These are system of linear first order ode’s where when solving using eigenvalues/eigenvector method, there were no defective eigenvevalues found. Number of problems in this table is 636
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) |
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-3 y \left (t \right ) \\ y^{\prime }\left (t \right )=3 x \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.593 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right )-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )+y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
1.081 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )+4 y \left (t \right )+3 \,{\mathrm e}^{t} \\ y^{\prime }\left (t \right )=5 x \left (t \right )-y \left (t \right )-t^{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
2.159 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=y \left (t \right )+z \left (t \right ) \\ y^{\prime }\left (t \right )=z \left (t \right )+x \left (t \right ) \\ z^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.736 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=2 x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=3 x_{4} \left (t \right ) \\ x_{4}^{\prime }\left (t \right )=4 x_{1} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
4 |
system of linear ODEs |
✓ |
✓ |
3.901 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{2} \left (t \right )+x_{3} \left (t \right )+1 \\ x_{2}^{\prime }\left (t \right )=x_{3} \left (t \right )+x_{4} \left (t \right )+t \\ x_{3}^{\prime }\left (t \right )=x_{1} \left (t \right )+x_{4} \left (t \right )+t^{2} \\ x_{4}^{\prime }\left (t \right )=x_{1} \left (t \right )+x_{2} \left (t \right )+t^{3} \end {array}\right ] \] |
1 |
1 |
4 |
system of linear ODEs |
✓ |
✓ |
7.091 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=6 x_{1} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-3 x_{1} \left (t \right )-x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.468 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-3 x_{1} \left (t \right )+2 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-3 x_{1} \left (t \right )+4 x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.549 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )+2 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=2 x_{1} \left (t \right )+x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.469 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=2 x_{1} \left (t \right )+3 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=2 x_{1} \left (t \right )+x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.518 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=3 x_{1} \left (t \right )+4 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=3 x_{1} \left (t \right )+2 x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.482 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=4 x_{1} \left (t \right )+x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=6 x_{1} \left (t \right )-x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.541 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=6 x_{1} \left (t \right )-7 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )-2 x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.505 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=9 x_{1} \left (t \right )+5 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-6 x_{1} \left (t \right )-2 x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.477 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-3 x_{1} \left (t \right )+4 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=6 x_{1} \left (t \right )-5 x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.551 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )-5 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )-x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.687 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=2 x_{1} \left (t \right )-5 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=4 x_{1} \left (t \right )-2 x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.577 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-3 x_{1} \left (t \right )-2 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=9 x_{1} \left (t \right )+3 x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.689 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )-2 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=2 x_{1} \left (t \right )+x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.482 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )-5 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )+3 x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.77 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=5 x_{1} \left (t \right )-9 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=2 x_{1} \left (t \right )-x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.8 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=3 x_{1} \left (t \right )-4 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=4 x_{1} \left (t \right )+3 x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.64 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=7 x_{1} \left (t \right )-5 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=4 x_{1} \left (t \right )+3 x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.782 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-50 x_{1} \left (t \right )+20 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=100 x_{1} \left (t \right )-60 x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.555 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=4 x_{1} \left (t \right )+x_{2} \left (t \right )+4 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )+7 x_{2} \left (t \right )+x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=4 x_{1} \left (t \right )+x_{2} \left (t \right )+4 x_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.752 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )+2 x_{2} \left (t \right )+2 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=2 x_{1} \left (t \right )+7 x_{2} \left (t \right )+x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=2 x_{1} \left (t \right )+x_{2} \left (t \right )+7 x_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.745 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=4 x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )+4 x_{2} \left (t \right )+x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=x_{1} \left (t \right )+x_{2} \left (t \right )+4 x_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.74 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=5 x_{1} \left (t \right )+x_{2} \left (t \right )+3 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )+7 x_{2} \left (t \right )+x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=3 x_{1} \left (t \right )+x_{2} \left (t \right )+5 x_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.76 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=5 x_{1} \left (t \right )-6 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=2 x_{1} \left (t \right )-x_{2} \left (t \right )-2 x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=4 x_{1} \left (t \right )-2 x_{2} \left (t \right )-4 x_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.834 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=3 x_{1} \left (t \right )+2 x_{2} \left (t \right )+2 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-5 x_{1} \left (t \right )-4 x_{2} \left (t \right )-2 x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=5 x_{1} \left (t \right )+5 x_{2} \left (t \right )+3 x_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.816 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=3 x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-5 x_{1} \left (t \right )-3 x_{2} \left (t \right )-x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=5 x_{1} \left (t \right )+5 x_{2} \left (t \right )+3 x_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.801 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=2 x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-4 x_{1} \left (t \right )-3 x_{2} \left (t \right )-x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=4 x_{1} \left (t \right )+4 x_{2} \left (t \right )+2 x_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
1.106 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=5 x_{1} \left (t \right )+5 x_{2} \left (t \right )+2 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-6 x_{1} \left (t \right )-6 x_{2} \left (t \right )-5 x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=6 x_{1} \left (t \right )+6 x_{2} \left (t \right )+5 x_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
1.207 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=3 x_{1} \left (t \right )+x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=9 x_{1} \left (t \right )-x_{2} \left (t \right )+2 x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=-9 x_{1} \left (t \right )+4 x_{2} \left (t \right )-x_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
1.155 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=2 x_{1} \left (t \right )+2 x_{2} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=3 x_{2} \left (t \right )+3 x_{3} \left (t \right ) \\ x_{4}^{\prime }\left (t \right )=4 x_{3} \left (t \right )+4 x_{4} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
4 |
system of linear ODEs |
✓ |
✓ |
1.102 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-2 x_{1} \left (t \right )+9 x_{4} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=4 x_{1} \left (t \right )+2 x_{2} \left (t \right )-10 x_{4} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=-x_{3} \left (t \right )+8 x_{4} \left (t \right ) \\ x_{4}^{\prime }\left (t \right )=x_{4} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
4 |
system of linear ODEs |
✓ |
✓ |
1.089 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=2 x_{1} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-21 x_{1} \left (t \right )-5 x_{2} \left (t \right )-27 x_{3} \left (t \right )-9 x_{4} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=5 x_{3} \left (t \right ) \\ x_{4}^{\prime }\left (t \right )=-21 x_{3} \left (t \right )-2 x_{4} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
4 |
system of linear ODEs |
✓ |
✓ |
1.135 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=4 x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right )+7 x_{4} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )+4 x_{2} \left (t \right )+10 x_{3} \left (t \right )+x_{4} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=x_{1} \left (t \right )+10 x_{2} \left (t \right )+4 x_{3} \left (t \right )+x_{4} \left (t \right ) \\ x_{4}^{\prime }\left (t \right )=7 x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right )+4 x_{4} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
4 |
system of linear ODEs |
✓ |
✓ |
1.414 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-40 x_{1} \left (t \right )-12 x_{2} \left (t \right )+54 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=35 x_{1} \left (t \right )+13 x_{2} \left (t \right )-46 x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=-25 x_{1} \left (t \right )-7 x_{2} \left (t \right )+34 x_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.879 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-20 x_{1} \left (t \right )+11 x_{2} \left (t \right )+13 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=12 x_{1} \left (t \right )-x_{2} \left (t \right )-7 x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=-48 x_{1} \left (t \right )+21 x_{2} \left (t \right )+31 x_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.928 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=147 x_{1} \left (t \right )+23 x_{2} \left (t \right )-202 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-90 x_{1} \left (t \right )-9 x_{2} \left (t \right )+129 x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=90 x_{1} \left (t \right )+15 x_{2} \left (t \right )-123 x_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.966 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=9 x_{1} \left (t \right )-7 x_{2} \left (t \right )-5 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-12 x_{1} \left (t \right )+7 x_{2} \left (t \right )+11 x_{3} \left (t \right )+9 x_{4} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=24 x_{1} \left (t \right )-17 x_{2} \left (t \right )-19 x_{3} \left (t \right )-9 x_{4} \left (t \right ) \\ x_{4}^{\prime }\left (t \right )=-18 x_{1} \left (t \right )+13 x_{2} \left (t \right )+17 x_{3} \left (t \right )+9 x_{4} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
4 |
system of linear ODEs |
✓ |
✓ |
1.44 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=13 x_{1} \left (t \right )-42 x_{2} \left (t \right )+106 x_{3} \left (t \right )+139 x_{4} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=2 x_{1} \left (t \right )-16 x_{2} \left (t \right )+52 x_{3} \left (t \right )+70 x_{4} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=x_{1} \left (t \right )+6 x_{2} \left (t \right )-20 x_{3} \left (t \right )-31 x_{4} \left (t \right ) \\ x_{4}^{\prime }\left (t \right )=-x_{1} \left (t \right )-6 x_{2} \left (t \right )+22 x_{3} \left (t \right )+33 x_{4} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
4 |
system of linear ODEs |
✓ |
✓ |
1.939 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=23 x_{1} \left (t \right )-18 x_{2} \left (t \right )-16 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-8 x_{1} \left (t \right )+6 x_{2} \left (t \right )+7 x_{3} \left (t \right )+9 x_{4} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=34 x_{1} \left (t \right )-27 x_{2} \left (t \right )-26 x_{3} \left (t \right )-9 x_{4} \left (t \right ) \\ x_{4}^{\prime }\left (t \right )=-26 x_{1} \left (t \right )+21 x_{2} \left (t \right )+25 x_{3} \left (t \right )+12 x_{4} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
4 |
system of linear ODEs |
✓ |
✓ |
1.567 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=47 x_{1} \left (t \right )-8 x_{2} \left (t \right )+5 x_{3} \left (t \right )-5 x_{4} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-10 x_{1} \left (t \right )+32 x_{2} \left (t \right )+18 x_{3} \left (t \right )-2 x_{4} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=139 x_{1} \left (t \right )-40 x_{2} \left (t \right )-167 x_{3} \left (t \right )-121 x_{4} \left (t \right ) \\ x_{4}^{\prime }\left (t \right )=-232 x_{1} \left (t \right )+64 x_{2} \left (t \right )+360 x_{3} \left (t \right )+248 x_{4} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
4 |
system of linear ODEs |
✓ |
✓ |
1.708 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=139 x_{1} \left (t \right )-14 x_{2} \left (t \right )-52 x_{3} \left (t \right )-14 x_{4} \left (t \right )+28 x_{5} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-22 x_{1} \left (t \right )+5 x_{2} \left (t \right )+7 x_{3} \left (t \right )+8 x_{4} \left (t \right )-7 x_{5} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=370 x_{1} \left (t \right )-38 x_{2} \left (t \right )-139 x_{3} \left (t \right )-38 x_{4} \left (t \right )+76 x_{5} \left (t \right ) \\ x_{4}^{\prime }\left (t \right )=152 x_{1} \left (t \right )-16 x_{2} \left (t \right )-59 x_{3} \left (t \right )-13 x_{4} \left (t \right )+35 x_{5} \left (t \right ) \\ x_{5}^{\prime }\left (t \right )=95 x_{1} \left (t \right )-10 x_{2} \left (t \right )-38 x_{3} \left (t \right )-7 x_{4} \left (t \right )+23 x_{5} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
5 |
system of linear ODEs |
✓ |
✓ |
