These are system of linear first order ode’s where when solving using eigenvalues/eigenvector method, there were defective eigenvevalues found. Number of problems in this table is 166
Column notations: A is ODE degree. B is Program Number of solutions generated. C is CAS Number of solutions generated.
|
# |
ODE |
A |
B |
C |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )-3 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=3 x_{1} \left (t \right )+7 x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.557 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{2} \left (t \right )+2 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-5 x_{1} \left (t \right )-3 x_{2} \left (t \right )-7 x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=x_{1} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.62 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{4} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=-2 x_{1} \left (t \right )+2 x_{2} \left (t \right )-3 x_{3} \left (t \right )+x_{4} \left (t \right ) \\ x_{4}^{\prime }\left (t \right )=2 x_{1} \left (t \right )-2 x_{2} \left (t \right )+x_{3} \left (t \right )-3 x_{4} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
4 |
system of linear ODEs |
✓ |
✓ |
0.855 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-2 x_{1} \left (t \right )+x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-x_{1} \left (t \right )-4 x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.535 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=3 x_{1} \left (t \right )-x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )+x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.51 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )-2 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=2 x_{1} \left (t \right )+5 x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.55 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=3 x_{1} \left (t \right )-x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )+5 x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.523 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=7 x_{1} \left (t \right )+x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-4 x_{1} \left (t \right )+3 x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.578 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )-4 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=4 x_{1} \left (t \right )+9 x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.546 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-3 x_{1} \left (t \right )-4 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-x_{1} \left (t \right )-x_{2} \left (t \right )-x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=x_{1} \left (t \right )+x_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.492 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-x_{1} \left (t \right )+x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-x_{2} \left (t \right )+x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=x_{1} \left (t \right )-x_{2} \left (t \right )-x_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.459 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-x_{1} \left (t \right )+x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{2} \left (t \right )-4 x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=x_{2} \left (t \right )-3 x_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.447 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-5 x_{1} \left (t \right )-x_{2} \left (t \right )-5 x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=4 x_{1} \left (t \right )+x_{2} \left (t \right )-2 x_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.579 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-2 x_{1} \left (t \right )-9 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )+4 x_{2} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=x_{1} \left (t \right )+3 x_{2} \left (t \right )+x_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.54 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-2 x_{1} \left (t \right )-2 x_{2} \left (t \right )-3 x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=2 x_{1} \left (t \right )+3 x_{2} \left (t \right )+4 x_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.511 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=18 x_{1} \left (t \right )+7 x_{2} \left (t \right )+4 x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=-27 x_{1} \left (t \right )-9 x_{2} \left (t \right )-5 x_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.549 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )+3 x_{2} \left (t \right )+x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=-2 x_{1} \left (t \right )-4 x_{2} \left (t \right )-x_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.509 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=2 x_{1} \left (t \right )+x_{2} \left (t \right )+x_{4} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=2 x_{2} \left (t \right )+x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=2 x_{3} \left (t \right )+x_{4} \left (t \right ) \\ x_{4}^{\prime }\left (t \right )=2 x_{4} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
4 |
system of linear ODEs |
✓ |
✓ |
0.569 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-x_{1} \left (t \right )-4 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )+3 x_{2} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=x_{1} \left (t \right )+2 x_{2} \left (t \right )+x_{3} \left (t \right ) \\ x_{4}^{\prime }\left (t \right )=x_{2} \left (t \right )+x_{4} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
4 |
system of linear ODEs |
✓ |
✓ |
0.523 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )+3 x_{2} \left (t \right )+7 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-x_{2} \left (t \right )-4 x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=x_{2} \left (t \right )+3 x_{3} \left (t \right ) \\ x_{4}^{\prime }\left (t \right )=-6 x_{2} \left (t \right )-14 x_{3} \left (t \right )+x_{4} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
4 |
system of linear ODEs |
✓ |
✓ |
