\right ) y^{\prime }+y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.106 |
|
| 1048 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (2 x -1\right ) y^{\prime }+2 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✗ |
✓ |
✗ |
✗ |
0.106 |
|
| 1049 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 \left (x +1\right ) y^{\prime }&=y \end {array} \]
Series expansion around \(x=0\). |
✗ |
✓ |
✓ |
✗ |
0.106 |
|
| 1050 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-1+x \right ) y^{\prime }+2 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✗ |
✓ |
✓ |
✗ |
0.106 |
|
| 1051 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 \left (-1+x \right ) y^{\prime }&=3 y \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.106 |
|
| 1052 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=y \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.106 |
|
| 1053 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=4 y \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.106 |
|
| 1054 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+9 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.107 |
|
| 1055 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=x \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.107 |
|
| 1056 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x +y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.107 |
|
| 1057 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime } x&=y \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.107 |
|
| 1058 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime }+y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.107 |
|
| 1059 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime }&=2 y \end {array} \]
Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
0.108 |
|
| 1060 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y+y^{\prime \prime }&=0\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=3\\ \end {array} \]
Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
0.108 |
|
| 1061 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y&=0\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.108 |
|
| 1062 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y-2 y^{\prime }+y^{\prime \prime }&=0\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
0.108 |
|
| 1063 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }-2 y&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-2\\ \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.108 |
|
| 1064 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x^{2} y^{\prime }+y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.108 |
|
| 1065 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=1+y^{2}\\ y \left (0\right )&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.108 |
|
| 1066 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-1\right ) y^{\prime \prime }+4 y^{\prime } x +2 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.108 |
|
| 1067 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+2\right ) y^{\prime \prime }+4 y^{\prime } x +2 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.108 |
|
| 1068 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime } x +y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.108 |
|
| 1069 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+1\right ) y^{\prime \prime }+6 y^{\prime } x +4 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.108 |
|
| 1070 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.109 |
|
| 1071 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-1\right ) y^{\prime \prime }-6 y^{\prime } x +12 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.109 |
|
| 1072 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+3\right ) y^{\prime \prime }-7 y^{\prime } x +16 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.109 |
|
| 1073 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-x^{2}+2\right ) y^{\prime \prime }-y^{\prime } x +16 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.109 |
|
| 1074 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-1\right ) y^{\prime \prime }+8 y^{\prime } x +12 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.109 |
|
| 1075 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 y^{\prime \prime }+y^{\prime } x -4 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.109 |
|
| 1076 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 5 y^{\prime \prime }-2 y^{\prime } x +10 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.109 |
|
| 1077 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-x^{2} y^{\prime }-3 y x&=0 \end {array} \]
Series expansion around \(x=0\). |
✗ |
✗ |
✗ |
✗ |
0.109 |
|
| 1078 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+x^{2} y^{\prime }+2 y x&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.109 |
|
| 1079 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y x&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.109 |
|
| 1080 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+x^{2} y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.109 |
|
| 1081 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y&=0\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.109 |
|
| 1082 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime } x -2 y&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
0.110 |
|
| 1083 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\left (-1+x \right ) y^{\prime }+y&=0\\ y \left (1\right )&=2\\ y^{\prime }\left (1\right )&=0\\ \end {array} \]
Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✗ |
0.110 |
|
| 1084 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-x^{2}+2 x \right ) y^{\prime \prime }-6 \left (-1+x \right ) y^{\prime }-4 y&=0\\ y \left (1\right )&=0\\ y^{\prime }\left (1\right )&=1\\ \end {array} \]
Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.110 |
|
| 1085 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-6 x +10\right ) y^{\prime \prime }-4 \left (x -3\right ) y^{\prime }+6 y&=0\\ y \left (3\right )&=2\\ y^{\prime }\left (3\right )&=0\\ \end {array} \]
Series expansion around \(x=3\). |
✓ |
✓ |
✓ |
✗ |
0.110 |
|
| 1086 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (4 x^{2}+16 x +17\right ) y^{\prime \prime }&=8 y\\ y \left (-2\right )&=1\\ y^{\prime }\left (-2\right )&=0\\ \end {array} \]
Series expansion around \(x=-2\). |
✗ |
✓ |
✓ |
✗ |
0.110 |
|
| 1087 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+6 x \right ) y^{\prime \prime }+\left (3 x +9\right ) y^{\prime }-3 y&=0\\ y \left (-3\right )&=1\\ y^{\prime }\left (-3\right )&=0\\ \end {array} \]
Series expansion around \(x=-3\). |
✓ |
✓ |
✓ |
✓ |
0.110 |
|
| 1088 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\left (x +1\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.110 |
|
| 1089 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-1\right ) y^{\prime \prime }+2 y^{\prime } x +2 y x&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.110 |
|
| 1090 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+x^{2} y^{\prime }+x^{2} y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.110 |
|
| 1091 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{3}+1\right ) y^{\prime \prime }+x^{4} y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.111 |
|
| 1092 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime } x +\left (2 x^{2}+1\right ) y&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-1\\ \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.111 |
|
| 1093 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+{\mathrm e}^{-x} y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.111 |
|
| 1094 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \cos \left (x \right ) y^{\prime \prime }+y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.111 |
|
| 1095 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +\sin \left (x \right ) y^{\prime }+y x&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.111 |
|
| 1096 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime } x +2 \alpha y&=0 \end {array} \]
Series expansion around \(x=0\). |
✗ |
✓ |
✗ |
✗ |
0.111 |
|
| 1097 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=y x \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.111 |
|
| 1098 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 y+y^{\prime }&={\mathrm e}^{-2 t}+t \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.111 |
|
| 1099 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -2 y+y^{\prime }&={\mathrm e}^{2 t} t^{2} \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.111 |
|
| 1100 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+y^{\prime }&=1+t \,{\mathrm e}^{-t} \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.111 |
|