2.461 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=9 x_{1} \left (t \right )+13 x_{2} \left (t \right )-13 x_{6} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-14 x_{1} \left (t \right )+19 x_{2} \left (t \right )-10 x_{3} \left (t \right )-20 x_{4} \left (t \right )+10 x_{5} \left (t \right )+4 x_{6} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=-30 x_{1} \left (t \right )+12 x_{2} \left (t \right )-7 x_{3} \left (t \right )-30 x_{4} \left (t \right )+12 x_{5} \left (t \right )+18 x_{6} \left (t \right ) \\ x_{4}^{\prime }\left (t \right )=-12 x_{1} \left (t \right )+10 x_{2} \left (t \right )-10 x_{3} \left (t \right )-9 x_{4} \left (t \right )+10 x_{5} \left (t \right )+2 x_{6} \left (t \right ) \\ x_{5}^{\prime }\left (t \right )=6 x_{1} \left (t \right )+9 x_{2} \left (t \right )+6 x_{4} \left (t \right )+5 x_{5} \left (t \right )-15 x_{6} \left (t \right ) \\ x_{6}^{\prime }\left (t \right )=-14 x_{1} \left (t \right )+23 x_{2} \left (t \right )-10 x_{3} \left (t \right )-20 x_{4} \left (t \right )+10 x_{5} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
6 |
system of linear ODEs |
✓ |
✓ |
4.611 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=9 x_{1} \left (t \right )+4 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-6 x_{1} \left (t \right )-x_{2} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=6 x_{1} \left (t \right )+4 x_{2} \left (t \right )+3 x_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.8 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=2 x_{1} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-7 x_{1} \left (t \right )+9 x_{2} \left (t \right )+7 x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=2 x_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.431 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=25 x_{1} \left (t \right )+12 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-18 x_{1} \left (t \right )-5 x_{2} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=6 x_{1} \left (t \right )+6 x_{2} \left (t \right )+13 x_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.778 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-19 x_{1} \left (t \right )+12 x_{2} \left (t \right )+84 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=5 x_{2} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=-8 x_{1} \left (t \right )+4 x_{2} \left (t \right )+33 x_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.8 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-13 x_{1} \left (t \right )+40 x_{2} \left (t \right )-48 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-8 x_{1} \left (t \right )+23 x_{2} \left (t \right )-24 x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=3 x_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.809 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )-4 x_{2} \left (t \right )-2 x_{4} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{2} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=6 x_{1} \left (t \right )-12 x_{2} \left (t \right )-x_{3} \left (t \right )-6 x_{4} \left (t \right ) \\ x_{4}^{\prime }\left (t \right )=-4 x_{2} \left (t \right )-x_{4} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
4 |
system of linear ODEs |
✓ |
✓ |
1.004 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=39 x_{1} \left (t \right )+8 x_{2} \left (t \right )-16 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-36 x_{1} \left (t \right )-5 x_{2} \left (t \right )+16 x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=72 x_{1} \left (t \right )+16 x_{2} \left (t \right )-29 x_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.908 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=28 x_{1} \left (t \right )+50 x_{2} \left (t \right )+100 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=15 x_{1} \left (t \right )+33 x_{2} \left (t \right )+60 x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=-15 x_{1} \left (t \right )-30 x_{2} \left (t \right )-57 x_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.974 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=11 x_{1} \left (t \right )-x_{2} \left (t \right )+26 x_{3} \left (t \right )+6 x_{4} \left (t \right )-3 x_{5} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=3 x_{2} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=-9 x_{1} \left (t \right )-24 x_{3} \left (t \right )-6 x_{4} \left (t \right )+3 x_{5} \left (t \right ) \\ x_{4}^{\prime }\left (t \right )=3 x_{1} \left (t \right )+9 x_{3} \left (t \right )+5 x_{4} \left (t \right )-x_{5} \left (t \right ) \\ x_{5}^{\prime }\left (t \right )=-48 x_{1} \left (t \right )-3 x_{2} \left (t \right )-138 x_{3} \left (t \right )-30 x_{4} \left (t \right )+18 x_{5} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
5 |
system of linear ODEs |
✓ |
✓ |
1.577 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-\frac {x_{1} \left (t \right )}{10}+\frac {3 x_{2} \left (t \right )}{40} \\ x_{2}^{\prime }\left (t \right )=\frac {x_{1} \left (t \right )}{10}-\frac {x_{2} \left (t \right )}{5} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.543 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=3 x_{1} \left (t \right )-2 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=4 x_{1} \left (t \right )-x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.799 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-x_{1} \left (t \right )-4 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )-x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.727 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=2 x_{1} \left (t \right )-5 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )-2 x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.682 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=2 x_{1} \left (t \right )-\frac {5 x_{2} \left (t \right )}{2} \\ x_{2}^{\prime }\left (t \right )=\frac {9 x_{1} \left (t \right )}{5}-x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.857 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )-x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=5 x_{1} \left (t \right )-3 x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.785 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )+2 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-5 x_{1} \left (t \right )-x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.781 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=2 x_{1} \left (t \right )+x_{2} \left (t \right )-2 x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=3 x_{1} \left (t \right )+2 x_{2} \left (t \right )+x_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
1.048 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-3 x_{1} \left (t \right )+2 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )-x_{2} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=-2 x_{1} \left (t \right )-x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
2.487 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )-5 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )-3 x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.594 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-3 x_{1} \left (t \right )+2 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-x_{1} \left (t \right )-x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.626 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=\frac {3 x_{1} \left (t \right )}{4}-2 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )-\frac {5 x_{2} \left (t \right )}{4} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.766 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-\frac {4 x_{1} \left (t \right )}{5}+2 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-x_{1} \left (t \right )+\frac {6 x_{2} \left (t \right )}{5} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.747 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-\frac {x_{1} \left (t \right )}{4}+x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-x_{1} \left (t \right )-\frac {x_{2} \left (t \right )}{4} \\ x_{3}^{\prime }\left (t \right )=-\frac {x_{3} \left (t \right )}{4} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.807 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-\frac {x_{1} \left (t \right )}{4}+x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-x_{1} \left (t \right )-\frac {x_{2} \left (t \right )}{4} \\ x_{3}^{\prime }\left (t \right )=\frac {x_{3} \left (t \right )}{10} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.834 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-\frac {x_{1} \left (t \right )}{2}-\frac {x_{2} \left (t \right )}{8} \\ x_{2}^{\prime }\left (t \right )=2 x_{1} \left (t \right )-\frac {x_{2} \left (t \right )}{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.736 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{2} \left (t \right )+x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )+x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=x_{1} \left (t \right )+x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.734 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-\frac {5 x_{1} \left (t \right )}{2}+x_{2} \left (t \right )+x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )-\frac {5 x_{2} \left (t \right )}{2}+x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=x_{1} \left (t \right )+x_{2} \left (t \right )-\frac {5 x_{3} \left (t \right )}{2} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.677 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=2 x_{1} \left (t \right )-x_{2} \left (t \right )+{\mathrm e}^{t} \\ x_{2}^{\prime }\left (t \right )=3 x_{1} \left (t \right )-2 x_{2} \left (t \right )+t \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
1.206 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )+\sqrt {3}\, x_{2} \left (t \right )+{\mathrm e}^{t} \\ x_{2}^{\prime }\left (t \right )=\sqrt {3}\, x_{1} \left (t \right )-x_{2} \left (t \right )+\sqrt {3}\, {\mathrm e}^{-t} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.966 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=2 x_{1} \left (t \right )-5 x_{2} \left (t \right )-\cos \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )-2 x_{2} \left (t \right )+\sin \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
1.969 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )+x_{2} \left (t \right )+{\mathrm e}^{-2 t} \\ x_{2}^{\prime }\left (t \right )=4 x_{1} \left (t \right )-2 x_{2} \left (t \right )-2 \,{\mathrm e}^{t} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
1.288 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-4 x_{1} \left (t \right )+2 x_{2} \left (t \right )+\frac {1}{t} \\ x_{2}^{\prime }\left (t \right )=2 x_{1} \left (t \right )-x_{2} \left (t \right )+\frac {2}{t}+4 \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.916 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )+x_{2} \left (t \right )+2 \,{\mathrm e}^{t} \\ x_{2}^{\prime }\left (t \right )=4 x_{1} \left (t \right )+x_{2} \left (t \right )-{\mathrm e}^{t} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
1.182 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=2 x_{1} \left (t \right )-x_{2} \left (t \right )+{\mathrm e}^{t} \\ x_{2}^{\prime }\left (t \right )=3 x_{1} \left (t \right )-2 x_{2} \left (t \right )-{\mathrm e}^{t} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
1.031 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-\frac {5 x_{1} \left (t \right )}{4}+\frac {3 x_{2} \left (t \right )}{4}+2 t \\ x_{2}^{\prime }\left (t \right )=\frac {3 x_{1} \left (t \right )}{4}-\frac {5 x_{2} \left (t \right )}{4}+{\mathrm e}^{t} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
1.267 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-3 x_{1} \left (t \right )+\sqrt {2}\, x_{2} \left (t \right )+{\mathrm e}^{-t} \\ x_{2}^{\prime }\left (t \right )=\sqrt {2}\, x_{1} \left (t \right )-2 x_{2} \left (t \right )-{\mathrm e}^{-t} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.92 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=2 x_{1} \left (t \right )-5 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )-2 x_{2} \left (t \right )+\cos \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
1.759 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=2 x_{1} \left (t \right )-5 x_{2} \left (t \right )+\csc \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )-2 x_{2} \left (t \right )+\sec \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
4.553 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-\frac {x_{1} \left (t \right )}{2}-\frac {x_{2} \left (t \right )}{8}+\frac {{\mathrm e}^{-\frac {t}{2}}}{2} \\ x_{2}^{\prime }\left (t \right )=2 x_{1} \left (t \right )-\frac {x_{2} \left (t \right )}{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
1.471 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-2 x_{1} \left (t \right )+x_{2} \left (t \right )+2 \,{\mathrm e}^{-t} \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )-2 x_{2} \left (t \right )+3 t \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.834 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=3 x_{1} \left (t \right )-2 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=2 x_{1} \left (t \right )-2 x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.564 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=5 x_{1} \left (t \right )-x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=3 x_{1} \left (t \right )+x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.542 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=2 x_{1} \left (t \right )-x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=3 x_{1} \left (t \right )-2 x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.51 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )-5 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )-3 x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.707 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=2 x_{1} \left (t \right )-5 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )-2 x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.613 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=3 x_{1} \left (t \right )-2 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=4 x_{1} \left (t \right )-x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.756 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-x_{1} \left (t \right )-x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-\frac {5 x_{2} \left (t \right )}{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.495 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )+2 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-5 x_{1} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
1.307 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-x_{1} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.416 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=2 x_{1} \left (t \right )-\frac {5 x_{2} \left (t \right )}{2} \\ x_{2}^{\prime }\left (t \right )=\frac {9 x_{1} \left (t \right )}{5}-x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.791 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )+x_{2} \left (t \right )-2 \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )-x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
1.484 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-2 x_{1} \left (t \right )+x_{2} \left (t \right )-2 \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )-2 x_{2} \left (t \right )+1 \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.953 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-x_{1} \left (t \right )-x_{2} \left (t \right )-1 \\ x_{2}^{\prime }\left (t \right )=2 x_{1} \left (t \right )-x_{2} \left (t \right )+5 \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