0.616 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-2 x_{1} \left (t \right )+17 x_{2} \left (t \right )+4 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-x_{1} \left (t \right )+6 x_{2} \left (t \right )+x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=x_{2} \left (t \right )+2 x_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.551 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=5 x_{1} \left (t \right )-x_{2} \left (t \right )+x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )+3 x_{2} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=-3 x_{1} \left (t \right )+2 x_{2} \left (t \right )+x_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.548 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-3 x_{1} \left (t \right )+5 x_{2} \left (t \right )-5 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=3 x_{1} \left (t \right )-x_{2} \left (t \right )+3 x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=8 x_{1} \left (t \right )-8 x_{2} \left (t \right )+10 x_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.577 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-15 x_{1} \left (t \right )-7 x_{2} \left (t \right )+4 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=34 x_{1} \left (t \right )+16 x_{2} \left (t \right )-11 x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=17 x_{1} \left (t \right )+7 x_{2} \left (t \right )+5 x_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.682 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right )-2 x_{4} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=7 x_{1} \left (t \right )-4 x_{2} \left (t \right )-6 x_{3} \left (t \right )+11 x_{4} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=5 x_{1} \left (t \right )-x_{2} \left (t \right )+x_{3} \left (t \right )+3 x_{4} \left (t \right ) \\ x_{4}^{\prime }\left (t \right )=6 x_{1} \left (t \right )-2 x_{2} \left (t \right )-2 x_{3} \left (t \right )+6 x_{4} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
4 |
system of linear ODEs |
✓ |
✓ |
1.176 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=2 x_{1} \left (t \right )+x_{2} \left (t \right )-2 x_{3} \left (t \right )+x_{4} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=3 x_{2} \left (t \right )-5 x_{3} \left (t \right )+3 x_{4} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=-13 x_{2} \left (t \right )+22 x_{3} \left (t \right )-12 x_{4} \left (t \right ) \\ x_{4}^{\prime }\left (t \right )=-27 x_{2} \left (t \right )+45 x_{3} \left (t \right )-25 x_{4} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
4 |
system of linear ODEs |
✓ |
✓ |
1.074 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=35 x_{1} \left (t \right )-12 x_{2} \left (t \right )+4 x_{3} \left (t \right )+30 x_{4} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=22 x_{1} \left (t \right )-8 x_{2} \left (t \right )+3 x_{3} \left (t \right )+19 x_{4} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=-10 x_{1} \left (t \right )+3 x_{2} \left (t \right )-9 x_{4} \left (t \right ) \\ x_{4}^{\prime }\left (t \right )=-27 x_{1} \left (t \right )+9 x_{2} \left (t \right )-3 x_{3} \left (t \right )-23 x_{4} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
4 |
system of linear ODEs |
✓ |
✓ |
1.053 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=3 x_{1} \left (t \right )-4 x_{2} \left (t \right )+x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=4 x_{1} \left (t \right )+3 x_{2} \left (t \right )+x_{4} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=3 x_{3} \left (t \right )-4 x_{4} \left (t \right ) \\ x_{4}^{\prime }\left (t \right )=4 x_{3} \left (t \right )+3 x_{4} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
4 |
system of linear ODEs |
✓ |
✓ |
0.792 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=2 x_{1} \left (t \right )-8 x_{3} \left (t \right )-3 x_{4} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-18 x_{1} \left (t \right )-x_{2} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=-9 x_{1} \left (t \right )-3 x_{2} \left (t \right )-25 x_{3} \left (t \right )-9 x_{4} \left (t \right ) \\ x_{4}^{\prime }\left (t \right )=33 x_{1} \left (t \right )+10 x_{2} \left (t \right )+90 x_{3} \left (t \right )+32 x_{4} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
4 |
system of linear ODEs |
✓ |
✓ |
1.805 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=3 x_{1} \left (t \right )-4 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )-x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.556 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=4 x_{1} \left (t \right )-2 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=8 x_{1} \left (t \right )-4 x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.439 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-\frac {3 x_{1} \left (t \right )}{2}+x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-\frac {x_{1} \left (t \right )}{4}-\frac {x_{2} \left (t \right )}{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.582 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-3 x_{1} \left (t \right )+\frac {5 x_{2} \left (t \right )}{2} \\ x_{2}^{\prime }\left (t \right )=-\frac {5 x_{1} \left (t \right )}{2}+2 x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.576 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=2 x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=-x_{2} \left (t \right )+x_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.964 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )-4 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=4 x_{1} \left (t \right )-7 x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.536 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-\frac {5 x_{1} \left (t \right )}{2}+\frac {3 x_{2} \left (t \right )}{2} \\ x_{2}^{\prime }\left (t \right )=-\frac {3 x_{1} \left (t \right )}{2}+\frac {x_{2} \left (t \right )}{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.546 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=2 x_{1} \left (t \right )+\frac {3 x_{2} \left (t \right )}{2} \\ x_{2}^{\prime }\left (t \right )=-\frac {3 x_{1} \left (t \right )}{2}-x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.545 