2.035 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-x \left (t \right ) \\ y^{\prime }\left (t \right )=-2 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.399 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-x \left (t \right ) \\ y^{\prime }\left (t \right )=2 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.363 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-x \left (t \right ) \\ y^{\prime }\left (t \right )=2 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.384 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.486 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.469 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=y_{1} \left (t \right )+2 y_{2} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=2 y_{1} \left (t \right )+y_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.524 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=-\frac {5 y_{1} \left (t \right )}{4}+\frac {3 y_{2} \left (t \right )}{4} \\ y_{2}^{\prime }\left (t \right )=\frac {3 y_{1} \left (t \right )}{4}-\frac {5 y_{2} \left (t \right )}{4} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.56 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=-\frac {4 y_{1} \left (t \right )}{5}+\frac {3 y_{2} \left (t \right )}{5} \\ y_{2}^{\prime }\left (t \right )=-\frac {2 y_{1} \left (t \right )}{5}-\frac {11 y_{2} \left (t \right )}{5} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.634 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=-y_{1} \left (t \right )-4 y_{2} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=-y_{1} \left (t \right )-y_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.597 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=2 y_{1} \left (t \right )-4 y_{2} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=-y_{1} \left (t \right )-y_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.61 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=4 y_{1} \left (t \right )-3 y_{2} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=2 y_{1} \left (t \right )-y_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.583 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=-6 y_{1} \left (t \right )-3 y_{2} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=y_{1} \left (t \right )-2 y_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.597 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=y_{1} \left (t \right )-y_{2} \left (t \right )-2 y_{3} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=y_{1} \left (t \right )-2 y_{2} \left (t \right )-3 y_{3} \left (t \right ) \\ y_{3}^{\prime }\left (t \right )=-4 y_{1} \left (t \right )+y_{2} \left (t \right )-y_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
1.138 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=-6 y_{1} \left (t \right )-4 y_{2} \left (t \right )-8 y_{3} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=-4 y_{1} \left (t \right )-4 y_{3} \left (t \right ) \\ y_{3}^{\prime }\left (t \right )=-8 y_{1} \left (t \right )-4 y_{2} \left (t \right )-6 y_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
1.02 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=3 y_{1} \left (t \right )+5 y_{2} \left (t \right )+8 y_{3} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=y_{1} \left (t \right )-y_{2} \left (t \right )-2 y_{3} \left (t \right ) \\ y_{3}^{\prime }\left (t \right )=-y_{1} \left (t \right )-y_{2} \left (t \right )-y_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
1.181 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=y_{1} \left (t \right )-y_{2} \left (t \right )+2 y_{3} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=12 y_{1} \left (t \right )-4 y_{2} \left (t \right )+10 y_{3} \left (t \right ) \\ y_{3}^{\prime }\left (t \right )=-6 y_{1} \left (t \right )+y_{2} \left (t \right )-7 y_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
1.054 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=4 y_{1} \left (t \right )-y_{2} \left (t \right )-4 y_{3} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=4 y_{1} \left (t \right )-3 y_{2} \left (t \right )-2 y_{3} \left (t \right ) \\ y_{3}^{\prime }\left (t \right )=y_{1} \left (t \right )-y_{2} \left (t \right )-y_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
1.065 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=-2 y_{1} \left (t \right )+2 y_{2} \left (t \right )-6 y_{3} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=2 y_{1} \left (t \right )+6 y_{2} \left (t \right )+2 y_{3} \left (t \right ) \\ y_{3}^{\prime }\left (t \right )=-2 y_{1} \left (t \right )-2 y_{2} \left (t \right )+2 y_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
1.086 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=3 y_{1} \left (t \right )+2 y_{2} \left (t \right )-2 y_{3} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=-2 y_{1} \left (t \right )+7 y_{2} \left (t \right )-2 y_{3} \left (t \right ) \\ y_{3}^{\prime }\left (t \right )=-10 y_{1} \left (t \right )+10 y_{2} \left (t \right )-5 y_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.992 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=3 y_{1} \left (t \right )+y_{2} \left (t \right )-y_{3} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=3 y_{1} \left (t \right )+5 y_{2} \left (t \right )+y_{3} \left (t \right ) \\ y_{3}^{\prime }\left (t \right )=-6 y_{1} \left (t \right )+2 y_{2} \left (t \right )+4 y_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
1.001 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=-7 y_{1} \left (t \right )-4 y_{2} \left (t \right )+4 y_{3} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=y_{1} \left (t \right )+y_{3} \left (t \right ) \\ y_{3}^{\prime }\left (t \right )=-9 y_{1} \left (t \right )-5 y_{2} \left (t \right )+6 y_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
1.47 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=4 y_{1} \left (t \right )-8 y_{2} \left (t \right )-4 y_{3} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=-3 y_{1} \left (t \right )-y_{2} \left (t \right )-4 y_{3} \left (t \right ) \\ y_{3}^{\prime }\left (t \right )=y_{1} \left (t \right )-y_{2} \left (t \right )+9 y_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
1.193 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=-y_{1} \left (t \right )+2 y_{2} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=-5 y_{1} \left (t \right )+5 y_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.893 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=-11 y_{1} \left (t \right )+4 y_{2} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=-26 y_{1} \left (t \right )+9 y_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.877 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=y_{1} \left (t \right )+2 y_{2} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=-4 y_{1} \left (t \right )+5 y_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.882 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=5 y_{1} \left (t \right )-6 y_{2} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=3 y_{1} \left (t \right )-y_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.83 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=-3 y_{1} \left (t \right )-3 y_{2} \left (t \right )+y_{3} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=2 y_{2} \left (t \right )+2 y_{3} \left (t \right ) \\ y_{3}^{\prime }\left (t \right )=5 y_{1} \left (t \right )+y_{2} \left (t \right )+y_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
23.811 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=-3 y_{1} \left (t \right )+3 y_{2} \left (t \right )+y_{3} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=y_{1} \left (t \right )-5 y_{2} \left (t \right )-3 y_{3} \left (t \right ) \\ y_{3}^{\prime }\left (t \right )=-3 y_{1} \left (t \right )+7 y_{2} \left (t \right )+3 y_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
1.683 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=2 y_{1} \left (t \right )+y_{2} \left (t \right )-y_{3} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=y_{2} \left (t \right )+y_{3} \left (t \right ) \\ y_{3}^{\prime }\left (t \right )=y_{1} \left (t \right )+y_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
1.149 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=-3 y_{1} \left (t \right )+y_{2} \left (t \right )-3 y_{3} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=4 y_{1} \left (t \right )-y_{2} \left (t \right )+2 y_{3} \left (t \right ) \\ y_{3}^{\prime }\left (t \right )=4 y_{1} \left (t \right )-2 y_{2} \left (t \right )+3 y_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.914 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=6 x_{1} \left (t \right )-3 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=2 x_{1} \left (t \right )+x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.634 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-2 x_{1} \left (t \right )+x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-4 x_{1} \left (t \right )+3 x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.577 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=3 x_{1} \left (t \right )+2 x_{2} \left (t \right )+4 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=2 x_{1} \left (t \right )+2 x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=4 x_{1} \left (t \right )+2 x_{2} \left (t \right )+3 x_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.983 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=7 x_{1} \left (t \right )-x_{2} \left (t \right )+6 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-10 x_{1} \left (t \right )+4 x_{2} \left (t \right )-12 x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=-2 x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
1.043 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-7 x_{1} \left (t \right )+6 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=5 x_{2} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=6 x_{1} \left (t \right )+2 x_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.905 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )+2 x_{2} \left (t \right )+3 x_{3} \left (t \right )+6 x_{4} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=3 x_{1} \left (t \right )+6 x_{2} \left (t \right )+9 x_{3} \left (t \right )+18 x_{4} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=5 x_{1} \left (t \right )+10 x_{2} \left (t \right )+15 x_{3} \left (t \right )+30 x_{4} \left (t \right ) \\ x_{4}^{\prime }\left (t \right )=7 x_{1} \left (t \right )+14 x_{2} \left (t \right )+21 x_{3} \left (t \right )+42 x_{4} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
4 |
system of linear ODEs |
✓ |
✓ |
1.295 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )+x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=4 x_{1} \left (t \right )+x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.558 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )-3 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-2 x_{1} \left (t \right )+2 x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.553 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=3 x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )+3 x_{2} \left (t \right )-x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=3 x_{1} \left (t \right )+3 x_{2} \left (t \right )-x_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.707 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )-x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )+2 x_{2} \left (t \right )+x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=x_{1} \left (t \right )+10 x_{2} \left (t \right )+2 x_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.896 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )-3 x_{2} \left (t \right )+2 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-x_{2} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=-x_{2} \left (t \right )-2 x_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.775 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=3 x_{1} \left (t \right )+x_{2} \left (t \right )-2 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-x_{1} \left (t \right )+2 x_{2} \left (t \right )+x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=4 x_{1} \left (t \right )+x_{2} \left (t \right )-3 x_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.901 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-3 x_{1} \left (t \right )+2 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-x_{1} \left (t \right )-x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.837 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )-5 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )-3 x_{2} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=x_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
1.045 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=3 x_{1} \left (t \right )+x_{2} \left (t \right )-2 x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=2 x_{1} \left (t \right )+2 x_{2} \left (t \right )+x_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
1.143 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )+x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{2} \left (t \right )-x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=-2 x_{1} \left (t \right )-x_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
1.194 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )-x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=5 x_{1} \left (t \right )-3 x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.64 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=3 x_{1} \left (t \right )-2 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=4 x_{1} \left (t \right )-x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.652 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-3 x_{1} \left (t \right )+2 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )-x_{2} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=-2 x_{1} \left (t \right )-x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
2.155 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=2 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-2 x_{1} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=-3 x_{4} \left (t \right ) \\ x_{4}^{\prime }\left (t \right )=3 x_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
4 |
system of linear ODEs |
✓ |
✓ |
3.183 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=2 x_{1} \left (t \right )+x_{2} \left (t \right )-2 x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=3 x_{1} \left (t \right )+2 x_{2} \left (t \right )+x_{3} \left (t \right )+{\mathrm e}^{t} \cos \left (2 t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
3.177 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )+{\mathrm e}^{c t} \\ x_{2}^{\prime }\left (t \right )=2 x_{1} \left (t \right )+x_{2} \left (t \right )-2 x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=3 x_{1} \left (t \right )+2 x_{2} \left (t \right )+x_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
4.136 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=4 x_{1} \left (t \right )+5 x_{2} \left (t \right )+4 \,{\mathrm e}^{t} \cos \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-2 x_{1} \left (t \right )-2 x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
1.867 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=2 x_{1} \left (t \right )-5 x_{2} \left (t \right )+\sin \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )-2 x_{2} \left (t \right )+\tan \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
3.764 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{2} \left (t \right )+f_{1} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-x_{1} \left (t \right )+f_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
2.004 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=2 x_{1} \left (t \right )+x_{2} \left (t \right )+{\mathrm e}^{3 t} \\ x_{2}^{\prime }\left (t \right )=3 x_{1} \left (t \right )-2 x_{2} \left (t \right )+{\mathrm e}^{3 t} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
2.088 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )+3 x_{2} \left (t \right )+2 x_{3} \left (t \right )+\sin \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-x_{1} \left (t \right )+2 x_{2} \left (t \right )+x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=4 x_{1} \left (t \right )-x_{2} \left (t \right )-x_{3} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
2.861 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-x_{1} \left (t \right )-x_{2} \left (t \right )+1 \\ x_{2}^{\prime }\left (t \right )=-4 x_{2} \left (t \right )-x_{3} \left (t \right )+t \\ x_{3}^{\prime }\left (t \right )=5 x_{2} \left (t \right )+{\mathrm e}^{t} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
4.827 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right )+{\mathrm e}^{2 t} \\ x_{2}^{\prime }\left (t \right )=2 x_{1} \left (t \right )+3 x_{2} \left (t \right )-4 x_{3} \left (t \right )+2 \,{\mathrm e}^{2 t} \\ x_{3}^{\prime }\left (t \right )=4 x_{1} \left (t \right )+x_{2} \left (t \right )-4 x_{3} \left (t \right )+{\mathrm e}^{2 t} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
2.149 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )-x_{2} \left (t \right )-x_{3} \left (t \right )+{\mathrm e}^{3 t} \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )+3 x_{2} \left (t \right )+x_{3} \left (t \right )-{\mathrm e}^{3 t} \\ x_{3}^{\prime }\left (t \right )=-3 x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right )-{\mathrm e}^{3 t} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
1.863 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=3 x_{1} \left (t \right )+2 x_{2} \left (t \right )+4 x_{3} \left (t \right )+2 \,{\mathrm e}^{8 t} \\ x_{2}^{\prime }\left (t \right )=2 x_{1} \left (t \right )+2 x_{3} \left (t \right )+{\mathrm e}^{8 t} \\ x_{3}^{\prime }\left (t \right )=4 x_{1} \left (t \right )+2 x_{2} \left (t \right )+3 x_{3} \left (t \right )+2 \,{\mathrm e}^{8 t} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
1.789 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )-x \left (t \right )=\cos \left (t \right ) \\ y^{\prime }\left (t \right )+y \left (t \right )=4 t \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
1.368 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )+5 x \left (t \right )=3 t^{2} \\ y^{\prime }\left (t \right )+y \left (t \right )={\mathrm e}^{3 t} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
1.252 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )+2 x \left (t \right )=3 t \\ x^{\prime }\left (t \right )+2 y^{\prime }\left (t \right )+y \left (t \right )=\cos \left (2 t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
1.914 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )-x \left (t \right )+y \left (t \right )=2 \sin \left (t \right ) \\ x^{\prime }\left (t \right )+y^{\prime }\left (t \right )=3 y \left (t \right )-3 x \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
1.687 |
|
|
\[ {}\left [\begin {array}{c} 2 x^{\prime }\left (t \right )+3 x \left (t \right )-y \left (t \right )={\mathrm e}^{t} \\ 5 x \left (t \right )-3 y^{\prime }\left (t \right )=y \left (t \right )+2 t \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
1.691 |
|
|
\[ {}\left [\begin {array}{c} 5 y^{\prime }\left (t \right )-3 x^{\prime }\left (t \right )-5 y \left (t \right )=5 t \\ 3 x^{\prime }\left (t \right )-5 y^{\prime }\left (t \right )-2 x \left (t \right )=0 \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.625 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )-y^{\prime }\left (t \right )+y \left (t \right )=-{\mathrm e}^{t} \\ x \left (t \right )+y^{\prime }\left (t \right )-y \left (t \right )={\mathrm e}^{2 t} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.679 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )+2 x \left (t \right )+y^{\prime }\left (t \right )+y \left (t \right )=t \\ 5 x \left (t \right )+y^{\prime }\left (t \right )+3 y \left (t \right )=t^{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
1.152 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )+x \left (t \right )+2 y^{\prime }\left (t \right )+7 y \left (t \right )={\mathrm e}^{t}+2 \\ -2 x \left (t \right )+y^{\prime }\left (t \right )+3 y \left (t \right )={\mathrm e}^{t}-1 \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
1.399 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )-x \left (t \right )+y^{\prime }\left (t \right )+3 y \left (t \right )={\mathrm e}^{-t}-1 \\ x^{\prime }\left (t \right )+2 x \left (t \right )+y^{\prime }\left (t \right )+3 y \left (t \right )={\mathrm e}^{2 t}+1 \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.407 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )-x \left (t \right )+y^{\prime }\left (t \right )+2 y \left (t \right )=1+{\mathrm e}^{t} \\ y^{\prime }\left (t \right )+2 y \left (t \right )+z^{\prime }\left (t \right )+z \left (t \right )={\mathrm e}^{t}+2 \\ x^{\prime }\left (t \right )-x \left (t \right )+z^{\prime }\left (t \right )+z \left (t \right )=3+{\mathrm e}^{t} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.734 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )+3 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=5 x_{1} \left (t \right )+3 x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.331 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=4 x_{1} \left (t \right )-x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=5 x_{1} \left (t \right )+2 x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.526 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-2 x_{1} \left (t \right )+x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )-2 x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.316 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-2 x_{1} \left (t \right )+x_{2} \left (t \right )+2 \,{\mathrm e}^{-t} \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )-2 x_{2} \left (t \right )+3 t \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.73 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )-2 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=3 x_{1} \left (t \right )-4 x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.309 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=3 x_{1} \left (t \right )-x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=4 x_{1} \left (t \right )-2 x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.274 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )+x_{2} \left (t \right )-8 \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )+x_{2} \left (t \right )+3 \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.674 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )+x_{2} \left (t \right )-8 \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )+x_{2} \left (t \right )+3 \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.466 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )=y_{2} \left (x \right ) \\ y_{2}^{\prime }\left (x \right )=6 y_{1} \left (x \right )+y_{2} \left (x \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.39 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )=y_{1} \left (x \right )+y_{2} \left (x \right ) \\ y_{2}^{\prime }\left (x \right )=y_{1} \left (x \right )+y_{2} \left (x \right )+{\mathrm e}^{3 x} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.546 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )=3 y_{1} \left (x \right )+x y_{3} \left (x \right ) \\ y_{2}^{\prime }\left (x \right )=y_{2} \left (x \right )+x^{3} y_{3} \left (x \right ) \\ y_{3}^{\prime }\left (x \right )=2 x y_{2} \left (x \right )-y_{2} \left (x \right )+{\mathrm e}^{x} y_{3} \left (x \right ) \end {array}\right ] \] |
1 |
0 |
3 |
system of linear ODEs |
✗ |
N/A |
0.033 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+3 y \left (t \right ) \\ y^{\prime }\left (t \right )=3 x \left (t \right )+y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.528 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+3 y \left (t \right ) \\ y^{\prime }\left (t \right )=3 x \left (t \right )+y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.533 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+2 y \left (t \right ) \\ y^{\prime }\left (t \right )=3 x \left (t \right )+2 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.507 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+2 y \left (t \right )+t -1 \\ y^{\prime }\left (t \right )=3 x \left (t \right )+2 y \left (t \right )-5 t -2 \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
1.434 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right ) \\ y^{\prime }\left (t \right )=y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.316 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-3 x \left (t \right )+4 y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right )+3 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.445 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=4 x \left (t \right )-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=5 x \left (t \right )+2 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.783 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=4 x \left (t \right )-3 y \left (t \right ) \\ y^{\prime }\left (t \right )=8 x \left (t \right )-6 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.502 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right ) \\ y^{\prime }\left (t \right )=3 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.315 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=7 x \left (t \right )+6 y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )+6 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.512 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=4 x \left (t \right )+5 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.746 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right )-5 t +2 \\ y^{\prime }\left (t \right )=4 x \left (t \right )-2 y \left (t \right )-8 t -8 \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
1.213 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right )-4 y \left (t \right ) \\ y^{\prime }\left (t \right )=4 x \left (t \right )-7 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.511 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=4 x \left (t \right )+y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.52 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-3 x \left (t \right )+\sqrt {2}\, y \left (t \right ) \\ y^{\prime }\left (t \right )=\sqrt {2}\, x \left (t \right )-2 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.451 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=5 x \left (t \right )+3 y \left (t \right ) \\ y^{\prime }\left (t \right )=-6 x \left (t \right )-4 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.542 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )+y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.62 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right )-5 y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )+2 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.707 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+2 y \left (t \right ) \\ y^{\prime }\left (t \right )=-4 x \left (t \right )+y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.826 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right )+2 y \left (t \right )+z \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right )-y \left (t \right )+3 z \left (t \right ) \\ z^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right )+z \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.849 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-x \left (t \right )+y \left (t \right )-z \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )-y \left (t \right )-4 z \left (t \right ) \\ z^{\prime }\left (t \right )=3 x \left (t \right )-y \left (t \right )+z \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
19.142 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+2 y \left (t \right )-4 t +1 \\ y^{\prime }\left (t \right )=-x \left (t \right )+2 y \left (t \right )+3 t +4 \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
4.825 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-2 x \left (t \right )+y \left (t \right )-t +3 \\ y^{\prime }\left (t \right )=x \left (t \right )+4 y \left (t \right )+t -2 \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
1.8 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-4 x \left (t \right )+y \left (t \right )-t +3 \\ y^{\prime }\left (t \right )=-x \left (t \right )-5 y \left (t \right )+t +1 \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
4.335 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right ) y \left (t \right )+1 \\ y^{\prime }\left (t \right )=-x \left (t \right )+y \left (t \right ) \end {array}\right ] \] |
1 |
0 |
0 |
system of linear ODEs |
✗ |
N/A |
0.273 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=t y \left (t \right )+1 \\ y^{\prime }\left (t \right )=-x \left (t \right ) t +y \left (t \right ) \end {array}\right ] \] |
1 |
0 |
0 |
system of linear ODEs |
✗ |
N/A |
0.026 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right )-5 y \left (t \right ) \\ y^{\prime }\left (t \right )=4 x \left (t \right )+8 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.996 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=4 x \left (t \right )-7 y \left (t \right ) \\ y^{\prime }\left (t \right )=5 x \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.978 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-3 x \left (t \right )+4 y \left (t \right )-9 z \left (t \right ) \\ y^{\prime }\left (t \right )=6 x \left (t \right )-y \left (t \right ) \\ z^{\prime }\left (t \right )=10 x \left (t \right )+4 y \left (t \right )+3 z \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
23.392 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )-y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+2 z \left (t \right ) \\ z^{\prime }\left (t \right )=-x \left (t \right )+z \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
18.528 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )-y \left (t \right )+z \left (t \right )+t -1 \\ y^{\prime }\left (t \right )=2 x \left (t \right )+y \left (t \right )-z \left (t \right )-3 t^{2} \\ z^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right )+z \left (t \right )+t^{2}-t +2 \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
11.493 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-3 x \left (t \right )+4 y \left (t \right )+{\mathrm e}^{-t} \sin \left (2 t \right ) \\ y^{\prime }\left (t \right )=5 x \left (t \right )+9 z \left (t \right )+4 \,{\mathrm e}^{-t} \cos \left (2 t \right ) \\ z^{\prime }\left (t \right )=y \left (t \right )+6 z \left (t \right )-{\mathrm e}^{-t} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
301.921 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=4 x \left (t \right )+2 y \left (t \right )+{\mathrm e}^{t} \\ y^{\prime }\left (t \right )=-x \left (t \right )+3 y \left (t \right )-{\mathrm e}^{t} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
2.681 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=7 x \left (t \right )+5 y \left (t \right )-9 z \left (t \right )-8 \,{\mathrm e}^{-2 t} \\ y^{\prime }\left (t \right )=4 x \left (t \right )+y \left (t \right )+z \left (t \right )+2 \,{\mathrm e}^{5 t} \\ z^{\prime }\left (t \right )=-2 y \left (t \right )+3 z \left (t \right )+{\mathrm e}^{5 t}-3 \,{\mathrm e}^{-2 t} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
117.423 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )-y \left (t \right )+2 z \left (t \right )+{\mathrm e}^{-t}-3 t \\ y^{\prime }\left (t \right )=3 x \left (t \right )-4 y \left (t \right )+z \left (t \right )+2 \,{\mathrm e}^{-t}+t \\ z^{\prime }\left (t \right )=-2 x \left (t \right )+5 y \left (t \right )+6 z \left (t \right )+2 \,{\mathrm e}^{-t}-t \end {array}\right ] \] |
1 |
1 |
0 |
system of linear ODEs |
✓ |
✓ |
208.704 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right )-7 y \left (t \right )+4 \sin \left (t \right )+\left (t -4\right ) {\mathrm e}^{4 t} \\ y^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right )+8 \sin \left (t \right )+\left (1+2 t \right ) {\mathrm e}^{4 t} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