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=3 x_{1} \left (t \right )+9 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-x_{1} \left (t \right )-3 x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.361 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-4 x_{1} \left (t \right )+x_{2} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=3 x_{1} \left (t \right )+6 x_{2} \left (t \right )+2 x_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.74 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=4 x_{1} \left (t \right )-2 x_{2} \left (t \right )+\frac {1}{t^{3}} \\ x_{2}^{\prime }\left (t \right )=8 x_{1} \left (t \right )-4 x_{2} \left (t \right )-\frac {1}{t^{2}} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.799 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )-4 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=4 x_{1} \left (t \right )-7 x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.547 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=3 x_{1} \left (t \right )-4 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )-x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.529 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=3 y_{1} \left (t \right )+4 y_{2} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=-y_{1} \left (t \right )+7 y_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.608 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=-y_{2} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=y_{1} \left (t \right )-2 y_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.573 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=-7 y_{1} \left (t \right )+4 y_{2} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=-y_{1} \left (t \right )-11 y_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.655 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=3 y_{1} \left (t \right )+y_{2} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=-y_{1} \left (t \right )+y_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.57 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=4 y_{1} \left (t \right )+12 y_{2} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=-3 y_{1} \left (t \right )-8 y_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.646 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=-10 y_{1} \left (t \right )+9 y_{2} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=-4 y_{1} \left (t \right )+2 y_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.659 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=-13 y_{1} \left (t \right )+16 y_{2} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=-9 y_{1} \left (t \right )+11 y_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.642 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=2 y_{2} \left (t \right )+y_{3} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=-4 y_{1} \left (t \right )+6 y_{2} \left (t \right )+y_{3} \left (t \right ) \\ y_{3}^{\prime }\left (t \right )=4 y_{2} \left (t \right )+2 y_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
1.056 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=\frac {y_{1} \left (t \right )}{3}+\frac {y_{2} \left (t \right )}{3}-y_{3} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=-\frac {4 y_{1} \left (t \right )}{3}-\frac {4 y_{2} \left (t \right )}{3}+y_{3} \left (t \right ) \\ y_{3}^{\prime }\left (t \right )=-\frac {2 y_{1} \left (t \right )}{3}+\frac {y_{2} \left (t \right )}{3} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
1.084 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=-y_{1} \left (t \right )+y_{2} \left (t \right )-y_{3} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=-2 y_{1} \left (t \right )+2 y_{3} \left (t \right ) \\ y_{3}^{\prime }\left (t \right )=-y_{1} \left (t \right )+3 y_{2} \left (t \right )-y_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.994 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=4 y_{1} \left (t \right )-2 y_{2} \left (t \right )-2 y_{3} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=-2 y_{1} \left (t \right )+3 y_{2} \left (t \right )-y_{3} \left (t \right ) \\ y_{3}^{\prime }\left (t \right )=2 y_{1} \left (t \right )-y_{2} \left (t \right )+3 y_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
1.005 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=6 y_{1} \left (t \right )-5 y_{2} \left (t \right )+3 y_{3} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=2 y_{1} \left (t \right )-y_{2} \left (t \right )+3 y_{3} \left (t \right ) \\ y_{3}^{\prime }\left (t \right )=2 y_{1} \left (t \right )+y_{2} \left (t \right )+y_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
1.015 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=-11 y_{1} \left (t \right )+8 y_{2} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=-2 y_{1} \left (t \right )-3 y_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.625 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=15 y_{1} \left (t \right )-9 y_{2} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=16 y_{1} \left (t \right )-9 y_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.637 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=-3 y_{1} \left (t \right )-4 y_{2} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=y_{1} \left (t \right )-7 y_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.607 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=-7 y_{1} \left (t \right )+24 y_{2} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=-6 y_{1} \left (t \right )+17 y_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.587 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=-7 y_{1} \left (t \right )+3 y_{2} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=-3 y_{1} \left (t \right )-y_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.558 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=-y_{1} \left (t \right )+y_{2} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=y_{1} \left (t \right )-y_{2} \left (t \right )-2 y_{3} \left (t \right ) \\ y_{3}^{\prime }\left (t \right )=-y_{1} \left (t \right )-y_{2} \left (t \right )-y_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