9.974 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right )-4 y \left (t \right ) \\ y^{\prime }\left (t \right )=4 x \left (t \right )-7 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.529 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-2 x \left (t \right )+5 y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right )+4 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.688 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-x \left (t \right )+\frac {y \left (t \right )}{4} \\ y^{\prime }\left (t \right )=x \left (t \right )-y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.477 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+2 y \left (t \right )+z \left (t \right ) \\ y^{\prime }\left (t \right )=6 x \left (t \right )-y \left (t \right ) \\ z^{\prime }\left (t \right )=-x \left (t \right )-2 y \left (t \right )-z \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.94 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=z \left (t \right )+x \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right ) \\ z^{\prime }\left (t \right )=-2 x \left (t \right )-z \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.938 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+2 y \left (t \right ) \\ y^{\prime }\left (t \right )=4 x \left (t \right )+3 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.464 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )+2 y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+3 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.447 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-4 x \left (t \right )+2 y \left (t \right ) \\ y^{\prime }\left (t \right )=-\frac {5 x \left (t \right )}{2}+2 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.509 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-\frac {5 x \left (t \right )}{2}+2 y \left (t \right ) \\ y^{\prime }\left (t \right )=\frac {3 x \left (t \right )}{4}-2 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.494 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=10 x \left (t \right )-5 y \left (t \right ) \\ y^{\prime }\left (t \right )=8 x \left (t \right )-12 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.517 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-6 x \left (t \right )+2 y \left (t \right ) \\ y^{\prime }\left (t \right )=-3 x \left (t \right )+y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.441 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right )-z \left (t \right ) \\ y^{\prime }\left (t \right )=2 y \left (t \right ) \\ z^{\prime }\left (t \right )=y \left (t \right )-z \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.622 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )-7 y \left (t \right ) \\ y^{\prime }\left (t \right )=5 x \left (t \right )+10 y \left (t \right )+4 z \left (t \right ) \\ z^{\prime }\left (t \right )=5 y \left (t \right )+2 z \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.806 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+2 y \left (t \right )+z \left (t \right ) \\ z^{\prime }\left (t \right )=3 y \left (t \right )-z \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.794 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=z \left (t \right )+x \left (t \right ) \\ y^{\prime }\left (t \right )=y \left (t \right ) \\ z^{\prime }\left (t \right )=z \left (t \right )+x \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.533 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-x \left (t \right )-y \left (t \right ) \\ y^{\prime }\left (t \right )=\frac {3 x \left (t \right )}{4}-\frac {3 y \left (t \right )}{2}+3 z \left (t \right ) \\ z^{\prime }\left (t \right )=\frac {x \left (t \right )}{8}+\frac {y \left (t \right )}{4}-\frac {z \left (t \right )}{2} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.841 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-x \left (t \right )-y \left (t \right ) \\ y^{\prime }\left (t \right )=\frac {3 x \left (t \right )}{4}-\frac {3 y \left (t \right )}{2}+3 z \left (t \right ) \\ z^{\prime }\left (t \right )=\frac {x \left (t \right )}{8}+\frac {y \left (t \right )}{4}-\frac {z \left (t \right )}{2} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.736 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-x \left (t \right )+4 y \left (t \right )+2 z \left (t \right ) \\ y^{\prime }\left (t \right )=4 x \left (t \right )-y \left (t \right )-2 z \left (t \right ) \\ z^{\prime }\left (t \right )=6 z \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.751 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=\frac {x \left (t \right )}{2} \\ y^{\prime }\left (t \right )=x \left (t \right )-\frac {y \left (t \right )}{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.385 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right )+4 z \left (t \right ) \\ y^{\prime }\left (t \right )=2 y \left (t \right ) \\ z^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right )+z \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.66 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=\frac {9 x \left (t \right )}{10}+\frac {21 y \left (t \right )}{10}+\frac {16 z \left (t \right )}{5} \\ y^{\prime }\left (t \right )=\frac {7 x \left (t \right )}{10}+\frac {13 y \left (t \right )}{2}+\frac {21 z \left (t \right )}{5} \\ z^{\prime }\left (t \right )=\frac {11 x \left (t \right )}{10}+\frac {17 y \left (t \right )}{10}+\frac {17 z \left (t \right )}{5} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
95.264 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )+2 x_{3} \left (t \right )-\frac {9 x_{4} \left (t \right )}{5} \\ x_{2}^{\prime }\left (t \right )=\frac {51 x_{2} \left (t \right )}{10}-x_{4} \left (t \right )+3 x_{5} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=x_{1} \left (t \right )+2 x_{2} \left (t \right )-3 x_{3} \left (t \right ) \\ x_{4}^{\prime }\left (t \right )=x_{2} \left (t \right )-\frac {31 x_{3} \left (t \right )}{10}+4 x_{4} \left (t \right ) \\ x_{5}^{\prime }\left (t \right )=-\frac {14 x_{1} \left (t \right )}{5}+\frac {3 x_{4} \left (t \right )}{2}-x_{5} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
5 |
system of linear ODEs |
✓ |
✓ |
151.959 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right )-y \left (t \right )-z \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right )-z \left (t \right ) \\ z^{\prime }\left (t \right )=x \left (t \right )-y \left (t \right )+z \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.678 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right )+2 y \left (t \right )+4 z \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )+2 z \left (t \right ) \\ z^{\prime }\left (t \right )=4 x \left (t \right )+2 y \left (t \right )+3 z \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.77 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=z \left (t \right ) \\ y^{\prime }\left (t \right )=y \left (t \right ) \\ z^{\prime }\left (t \right )=x \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.489 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=6 x \left (t \right )-y \left (t \right ) \\ y^{\prime }\left (t \right )=5 x \left (t \right )+2 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.692 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right )-y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.588 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=5 x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right )+3 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.664 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=4 x \left (t \right )+5 y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right )+6 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.743 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=4 x \left (t \right )-5 y \left (t \right ) \\ y^{\prime }\left (t \right )=5 x \left (t \right )-4 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.663 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )-8 y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )-3 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.687 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=z \left (t \right ) \\ y^{\prime }\left (t \right )=-z \left (t \right ) \\ z^{\prime }\left (t \right )=y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.654 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )+y \left (t \right )+2 z \left (t \right ) \\ y^{\prime }\left (t \right )=3 x \left (t \right )+6 z \left (t \right ) \\ z^{\prime }\left (t \right )=-4 x \left (t \right )-3 z \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
1.451 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )-12 y \left (t \right )-14 z \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+2 y \left (t \right )-3 z \left (t \right ) \\ z^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right )-2 z \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.919 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )+3 y \left (t \right )-7 \\ y^{\prime }\left (t \right )=-x \left (t \right )-2 y \left (t \right )+5 \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.918 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-2 x \left (t \right )+3 y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right )+5 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.421 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-x \left (t \right )+4 y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )-3 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.427 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )-y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )+2 y \left (t \right )+4 \,{\mathrm e}^{t} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.872 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=6 x \left (t \right )-7 y \left (t \right )+10 \\ y^{\prime }\left (t \right )=x \left (t \right )-2 y \left (t \right )-2 \,{\mathrm e}^{t} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
1.278 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=9 x \left (t \right )+4 y \left (t \right ) \\ y^{\prime }\left (t \right )=-6 x \left (t \right )-y \left (t \right ) \\ z^{\prime }\left (t \right )=6 x \left (t \right )+4 y \left (t \right )+3 z \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.681 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+2 y \left (t \right )+2 t +1 \\ y^{\prime }\left (t \right )=5 x \left (t \right )+y \left (t \right )+3 t -1 \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
2.147 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )=t +y \left (t \right ) \\ x^{\prime }\left (t \right )+y^{\prime }\left (t \right )=2 x \left (t \right )+3 y \left (t \right )+{\mathrm e}^{t} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.544 |
|
|
\[ {}\left [\begin {array}{c} 2 x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )=t +y \left (t \right ) \\ x^{\prime }\left (t \right )+y^{\prime }\left (t \right )=2 x \left (t \right )+3 y \left (t \right )+{\mathrm e}^{t} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
3.087 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )=y \left (t \right )+t +\sin \left (t \right )+\cos \left (t \right ) \\ x^{\prime }\left (t \right )+y^{\prime }\left (t \right )=2 x \left (t \right )+3 y \left (t \right )+{\mathrm e}^{t} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.885 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=a x \left (t \right ) \\ y^{\prime }\left (t \right )=b \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.379 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=a y \left (t \right ) \\ y^{\prime }\left (t \right )=-a x \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.274 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=a y \left (t \right ) \\ y^{\prime }\left (t \right )=b x \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.333 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=a x \left (t \right )-y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+a y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.277 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=a x \left (t \right )+b y \left (t \right ) \\ y^{\prime }\left (t \right )=c x \left (t \right )+b y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.655 |
|
|
\[ {}\left [\begin {array}{c} a x^{\prime }\left (t \right )+b y^{\prime }\left (t \right )=\alpha x \left (t \right )+\beta y \left (t \right ) \\ b x^{\prime }\left (t \right )-a y^{\prime }\left (t \right )=\beta x \left (t \right )-\alpha y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.619 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )+2 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.486 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )+3 x \left (t \right )+4 y \left (t \right )=0 \\ y^{\prime }\left (t \right )+2 x \left (t \right )+5 y \left (t \right )=0 \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.329 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-5 x \left (t \right )-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )-7 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.46 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=a_{1} x \left (t \right )+b_{1} y \left (t \right )+c_{1} \\ y^{\prime }\left (t \right )=a_{2} x \left (t \right )+b_{2} y \left (t \right )+c_{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
1.484 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )+2 y \left (t \right )=3 t \\ y^{\prime }\left (t \right )-2 x \left (t \right )=4 \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
1.073 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )+y \left (t \right )-t^{2}+6 t +1=0 \\ y^{\prime }\left (t \right )-x \left (t \right )=-3 t^{2}+3 t +1 \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.967 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )+2 x \left (t \right )+y^{\prime }\left (t \right )+y \left (t \right )={\mathrm e}^{2 t}+t \\ x^{\prime }\left (t \right )-x \left (t \right )+y^{\prime }\left (t \right )+3 y \left (t \right )={\mathrm e}^{t}-1 \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.428 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-y \left (t \right )={\mathrm e}^{t} \\ 2 x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+2 y \left (t \right )=\cos \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.898 |
|
|
\[ {}\left [\begin {array}{c} 4 x^{\prime }\left (t \right )+9 y^{\prime }\left (t \right )+2 x \left (t \right )+31 y \left (t \right )={\mathrm e}^{t} \\ 3 x^{\prime }\left (t \right )+7 y^{\prime }\left (t \right )+x \left (t \right )+24 y \left (t \right )=3 \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
1.455 |
|
|
\[ {}\left [\begin {array}{c} 4 x^{\prime }\left (t \right )+9 y^{\prime }\left (t \right )+44 x \left (t \right )+49 y \left (t \right )=t \\ 3 x^{\prime }\left (t \right )+7 y^{\prime }\left (t \right )+34 x \left (t \right )+38 y \left (t \right )={\mathrm e}^{t} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.813 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right ) f \left (t \right )+y \left (t \right ) g \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right ) g \left (t \right )+y \left (t \right ) f \left (t \right ) \end {array}\right ] \] |
1 |
0 |
2 |
system of linear ODEs |
✗ |
N/A |
0.024 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )+\left (a x \left (t \right )+b y \left (t \right )\right ) f \left (t \right )=g \left (t \right ) \\ y^{\prime }\left (t \right )+\left (c x \left (t \right )+d y \left (t \right )\right ) f \left (t \right )=h \left (t \right ) \end {array}\right ] \] |
1 |
0 |
2 |
system of linear ODEs |
✗ |
N/A |
0.026 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right ) \cos \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right ) {\mathrm e}^{-\sin \left (t \right )} \end {array}\right ] \] |
1 |
0 |
2 |
system of linear ODEs |
✗ |
N/A |
0.023 |
|
|
\[ {}\left [\begin {array}{c} t x^{\prime }\left (t \right )+y \left (t \right )=0 \\ t y^{\prime }\left (t \right )+x \left (t \right )=0 \end {array}\right ] \] |
1 |
0 |
2 |
system of linear ODEs |
✗ |
N/A |
0.02 |
|
|
\[ {}\left [\begin {array}{c} t x^{\prime }\left (t \right )+2 x \left (t \right )=t \\ t y^{\prime }\left (t \right )-\left (2+t \right ) x \left (t \right )-t y \left (t \right )=-t \end {array}\right ] \] |
1 |
0 |
2 |
system of linear ODEs |
✗ |
N/A |
0.023 |
|
|
\[ {}\left [\begin {array}{c} t x^{\prime }\left (t \right )+2 x \left (t \right )-2 y \left (t \right )=t \\ t y^{\prime }\left (t \right )+x \left (t \right )+5 y \left (t \right )=t^{2} \end {array}\right ] \] |
1 |
0 |
2 |
system of linear ODEs |
✗ |
N/A |
0.026 |
|
|
\[ {}\left [\begin {array}{c} t^{2} \left (1-\sin \left (t \right )\right ) x^{\prime }\left (t \right )=t \left (1-2 \sin \left (t \right )\right ) x \left (t \right )+t^{2} y \left (t \right ) \\ t^{2} \left (1-\sin \left (t \right )\right ) y^{\prime }\left (t \right )=\left (t \cos \left (t \right )-\sin \left (t \right )\right ) x \left (t \right )+t \left (1-t \cos \left (t \right )\right ) y \left (t \right ) \end {array}\right ] \] |
1 |
0 |
2 |
system of linear ODEs |
✗ |
N/A |
0.043 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right ) \\ y^{\prime }\left (t \right )=3 x \left (t \right )-2 y \left (t \right ) \\ z^{\prime }\left (t \right )=2 y \left (t \right )+3 z \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.443 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=4 x \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )-2 y \left (t \right ) \\ z^{\prime }\left (t \right )=x \left (t \right )-4 y \left (t \right )+z \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.453 |
|
|
\[ {}\left [\begin {array}{c} a x^{\prime }\left (t \right )=b c \left (y \left (t \right )-z \left (t \right )\right ) \\ b y^{\prime }\left (t \right )=c a \left (-x \left (t \right )+z \left (t \right )\right ) \\ c z^{\prime }\left (t \right )=a b \left (x \left (t \right )-y \left (t \right )\right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
1.363 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=c y \left (t \right )-b z \left (t \right ) \\ y^{\prime }\left (t \right )=a z \left (t \right )-c x \left (t \right ) \\ z^{\prime }\left (t \right )=b x \left (t \right )-a y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
1.073 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=h \left (t \right ) y \left (t \right )-g \left (t \right ) z \left (t \right ) \\ y^{\prime }\left (t \right )=f \left (t \right ) z \left (t \right )-h \left (t \right ) x \left (t \right ) \\ z^{\prime }\left (t \right )=x \left (t \right ) g \left (t \right )-y \left (t \right ) f \left (t \right ) \end {array}\right ] \] |
1 |
0 |
3 |
system of linear ODEs |
✗ |
N/A |
0.032 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right )-z \left (t \right ) \\ y^{\prime }\left (t \right )=y \left (t \right )+z \left (t \right )-x \left (t \right ) \\ z^{\prime }\left (t \right )=x \left (t \right )-y \left (t \right )+z \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.855 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-3 x \left (t \right )+48 y \left (t \right )-28 z \left (t \right ) \\ y^{\prime }\left (t \right )=-4 x \left (t \right )+40 y \left (t \right )-22 z \left (t \right ) \\ z^{\prime }\left (t \right )=-6 x \left (t \right )+57 y \left (t \right )-31 z \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.529 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=6 x \left (t \right )-72 y \left (t \right )+44 z \left (t \right ) \\ y^{\prime }\left (t \right )=4 x \left (t \right )-4 y \left (t \right )+26 z \left (t \right ) \\ z^{\prime }\left (t \right )=6 x \left (t \right )-63 y \left (t \right )+38 z \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
23.843 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=a x \left (t \right )+g y \left (t \right )+\beta z \left (t \right ) \\ y^{\prime }\left (t \right )=g x \left (t \right )+b y \left (t \right )+\alpha z \left (t \right ) \\ z^{\prime }\left (t \right )=\beta x \left (t \right )+\alpha y \left (t \right )+c z \left (t \right ) \end {array}\right ] \] |
1 |
0 |
3 |
system of linear ODEs |
✗ |
N/A |
127.673 |
|
|
\[ {}\left [\begin {array}{c} t x^{\prime }\left (t \right )=2 x \left (t \right )-t \\ t^{3} y^{\prime }\left (t \right )=-x \left (t \right )+t^{2} y \left (t \right )+t \\ t^{4} z^{\prime }\left (t \right )=-x \left (t \right )-t^{2} y \left (t \right )+t^{3} z \left (t \right )+t \end {array}\right ] \] |
1 |
0 |
3 |
system of linear ODEs |
✗ |
N/A |
0.032 |
|
|
\[ {}\left [\begin {array}{c} a t x^{\prime }\left (t \right )=b c \left (y \left (t \right )-z \left (t \right )\right ) \\ b t y^{\prime }\left (t \right )=c a \left (-x \left (t \right )+z \left (t \right )\right ) \\ c t z^{\prime }\left (t \right )=a b \left (x \left (t \right )-y \left (t \right )\right ) \end {array}\right ] \] |
1 |
0 |
3 |
system of linear ODEs |
✗ |
N/A |
0.033 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=a x_{2} \left (t \right )+b x_{3} \left (t \right ) \cos \left (c t \right )+b x_{4} \left (t \right ) \sin \left (c t \right ) \\ x_{2}^{\prime }\left (t \right )=-a x_{1} \left (t \right )+b x_{3} \left (t \right ) \sin \left (c t \right )-b x_{4} \left (t \right ) \cos \left (c t \right ) \\ x_{3}^{\prime }\left (t \right )=-b x_{1} \left (t \right ) \cos \left (c t \right )-b x_{2} \left (t \right ) \sin \left (c t \right )+a x_{4} \left (t \right ) \\ x_{4}^{\prime }\left (t \right )=-b x_{1} \left (t \right ) \sin \left (c t \right )+b x_{2} \left (t \right ) \cos \left (c t \right )-a x_{3} \left (t \right ) \end {array}\right ] \] |
1 |
0 |
2 |
system of linear ODEs |
✗ |
N/A |
0.05 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-x \left (t \right ) \left (x \left (t \right )+y \left (t \right )\right ) \\ y^{\prime }\left (t \right )=y \left (t \right ) \left (x \left (t \right )+y \left (t \right )\right ) \end {array}\right ] \] |
1 |
0 |
2 |
system of linear ODEs |
✗ |
N/A |
0.436 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=\left (a y \left (t \right )+b \right ) x \left (t \right ) \\ y^{\prime }\left (t \right )=\left (c x \left (t \right )+d \right ) y \left (t \right ) \end {array}\right ] \] |
1 |
0 |
2 |
system of linear ODEs |
✗ |
N/A |
0.308 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right ) \left (a \left (p x \left (t \right )+q y \left (t \right )\right )+\alpha \right ) \\ y^{\prime }\left (t \right )=y \left (t \right ) \left (\beta +b \left (p x \left (t \right )+q y \left (t \right )\right )\right ) \end {array}\right ] \] |
1 |
0 |
2 |
system of linear ODEs |
✗ |
N/A |
0.303 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=h \left (a -x \left (t \right )\right ) \left (c -x \left (t \right )-y \left (t \right )\right ) \\ y^{\prime }\left (t \right )=k \left (b -y \left (t \right )\right ) \left (c -x \left (t \right )-y \left (t \right )\right ) \end {array}\right ] \] |
1 |
0 |
2 |
system of linear ODEs |
✗ |
N/A |
0.315 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=y \left (t \right )^{2}-\cos \left (x \left (t \right )\right ) \\ y^{\prime }\left (t \right )=-y \left (t \right ) \sin \left (x \left (t \right )\right ) \end {array}\right ] \] |
1 |
0 |
2 |
system of linear ODEs |
✗ |
N/A |
0.326 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-x \left (t \right ) y \left (t \right )^{2}+x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )^{2} y \left (t \right )-x \left (t \right )-y \left (t \right ) \end {array}\right ] \] |
1 |
0 |
2 |
system of linear ODEs |
✗ |
N/A |
0.315 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right )-x \left (t \right ) \left (x \left (t \right )^{2}+y \left (t \right )^{2}\right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )+y \left (t \right )-y \left (t \right ) \left (x \left (t \right )^{2}+y \left (t \right )^{2}\right ) \end {array}\right ] \] |
1 |
0 |
2 |
system of linear ODEs |
✗ |
N/A |
0.318 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-y \left (t \right )+x \left (t \right ) \left (x \left (t \right )^{2}+y \left (t \right )^{2}-1\right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right ) \left (x \left (t \right )^{2}+y \left (t \right )^{2}-1\right ) \end {array}\right ] \] |
1 |
0 |
2 |
system of linear ODEs |
✗ |
N/A |
0.316 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-y \left (t \right ) \left (x \left (t \right )^{2}+y \left (t \right )^{2}\right ) \\ y^{\prime }\left (t \right )=\left \{\begin {array}{cc} x \left (t \right )^{2}+y \left (t \right )^{2} & 2 x \left (t \right )\le x \left (t \right )^{2}+y \left (t \right )^{2} \\ \left (\frac {x \left (t \right )}{2}-\frac {y \left (t \right )^{2}}{2 x \left (t \right )}\right ) \left (x \left (t \right )^{2}+y \left (t \right )^{2}\right ) & \operatorname {otherwise} \end {array}\right . \end {array}\right ] \] |
1 |
0 |
0 |
system of linear ODEs |
✗ |
N/A |
0.34 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-y \left (t \right )+\left \{\begin {array}{cc} x \left (t \right ) \left (x \left (t \right )^{2}+y \left (t \right )^{2}-1\right ) \sin \left (\frac {1}{x \left (t \right )^{2}+y \left (t \right )^{2}}\right ) & x \left (t \right )^{2}+y \left (t \right )^{2}\neq 1 \\ 0 & \operatorname {otherwise} \end {array}\right . \\ y^{\prime }\left (t \right )=x \left (t \right )+\left \{\begin {array}{cc} y \left (t \right ) \left (x \left (t \right )^{2}+y \left (t \right )^{2}-1\right ) \sin \left (\frac {1}{x \left (t \right )^{2}+y \left (t \right )^{2}}\right ) & x \left (t \right )^{2}+y \left (t \right )^{2}\neq 1 \\ 0 & \operatorname {otherwise} \end {array}\right . \end {array}\right ] \] |
1 |
0 |
0 |
system of linear ODEs |
✗ |
N/A |
0.341 |
|
|
\[ {}\left [\begin {array}{c} \left (t^{2}+1\right ) x^{\prime }\left (t \right )=-x \left (t \right ) t +y \left (t \right ) \\ \left (t^{2}+1\right ) y^{\prime }\left (t \right )=-x \left (t \right )-t y \left (t \right ) \end {array}\right ] \] |
1 |
0 |
2 |
system of linear ODEs |
✗ |
N/A |
0.026 |
|
|
\[ {}\left [\begin {array}{c} \left (x \left (t \right )^{2}+y \left (t \right )^{2}-t^{2}\right ) x^{\prime }\left (t \right )=-2 x \left (t \right ) t \\ \left (x \left (t \right )^{2}+y \left (t \right )^{2}-t^{2}\right ) y^{\prime }\left (t \right )=-2 t y \left (t \right ) \end {array}\right ] \] |
1 |
0 |
2 |
system of linear ODEs |
✗ |
N/A |
0.311 |
|
|
\[ {}\left [\begin {array}{c} {x^{\prime }\left (t \right )}^{2}+t x^{\prime }\left (t \right )+a y^{\prime }\left (t \right )-x \left (t \right )=0 \\ x^{\prime }\left (t \right ) y^{\prime }\left (t \right )+t y^{\prime }\left (t \right )-y \left (t \right )=0 \end {array}\right ] \] |
1 |
0 |
3 |
system of linear ODEs |
✗ |
N/A |
0.364 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=y \left (t \right )-z \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )^{2}+y \left (t \right ) \\ z^{\prime }\left (t \right )=x \left (t \right )^{2}+z \left (t \right ) \end {array}\right ] \] |
1 |
0 |
3 |
system of linear ODEs |
✗ |
N/A |
0.481 |
|
|
\[ {}\left [\begin {array}{c} a x^{\prime }\left (t \right )=\left (b -c \right ) y \left (t \right ) z \left (t \right ) \\ b y^{\prime }\left (t \right )=\left (c -a \right ) z \left (t \right ) x \left (t \right ) \\ c z^{\prime }\left (t \right )=\left (-b +a \right ) x \left (t \right ) y \left (t \right ) \end {array}\right ] \] |
1 |
0 |
4 |
system of linear ODEs |
✗ |
N/A |
0.716 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right ) \left (y \left (t \right )-z \left (t \right )\right ) \\ y^{\prime }\left (t \right )=y \left (t \right ) \left (-x \left (t \right )+z \left (t \right )\right ) \\ z^{\prime }\left (t \right )=z \left (t \right ) \left (x \left (t \right )-y \left (t \right )\right ) \end {array}\right ] \] |
1 |
0 |
5 |
system of linear ODEs |
✗ |
N/A |
0.71 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )+y^{\prime }\left (t \right )=x \left (t \right ) y \left (t \right ) \\ y^{\prime }\left (t \right )+z^{\prime }\left (t \right )=y \left (t \right ) z \left (t \right ) \\ x^{\prime }\left (t \right )+z^{\prime }\left (t \right )=x \left (t \right ) z \left (t \right ) \end {array}\right ] \] |
1 |
0 |
3 |
system of linear ODEs |
✗ |
N/A |
0.678 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=\frac {x \left (t \right )^{2}}{2}-\frac {y \left (t \right )}{24} \\ y^{\prime }\left (t \right )=2 x \left (t \right ) y \left (t \right )-3 z \left (t \right ) \\ z^{\prime }\left (t \right )=3 x \left (t \right ) z \left (t \right )-\frac {y \left (t \right )^{2}}{6} \end {array}\right ] \] |
1 |
0 |
3 |
system of linear ODEs |
✗ |
N/A |
0.702 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right ) \left (y \left (t \right )^{2}-z \left (t \right )^{2}\right ) \\ y^{\prime }\left (t \right )=y \left (t \right ) \left (z \left (t \right )^{2}-x \left (t \right )^{2}\right ) \\ z^{\prime }\left (t \right )=z \left (t \right ) \left (x \left (t \right )^{2}-y \left (t \right )^{2}\right ) \end {array}\right ] \] |
1 |
0 |
8 |
system of linear ODEs |
✗ |
N/A |
0.713 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right ) \left (y \left (t \right )^{2}-z \left (t \right )^{2}\right ) \\ y^{\prime }\left (t \right )=-y \left (t \right ) \left (z \left (t \right )^{2}+x \left (t \right )^{2}\right ) \\ z^{\prime }\left (t \right )=z \left (t \right ) \left (x \left (t \right )^{2}+y \left (t \right )^{2}\right ) \end {array}\right ] \] |
1 |
0 |
5 |
system of linear ODEs |
✗ |
N/A |
0.704 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-x \left (t \right ) y \left (t \right )^{2}+x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )^{2} y \left (t \right )-x \left (t \right )-y \left (t \right ) \\ z^{\prime }\left (t \right )=y \left (t \right )^{2}-x \left (t \right )^{2} \end {array}\right ] \] |
1 |
0 |
2 |
system of linear ODEs |
✗ |
N/A |
0.71 |
|
|
\[ {}\left [\begin {array}{c} \left (x \left (t \right )-y \left (t \right )\right ) \left (x \left (t \right )-z \left (t \right )\right ) x^{\prime }\left (t \right )=f \left (t \right ) \\ \left (-x \left (t \right )+y \left (t \right )\right ) \left (y \left (t \right )-z \left (t \right )\right ) y^{\prime }\left (t \right )=f \left (t \right ) \\ \left (-x \left (t \right )+z \left (t \right )\right ) \left (-y \left (t \right )+z \left (t \right )\right ) z^{\prime }\left (t \right )=f \left (t \right ) \end {array}\right ] \] |
1 |
0 |
3 |
system of linear ODEs |
✗ |
N/A |
0.708 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right ) \sin \left (x_{2} \left (t \right )\right )=x_{4} \left (t \right ) \sin \left (x_{3} \left (t \right )\right )+x_{5} \left (t \right ) \cos \left (x_{3} \left (t \right )\right ) \\ x_{2}^{\prime }\left (t \right )=x_{4} \left (t \right ) \cos \left (x_{3} \left (t \right )\right )-x_{5} \left (t \right ) \sin \left (x_{3} \left (t \right )\right ) \\ x_{3}^{\prime }\left (t \right )+x_{1}^{\prime }\left (t \right ) \cos \left (x_{2} \left (t \right )\right )=a \\ x_{4}^{\prime }\left (t \right )-\left (1-\lambda \right ) a x_{5} \left (t \right )=-m \sin \left (x_{2} \left (t \right )\right ) \cos \left (x_{3} \left (t \right )\right ) \\ x_{5}^{\prime }\left (t \right )+\left (1-\lambda \right ) a x_{4} \left (t \right )=m \sin \left (x_{2} \left (t \right )\right ) \sin \left (x_{3} \left (t \right )\right ) \end {array}\right ] \] |
1 |
0 |
0 |
system of linear ODEs |
✗ |
N/A |
1.958 |
|
|