1.085 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=-2 y_{1} \left (t \right )+2 y_{2} \left (t \right )+y_{3} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=-2 y_{1} \left (t \right )+2 y_{2} \left (t \right )+y_{3} \left (t \right ) \\ y_{3}^{\prime }\left (t \right )=-3 y_{1} \left (t \right )+3 y_{2} \left (t \right )+2 y_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.724 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=-y_{1} \left (t \right )-4 y_{2} \left (t \right )-y_{3} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=3 y_{1} \left (t \right )+6 y_{2} \left (t \right )+y_{3} \left (t \right ) \\ y_{3}^{\prime }\left (t \right )=-3 y_{1} \left (t \right )-2 y_{2} \left (t \right )+3 y_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.972 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=-5 y_{1} \left (t \right )-y_{2} \left (t \right )+11 y_{3} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=-7 y_{1} \left (t \right )+y_{2} \left (t \right )+13 y_{3} \left (t \right ) \\ y_{3}^{\prime }\left (t \right )=-4 y_{1} \left (t \right )+8 y_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.786 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=5 y_{1} \left (t \right )-y_{2} \left (t \right )+y_{3} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=-y_{1} \left (t \right )+9 y_{2} \left (t \right )-3 y_{3} \left (t \right ) \\ y_{3}^{\prime }\left (t \right )=-2 y_{1} \left (t \right )+2 y_{2} \left (t \right )+4 y_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.747 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=y_{1} \left (t \right )+10 y_{2} \left (t \right )-12 y_{3} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=2 y_{1} \left (t \right )+2 y_{2} \left (t \right )+3 y_{3} \left (t \right ) \\ y_{3}^{\prime }\left (t \right )=2 y_{1} \left (t \right )-y_{2} \left (t \right )+6 y_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.734 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=-6 y_{1} \left (t \right )-4 y_{2} \left (t \right )-4 y_{3} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=2 y_{1} \left (t \right )-y_{2} \left (t \right )+y_{3} \left (t \right ) \\ y_{3}^{\prime }\left (t \right )=2 y_{1} \left (t \right )+3 y_{2} \left (t \right )+y_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.707 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=2 y_{2} \left (t \right )-2 y_{3} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=-y_{1} \left (t \right )+5 y_{2} \left (t \right )-3 y_{3} \left (t \right ) \\ y_{3}^{\prime }\left (t \right )=y_{1} \left (t \right )+y_{2} \left (t \right )+y_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.686 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=-2 y_{1} \left (t \right )-12 y_{2} \left (t \right )+10 y_{3} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=2 y_{1} \left (t \right )-24 y_{2} \left (t \right )+11 y_{3} \left (t \right ) \\ y_{3}^{\prime }\left (t \right )=2 y_{1} \left (t \right )-24 y_{2} \left (t \right )+8 y_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.866 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=-y_{1} \left (t \right )-12 y_{2} \left (t \right )+8 y_{3} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=y_{1} \left (t \right )-9 y_{2} \left (t \right )+4 y_{3} \left (t \right ) \\ y_{3}^{\prime }\left (t \right )=y_{1} \left (t \right )-6 y_{2} \left (t \right )+y_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.72 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=-4 y_{1} \left (t \right )-y_{3} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=-y_{1} \left (t \right )-3 y_{2} \left (t \right )-y_{3} \left (t \right ) \\ y_{3}^{\prime }\left (t \right )=y_{1} \left (t \right )-2 y_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.576 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=-3 y_{1} \left (t \right )-3 y_{2} \left (t \right )+4 y_{3} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=4 y_{1} \left (t \right )+5 y_{2} \left (t \right )-8 y_{3} \left (t \right ) \\ y_{3}^{\prime }\left (t \right )=2 y_{1} \left (t \right )+3 y_{2} \left (t \right )-5 y_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.721 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=-3 y_{1} \left (t \right )-y_{2} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=y_{1} \left (t \right )-y_{2} \left (t \right ) \\ y_{3}^{\prime }\left (t \right )=-y_{1} \left (t \right )-y_{2} \left (t \right )-2 y_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.562 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )+x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{2} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=2 x_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.459 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=2 x_{1} \left (t \right )+x_{2} \left (t \right )+3 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=2 x_{2} \left (t \right )-x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=2 x_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.698 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-x_{2} \left (t \right )+x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=2 x_{1} \left (t \right )-3 x_{2} \left (t \right )+x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=x_{1} \left (t \right )-x_{2} \left (t \right )-x_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.903 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=2 x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=-3 x_{1} \left (t \right )+2 x_{2} \left (t \right )+4 x_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.668 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-x_{1} \left (t \right )-x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-x_{2} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=-2 x_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.471 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=2 x_{1} \left (t \right )-x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=2 x_{2} \left (t \right )+x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=2 x_{3} \left (t \right ) \\ x_{4}^{\prime }\left (t \right )=-x_{3} \left (t \right )+2 x_{4} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