\[ {}\left [\begin {array}{c} 3 x^{\prime }\left (t \right )+3 x \left (t \right )+2 y \left (t \right )={\mathrm e}^{t} \\ 4 x \left (t \right )-3 y^{\prime }\left (t \right )+3 y \left (t \right )=3 t \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.904 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-3 y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.557 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=-4 x \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.459 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-3 x \left (t \right ) \\ y^{\prime }\left (t \right )=2 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.271 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=4 y \left (t \right ) \\ y^{\prime }\left (t \right )=2 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.308 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+2 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.297 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )-y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.471 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+2 y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.359 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-x \left (t \right )-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )-y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.488 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-2 x \left (t \right )-3 y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )+4 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.585 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-3 y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right )+y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.393 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-2 x \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.296 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-2 x \left (t \right )-y \left (t \right ) \\ y^{\prime }\left (t \right )=-4 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.329 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right )+4 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.369 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-6 y \left (t \right ) \\ y^{\prime }\left (t \right )=6 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.3 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )+3 y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )-14 \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
2.5 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 y \left (t \right )-3 x \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+2 y \left (t \right )-1 \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
1.289 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=-3 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.324 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right ) \\ y^{\prime }\left (t \right )=3 x \left (t \right )-4 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.327 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )-2 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.533 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=3 y \left (t \right )-3 x \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.98 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=3 x \left (t \right )-4 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.368 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=5 x \left (t \right )-y \left (t \right ) \\ y^{\prime }\left (t \right )=3 x \left (t \right )+y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.342 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+2 y \left (t \right ) \\ y^{\prime }\left (t \right )=3 x \left (t \right )+2 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.375 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )+2 y \left (t \right ) \\ y^{\prime }\left (t \right )=6 x \left (t \right )+3 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.396 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-5 x \left (t \right )+3 y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )-10 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.393 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right ) \\ y^{\prime }\left (t \right )=2 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.276 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right )-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=4 x \left (t \right )-y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.563 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=9 y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.471 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right )+4 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.347 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-5 x \left (t \right )+3 y \left (t \right )+{\mathrm e}^{-t} \\ y^{\prime }\left (t \right )=2 x \left (t \right )-10 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.699 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )+\cos \left (t w \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
1.711 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right )+2 y \left (t \right )+3 \\ y^{\prime }\left (t \right )=7 x \left (t \right )+5 y \left (t \right )+2 t \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
1.359 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-2 x \left (t \right )-4 y \left (t \right )={\mathrm e}^{t} \\ x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-y \left (t \right )={\mathrm e}^{4 t} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.43 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )=-2 t \\ x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-3 x \left (t \right )-y \left (t \right )=t^{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.462 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )-3 y \left (t \right )={\mathrm e}^{t} \\ x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+x \left (t \right )={\mathrm e}^{3 t} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.526 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )-2 y \left (t \right )=2 \,{\mathrm e}^{t} \\ x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-3 x \left (t \right )-4 y \left (t \right )={\mathrm e}^{2 t} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.21 |
|
|
\[ {}\left [\begin {array}{c} 2 x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )-y \left (t \right )={\mathrm e}^{-t} \\ x^{\prime }\left (t \right )+2 x \left (t \right )+y^{\prime }\left (t \right )+y \left (t \right )={\mathrm e}^{t} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
1.411 |
|
|
\[ {}\left [\begin {array}{c} 2 x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-3 x \left (t \right )-y \left (t \right )=t \\ x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-4 x \left (t \right )-y \left (t \right )={\mathrm e}^{t} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.979 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )-6 y \left (t \right )={\mathrm e}^{3 t} \\ x^{\prime }\left (t \right )+2 y^{\prime }\left (t \right )-2 x \left (t \right )-6 y \left (t \right )=t \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
1.345 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )-3 y \left (t \right )=3 t \\ x^{\prime }\left (t \right )+2 y^{\prime }\left (t \right )-2 x \left (t \right )-3 y \left (t \right )=1 \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
1.229 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+2 y \left (t \right )=\sin \left (t \right ) \\ x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )-y \left (t \right )=0 \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.807 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )-y^{\prime }\left (t \right )-2 x \left (t \right )+4 y \left (t \right )=t \\ x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )-y \left (t \right )=1 \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
1.054 |
|
|
\[ {}\left [\begin {array}{c} 2 x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+x \left (t \right )+5 y \left (t \right )=4 t \\ x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+2 x \left (t \right )+2 y \left (t \right )=2 \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.969 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )+5 y \left (t \right )=t^{2} \\ x^{\prime }\left (t \right )+2 y^{\prime }\left (t \right )-2 x \left (t \right )+4 y \left (t \right )=1+2 t \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
3.727 |
|
|
\[ {}\left [\begin {array}{c} 2 x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+x \left (t \right )+y \left (t \right )=t^{2}+4 t \\ x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+2 x \left (t \right )+2 y \left (t \right )=2 t^{2}-2 t \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
1.026 |
|
|
\[ {}\left [\begin {array}{c} 3 x^{\prime }\left (t \right )+2 y^{\prime }\left (t \right )-x \left (t \right )+y \left (t \right )=-1+t \\ x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )=2+t \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
1.704 |
|
|
\[ {}\left [\begin {array}{c} 2 x^{\prime }\left (t \right )+4 y^{\prime }\left (t \right )+x \left (t \right )-y \left (t \right )=3 \,{\mathrm e}^{t} \\ x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+2 x \left (t \right )+2 y \left (t \right )={\mathrm e}^{t} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
1.049 |
|
|
\[ {}\left [\begin {array}{c} 2 x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )-y \left (t \right )=-2 t \\ x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+x \left (t \right )-y \left (t \right )=t^{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.976 |
|
|
\[ {}\left [\begin {array}{c} 2 x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )-y \left (t \right )=1 \\ x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+2 x \left (t \right )-y \left (t \right )=t \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.957 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right )+4 y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )+y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.393 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=5 x \left (t \right )+3 y \left (t \right ) \\ y^{\prime }\left (t \right )=4 x \left (t \right )+y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.423 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=5 x \left (t \right )+2 y \left (t \right )+5 t \\ y^{\prime }\left (t \right )=3 x \left (t \right )+4 y \left (t \right )+17 t \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
1.084 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=5 x \left (t \right )-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=4 x \left (t \right )-y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.416 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=5 x \left (t \right )-y \left (t \right ) \\ y^{\prime }\left (t \right )=3 x \left (t \right )+y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.416 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-2 x \left (t \right )+7 y \left (t \right ) \\ y^{\prime }\left (t \right )=3 x \left (t \right )+2 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.392 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-2 x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=7 x \left (t \right )+4 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.469 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right )-z \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )+3 y \left (t \right )-4 z \left (t \right ) \\ z^{\prime }\left (t \right )=4 x \left (t \right )+y \left (t \right )-4 z \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.762 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )-y \left (t \right )-z \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+3 y \left (t \right )+z \left (t \right ) \\ z^{\prime }\left (t \right )=-3 x \left (t \right )-6 y \left (t \right )+6 z \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.722 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=4 x \left (t \right )-y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )+y \left (t \right )+t^{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.843 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )-4 y \left (t \right )+\cos \left (2 t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
1.29 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )+2 y \left (t \right ) \\ y^{\prime }\left (t \right )=6 x \left (t \right )+3 y \left (t \right )+{\mathrm e}^{t} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.815 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )+5 y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right )+\cos \left (3 t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
1.639 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right )+{\mathrm e}^{-t} \\ y^{\prime }\left (t \right )=4 x \left (t \right )-2 y \left (t \right )+{\mathrm e}^{2 t} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
1.054 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=8 x \left (t \right )+14 y \left (t \right ) \\ y^{\prime }\left (t \right )=7 x \left (t \right )+y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.451 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=8 x \left (t \right )+14 y \left (t \right ) \\ y^{\prime }\left (t \right )=7 x \left (t \right )+y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.428 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right ) \\ y^{\prime }\left (t \right )=-5 x \left (t \right )-3 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.363 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=11 x \left (t \right )-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=3 x \left (t \right )+4 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.445 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+20 y \left (t \right ) \\ y^{\prime }\left (t \right )=40 x \left (t \right )-19 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.45 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-2 x \left (t \right )+2 y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )-y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.407 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )-y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
1.425 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-2 x \left (t \right )+3 y \left (t \right ) \\ y^{\prime }\left (t \right )=-6 x \left (t \right )+4 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.66 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-11 x \left (t \right )-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=13 x \left (t \right )-9 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.72 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=7 x \left (t \right )-5 y \left (t \right ) \\ y^{\prime }\left (t \right )=10 x \left (t \right )-3 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.666 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=13 x \left (t \right ) \\ y^{\prime }\left (t \right )=13 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.308 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.246 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )+5 x \left (t \right )+y \left (t \right )={\mathrm e}^{t} \\ y^{\prime }\left (t \right )-x \left (t \right )-3 y \left (t \right )={\mathrm e}^{2 t} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
1.343 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=y \left (t \right ) \\ y^{\prime }\left (t \right )=z \left (t \right ) \\ z^{\prime }\left (t \right )=x \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
1.012 |
|
|
|
||||||||
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=y \left (t \right ) \\ y^{\prime }\left (t \right )=\frac {y \left (t \right )^{2}}{x \left (t \right )} \end {array}\right ] \] |
1 |
0 |
2 |
system of linear ODEs |
✗ |
N/A |