4 |
system of linear ODEs |
✓ |
✓ |
0.6 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-x_{1} \left (t \right )+x_{2} \left (t \right )+2 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=-2 x_{1} \left (t \right )+x_{2} \left (t \right )+3 x_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.634 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-4 x_{1} \left (t \right )-4 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=10 x_{1} \left (t \right )+9 x_{2} \left (t \right )+x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=-4 x_{1} \left (t \right )-3 x_{2} \left (t \right )+x_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
1.067 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )+2 x_{2} \left (t \right )-3 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )+x_{2} \left (t \right )+2 x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=x_{1} \left (t \right )-x_{2} \left (t \right )+4 x_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.681 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=3 x_{1} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )+3 x_{2} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=3 x_{3} \left (t \right ) \\ x_{4}^{\prime }\left (t \right )=2 x_{3} \left (t \right )+3 x_{4} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
4 |
system of linear ODEs |
✓ |
✓ |
0.817 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=3 x_{1} \left (t \right )-4 x_{2} \left (t \right )+{\mathrm e}^{t} \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )-x_{2} \left (t \right )+{\mathrm e}^{t} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
1.023 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=2 x_{1} \left (t \right )+x_{3} \left (t \right )+{\mathrm e}^{2 t} \\ x_{2}^{\prime }\left (t \right )=2 x_{2} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=x_{2} \left (t \right )+3 x_{3} \left (t \right )+{\mathrm e}^{2 t} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
1.121 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-x_{1} \left (t \right )-x_{2} \left (t \right )-2 x_{3} \left (t \right )+{\mathrm e}^{t} \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=2 x_{1} \left (t \right )+x_{2} \left (t \right )+3 x_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
1.353 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )-x_{2} \left (t \right )-t^{2} \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )+3 x_{2} \left (t \right )+2 t \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
1.409 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )+2 x_{2} \left (t \right )-3 x_{3} \left (t \right )+{\mathrm e}^{t} \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )+x_{2} \left (t \right )+2 x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=x_{1} \left (t \right )-x_{2} \left (t \right )+4 x_{3} \left (t \right )-{\mathrm e}^{t} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
1.233 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )+3 y \left (t \right ) \\ z^{\prime }\left (t \right )=3 y \left (t \right )-2 z \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.937 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=3 x_{1} \left (t \right )-18 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=2 x_{1} \left (t \right )-9 x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.357 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-x_{1} \left (t \right )+3 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-3 x_{1} \left (t \right )+5 x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.296 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=3 x_{1} \left (t \right )-x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=16 x_{1} \left (t \right )-5 x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.303 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=3 x_{1} \left (t \right )-18 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=2 x_{1} \left (t \right )-9 x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.372 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-x_{1} \left (t \right )+3 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-3 x_{1} \left (t \right )+5 x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.237 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=3 x_{1} \left (t \right )-18 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=2 x_{1} \left (t \right )-9 x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.256 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )=y_{1} \left (x \right ) \\ y_{2}^{\prime }\left (x \right )=y_{1} \left (x \right )+y_{2} \left (x \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.253 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.276 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=5 x \left (t \right )+4 y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )+y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.49 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-4 x \left (t \right )-y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )-2 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.53 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right )+2 y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right )-y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.47 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.49 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right )-y \left (t \right ) \\ y^{\prime }\left (t \right )=9 x \left (t \right )-3 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.371 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-6 x \left (t \right )+5 y \left (t \right ) \\ y^{\prime }\left (t \right )=-5 x \left (t \right )+4 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.497 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-x \left (t \right )+3 y \left (t \right ) \\ y^{\prime }\left (t \right )=-3 x \left (t \right )+5 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.52 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=12 x \left (t \right )-9 y \left (t \right ) \\ y^{\prime }\left (t \right )=4 x \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.522 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=5 x \left (t \right )-4 y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+2 z \left (t \right ) \\ z^{\prime }\left (t \right )=2 y \left (t \right )+5 z \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.576 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right ) \\ y^{\prime }\left (t \right )=3 y \left (t \right )+z \left (t \right ) \\ z^{\prime }\left (t \right )=-y \left (t \right )+z \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.624 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )+2 y \left (t \right )-z \left (t \right ) \\ z^{\prime }\left (t \right )=y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.434 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=4 x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=4 y \left (t \right )+z \left (t \right ) \\ z^{\prime }\left (t \right )=4 z \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.366 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )+4 y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )+6 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.464 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=5 x \left (t \right )+9 y \left (t \right )+2 \\ y^{\prime }\left (t \right )=-x \left (t \right )+11 y \left (t \right )+6 \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
1.015 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )-3 y \left (t \right ) \\ y^{\prime }\left (t \right )=3 x \left (t \right )+7 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.481 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )+5 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.477 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=7 x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=-4 x \left (t \right )+3 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.495 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=y \left (t \right ) \\ z^{\prime }\left (t \right )=z \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.34 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )+y \left (t \right )-z \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )+2 z \left (t \right ) \\ z^{\prime }\left (t \right )=-x \left (t \right )-2 y \left (t \right )+4 z \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.473 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )+y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.668 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )+3 x \left (t \right )-y \left (t \right )={\mathrm e}^{2 t} \\ y^{\prime }\left (t \right )+x \left (t \right )+5 y \left (t \right )={\mathrm e}^{t} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.792 |
|
|
\[ {}\left [\begin {array}{c} 4 x^{\prime }\left (t \right )+9 y^{\prime }\left (t \right )+11 x \left (t \right )+31 y \left (t \right )={\mathrm e}^{t} \\ 3 x^{\prime }\left (t \right )+7 y^{\prime }\left (t \right )+8 x \left (t \right )+24 y \left (t \right )={\mathrm e}^{2 t} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.793 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=y \left (t \right )-z \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right ) \\ z^{\prime }\left (t \right )=z \left (t \right )+x \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.419 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )-y \left (t \right )+z \left (t \right )=0 \\ y^{\prime }\left (t \right )-x \left (t \right )-y \left (t \right )=t \\ z^{\prime }\left (t \right )-x \left (t \right )-z \left (t \right )=t \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.564 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-3 x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=-3 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.208 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )-y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+3 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.354 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-3 x \left (t \right )+4 y \left (t \right ) \\ y^{\prime }\left (t \right )=-3 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.217 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=5 x \left (t \right )-4 y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.378 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.265 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right )-y \left (t \right )+1 \\ y^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right )+2 \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.594 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )-3 y \left (t \right ) \\ y^{\prime }\left (t \right )=3 x \left (t \right )+7 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.378 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=5 x \left (t \right )-4 y \left (t \right )+{\mathrm e}^{3 t} \\ y^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.822 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=5 x \left (t \right )-4 y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.413 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-6 x \left (t \right )+2 y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right )-2 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.428 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-3 x \left (t \right )-y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )-5 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.427 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=7 x \left (t \right )-4 y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+3 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.435 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )+y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.297 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )+x \left (t \right )-z \left (t \right )=0 \\ x \left (t \right )+y^{\prime }\left (t \right )-y \left (t \right )=0 \\ z^{\prime }\left (t \right )+x \left (t \right )+2 y \left (t \right )-3 z \left (t \right )=0 \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.345 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right )-2 y \left (t \right )+3 z \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )-y \left (t \right )+2 z \left (t \right )+2 \,{\mathrm e}^{-t} \\ z^{\prime }\left (t \right )=-2 x \left (t \right )+2 y \left (t \right )-2 z \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.945 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=7 x \left (t \right )+y \left (t \right )-1-6 \,{\mathrm e}^{t} \\ y^{\prime }\left (t \right )=-4 x \left (t \right )+3 y \left (t \right )+4 \,{\mathrm e}^{t}-3 \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.606 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=12 x \left (t \right )+18 y \left (t \right ) \\ y^{\prime }\left (t \right )=-8 x \left (t \right )-12 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.224 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )-3 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.322 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right )-y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.288 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=0 \\ y^{\prime }\left (t \right )=x \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.186 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-x \left (t \right )+2 y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right )+3 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.344 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )-y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )-y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.424 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )+y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.51 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )-y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+3 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.487 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=1 \\ y^{\prime }\left (t \right )=x \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.517 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )+4 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.598 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-\frac {x \left (t \right )}{2} \\ y^{\prime }\left (t \right )=x \left (t \right )-\frac {y \left (t \right )}{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.545 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-3 x \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )-3 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.441 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-2 x \left (t \right )-y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )-4 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.49 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )-2 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.504 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-3 x \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )-3 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.413 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )+4 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.462 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-2 x \left (t \right )-y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )-4 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.433 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )-2 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.438 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 y \left (t \right ) \\ y^{\prime }\left (t \right )=0 \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.369 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=0 \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.375 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-3 x \left (t \right )-y \left (t \right ) \\ y^{\prime }\left (t \right )=4 x \left (t \right )+y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.525 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-2 x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 y \left (t \right ) \\ z^{\prime }\left (t \right )=-z \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.467 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-2 x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 y \left (t \right ) \\ z^{\prime }\left (t \right )=z \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.466 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-2 x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 y \left (t \right )+z \left (t \right ) \\ z^{\prime }\left (t \right )=-2 z \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.465 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=y \left (t \right ) \\ y^{\prime }\left (t \right )=z \left (t \right ) \\ z^{\prime }\left (t \right )=0 \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.48 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=y \left (t \right ) \\ y^{\prime }\left (t \right )=-4 x \left (t \right )-4 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.376 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=8 x \left (t \right )-y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+6 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.408 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+y \left (t \right )={\mathrm e}^{-t} \\ 2 x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+2 y \left (t \right )=\sin \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.443 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )+x \left (t \right )+2 y \left (t \right )=2 \,{\mathrm e}^{-t} \\ y^{\prime }\left (t \right )+y \left (t \right )+z \left (t \right )=1 \\ z^{\prime }\left (t \right )+z \left (t \right )=1 \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.564 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )+4 y \left (t \right )+\cos \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )-2 y \left (t \right )+\sin \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.385 |
|
|
|
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