0.253 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=3 x \left (t \right )-4 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.272 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=\frac {5 x \left (t \right )}{4}+\frac {3 y \left (t \right )}{4} \\ y^{\prime }\left (t \right )=\frac {x \left (t \right )}{2}-\frac {3 y \left (t \right )}{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.433 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )-x \left (t \right )+2 y \left (t \right )=0 \\ y^{\prime }\left (t \right )+y \left (t \right )-x \left (t \right )=0 \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.327 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )+5 x \left (t \right )-2 y \left (t \right )=0 \\ y^{\prime }\left (t \right )+2 x \left (t \right )-y \left (t \right )=0 \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.43 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )-3 x \left (t \right )+2 y \left (t \right )=0 \\ y^{\prime }\left (t \right )-x \left (t \right )+3 y \left (t \right )=0 \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.405 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-\frac {x \left (t \right )}{2}+2 y \left (t \right )-3 z \left (t \right ) \\ y^{\prime }\left (t \right )=y \left (t \right )-\frac {z \left (t \right )}{2} \\ z^{\prime }\left (t \right )=-2 x \left (t \right )+z \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.865 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )+y^{\prime }\left (t \right )=y \left (t \right ) \\ x^{\prime }\left (t \right )-y^{\prime }\left (t \right )=x \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.333 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )+2 y^{\prime }\left (t \right )=t \\ x^{\prime }\left (t \right )-y^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.685 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )-y^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right )-t \\ 2 x^{\prime }\left (t \right )+3 y^{\prime }\left (t \right )=2 x \left (t \right )+6 \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.708 |
|
|
\[ {}\left [\begin {array}{c} 2 x^{\prime }\left (t \right )-y^{\prime }\left (t \right )=t \\ 3 x^{\prime }\left (t \right )+2 y^{\prime }\left (t \right )=y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.636 |
|
|
\[ {}\left [\begin {array}{c} 5 x^{\prime }\left (t \right )-3 y^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right ) \\ 3 x^{\prime }\left (t \right )-y^{\prime }\left (t \right )=t \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.704 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )-4 y^{\prime }\left (t \right )=0 \\ 2 x^{\prime }\left (t \right )-3 y^{\prime }\left (t \right )=t +y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.625 |
|
|
\[ {}\left [\begin {array}{c} 3 x^{\prime }\left (t \right )+2 y^{\prime }\left (t \right )=\sin \left (t \right ) \\ x^{\prime }\left (t \right )-2 y^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right )+t \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.893 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-4 x \left (t \right )+9 y \left (t \right )+12 \,{\mathrm e}^{-t} \\ y^{\prime }\left (t \right )=-5 x \left (t \right )+2 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.824 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-7 x \left (t \right )+6 y \left (t \right )+6 \,{\mathrm e}^{-t} \\ y^{\prime }\left (t \right )=-12 x \left (t \right )+5 y \left (t \right )+37 \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
1.575 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-7 x \left (t \right )+10 y \left (t \right )+18 \,{\mathrm e}^{t} \\ y^{\prime }\left (t \right )=-10 x \left (t \right )+9 y \left (t \right )+37 \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
2.152 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-14 x \left (t \right )+39 y \left (t \right )+78 \sinh \left (t \right ) \\ y^{\prime }\left (t \right )=-6 x \left (t \right )+16 y \left (t \right )+6 \cosh \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
2.599 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )+4 y \left (t \right )-2 z \left (t \right )-2 \sinh \left (t \right ) \\ y^{\prime }\left (t \right )=4 x \left (t \right )+2 y \left (t \right )-2 z \left (t \right )+10 \cosh \left (t \right ) \\ z^{\prime }\left (t \right )=-x \left (t \right )+3 y \left (t \right )+z \left (t \right )+5 \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
10.472 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )+6 y \left (t \right )-2 z \left (t \right )+50 \,{\mathrm e}^{t} \\ y^{\prime }\left (t \right )=6 x \left (t \right )+2 y \left (t \right )-2 z \left (t \right )+21 \,{\mathrm e}^{-t} \\ z^{\prime }\left (t \right )=-x \left (t \right )+6 y \left (t \right )+z \left (t \right )+9 \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
1.638 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-2 x \left (t \right )-2 y \left (t \right )+4 z \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right )+y \left (t \right )+2 z \left (t \right ) \\ z^{\prime }\left (t \right )=-4 x \left (t \right )-2 y \left (t \right )+6 z \left (t \right )+{\mathrm e}^{2 t} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
1.344 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right )-2 y \left (t \right )+24 \sin \left (t \right ) \\ y^{\prime }\left (t \right )=9 x \left (t \right )-3 y \left (t \right )+12 \cos \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
1.343 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=7 x \left (t \right )-4 y \left (t \right )+10 \,{\mathrm e}^{t} \\ y^{\prime }\left (t \right )=3 x \left (t \right )+14 y \left (t \right )+6 \,{\mathrm e}^{2 t} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.618 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-7 x \left (t \right )+4 y \left (t \right )+6 \,{\mathrm e}^{3 t} \\ y^{\prime }\left (t \right )=-5 x \left (t \right )+2 y \left (t \right )+6 \,{\mathrm e}^{2 t} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.687 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-3 x \left (t \right )-3 y \left (t \right )+z \left (t \right ) \\ y^{\prime }\left (t \right )=2 y \left (t \right )+2 z \left (t \right )+29 \,{\mathrm e}^{-t} \\ z^{\prime }\left (t \right )=5 x \left (t \right )+y \left (t \right )+z \left (t \right )+39 \,{\mathrm e}^{t} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
31.909 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )+y \left (t \right )-z \left (t \right )+5 \sin \left (t \right ) \\ y^{\prime }\left (t \right )=y \left (t \right )+z \left (t \right )-10 \cos \left (t \right ) \\ z^{\prime }\left (t \right )=x \left (t \right )+z \left (t \right )+2 \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
1.967 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-3 x \left (t \right )+3 y \left (t \right )+z \left (t \right )+5 \sin \left (2 t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )-5 y \left (t \right )-3 z \left (t \right )+5 \cos \left (2 t \right ) \\ z^{\prime }\left (t \right )=-3 x \left (t \right )+7 y \left (t \right )+3 z \left (t \right )+23 \,{\mathrm e}^{t} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
2.759 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-3 x \left (t \right )+y \left (t \right )-3 z \left (t \right )+2 \,{\mathrm e}^{t} \\ y^{\prime }\left (t \right )=4 x \left (t \right )-y \left (t \right )+2 z \left (t \right )+4 \,{\mathrm e}^{t} \\ z^{\prime }\left (t \right )=4 x \left (t \right )-2 y \left (t \right )+3 z \left (t \right )+4 \,{\mathrm e}^{t} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
1.853 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+5 y \left (t \right )+10 \sinh \left (t \right ) \\ y^{\prime }\left (t \right )=19 x \left (t \right )-13 y \left (t \right )+24 \sinh \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
29.035 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=9 x \left (t \right )-3 y \left (t \right )-6 t \\ y^{\prime }\left (t \right )=-x \left (t \right )+11 y \left (t \right )+10 t \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.793 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=y \left (t \right )+1 \\ y^{\prime }\left (t \right )=1+x \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.499 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )-y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.275 |
|
|
\[ {}\left [\begin {array}{c} 4 x^{\prime }\left (t \right )-y^{\prime }\left (t \right )+3 x \left (t \right )=\sin \left (t \right ) \\ x^{\prime }\left (t \right )+y \left (t \right )=\cos \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.961 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )-3 y \left (t \right ) \\ y^{\prime }\left (t \right )=5 x \left (t \right )+6 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.704 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-4 x \left (t \right )-10 y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )-2 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.426 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )-5 y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )-y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.38 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )-2 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.441 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-4 x \left (t \right )+2 y \left (t \right ) \\ y^{\prime }\left (t \right )=3 x \left (t \right )-2 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.448 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+2 y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )+2 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.432 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=4 x \left (t \right )-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=3 x \left (t \right )-y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.287 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )+y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.66 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )-y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )-2 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.262 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )-3 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.255 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+3 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.242 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )-4 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.428 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right ) \\ y^{\prime }\left (t \right )=y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.218 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )-5 y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )-y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.387 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )=2 y_{1} \left (x \right )-3 y_{2} \left (x \right ) \\ y_{2}^{\prime }\left (x \right )=y_{1} \left (x \right )-2 y_{2} \left (x \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.328 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )=y_{1} \left (x \right )-2 y_{2} \left (x \right ) \\ y_{2}^{\prime }\left (x \right )=y_{1} \left (x \right )+3 y_{2} \left (x \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.47 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )=y_{1} \left (x \right )+2 y_{2} \left (x \right )+x -1 \\ y_{2}^{\prime }\left (x \right )=3 y_{1} \left (x \right )+2 y_{2} \left (x \right )-5 x -2 \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.6 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )=\frac {2 y_{1} \left (x \right )}{x}-\frac {y_{2} \left (x \right )}{x^{2}}-3+\frac {1}{x}-\frac {1}{x^{2}} \\ y_{2}^{\prime }\left (x \right )=2 y_{1} \left (x \right )+1-6 x \end {array}\right ] \] |
1 |
0 |
2 |
system of linear ODEs |
✗ |
N/A |
0.026 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )=\frac {5 y_{1} \left (x \right )}{x}+\frac {4 y_{2} \left (x \right )}{x}-2 x \\ y_{2}^{\prime }\left (x \right )=-\frac {6 y_{1} \left (x \right )}{x}-\frac {5 y_{2} \left (x \right )}{x}+5 x \end {array}\right ] \] |
1 |
0 |
2 |
system of linear ODEs |
✗ |
N/A |
0.029 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )=3 y_{1} \left (x \right )-2 y_{2} \left (x \right ) \\ y_{2}^{\prime }\left (x \right )=-y_{1} \left (x \right )+y_{2} \left (x \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.642 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )=\sin \left (x \right ) y_{1} \left (x \right )+\sqrt {x}\, y_{2} \left (x \right )+\ln \left (x \right ) \\ y_{2}^{\prime }\left (x \right )=\tan \left (x \right ) y_{1} \left (x \right )-{\mathrm e}^{x} y_{2} \left (x \right )+1 \end {array}\right ] \] |
1 |
0 |
0 |
system of linear ODEs |
✗ |
N/A |
0.028 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )=\sin \left (x \right ) y_{1} \left (x \right )+\sqrt {x}\, y_{2} \left (x \right )+\ln \left (x \right ) \\ y_{2}^{\prime }\left (x \right )=\tan \left (x \right ) y_{1} \left (x \right )-{\mathrm e}^{x} y_{2} \left (x \right )+1 \end {array}\right ] \] |
1 |
0 |
0 |
system of linear ODEs |
✗ |
N/A |
0.026 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )={\mathrm e}^{-x} y_{1} \left (x \right )-\sqrt {1+x}\, y_{2} \left (x \right )+x^{2} \\ y_{2}^{\prime }\left (x \right )=\frac {y_{1} \left (x \right )}{\left (-2+x \right )^{2}} \end {array}\right ] \] |
1 |
0 |
0 |
system of linear ODEs |
✗ |
N/A |
0.027 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )={\mathrm e}^{-x} y_{1} \left (x \right )-\sqrt {1+x}\, y_{2} \left (x \right )+x^{2} \\ y_{2}^{\prime }\left (x \right )=\frac {y_{1} \left (x \right )}{\left (-2+x \right )^{2}} \end {array}\right ] \] |
1 |
0 |
0 |
system of linear ODEs |
✗ |
N/A |
0.03 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )=2 y_{1} \left (x \right )-3 y_{2} \left (x \right )+5 \,{\mathrm e}^{x} \\ y_{2}^{\prime }\left (x \right )=y_{1} \left (x \right )+4 y_{2} \left (x \right )-2 \,{\mathrm e}^{-x} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
2.425 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )=y_{2} \left (x \right )-2 y_{1} \left (x \right )+\sin \left (2 x \right ) \\ y_{2}^{\prime }\left (x \right )=-3 y_{1} \left (x \right )+y_{2} \left (x \right )-2 \cos \left (3 x \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
6.501 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )=2 y_{2} \left (x \right ) \\ y_{2}^{\prime }\left (x \right )=3 y_{1} \left (x \right ) \\ y_{3}^{\prime }\left (x \right )=2 y_{3} \left (x \right )-y_{1} \left (x \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.733 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )=2 x y_{1} \left (x \right )-x^{2} y_{2} \left (x \right )+4 x \\ y_{2}^{\prime }\left (x \right )={\mathrm e}^{x} y_{1} \left (x \right )+3 \,{\mathrm e}^{-x} y_{2} \left (x \right )-\cos \left (3 x \right ) \end {array}\right ] \] |
1 |
0 |
2 |
system of linear ODEs |
✗ |
N/A |
0.03 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )=2 y_{1} \left (x \right )-3 y_{2} \left (x \right ) \\ y_{2}^{\prime }\left (x \right )=y_{1} \left (x \right )-2 y_{2} \left (x \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.307 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )=2 y_{1} \left (x \right )-3 y_{2} \left (x \right )+4 x -2 \\ y_{2}^{\prime }\left (x \right )=y_{1} \left (x \right )-2 y_{2} \left (x \right )+3 x \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.758 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )=\frac {5 y_{1} \left (x \right )}{x}+\frac {4 y_{2} \left (x \right )}{x} \\ y_{2}^{\prime }\left (x \right )=-\frac {6 y_{1} \left (x \right )}{x}-\frac {5 y_{2} \left (x \right )}{x} \end {array}\right ] \] |
1 |
0 |
2 |
system of linear ODEs |
✗ |
N/A |
0.025 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )=\frac {5 y_{1} \left (x \right )}{x}+\frac {4 y_{2} \left (x \right )}{x}-2 x \\ y_{2}^{\prime }\left (x \right )=-\frac {6 y_{1} \left (x \right )}{x}-\frac {5 y_{2} \left (x \right )}{x}+5 x \end {array}\right ] \] |
1 |
0 |
2 |
system of linear ODEs |
✗ |
N/A |
0.026 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )=2 y_{1} \left (x \right )+y_{2} \left (x \right )-2 y_{3} \left (x \right ) \\ y_{2}^{\prime }\left (x \right )=3 y_{2} \left (x \right )-2 y_{3} \left (x \right ) \\ y_{3}^{\prime }\left (x \right )=3 y_{1} \left (x \right )+y_{2} \left (x \right )-3 y_{3} \left (x \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.497 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )=5 y_{1} \left (x \right )-5 y_{2} \left (x \right )-5 y_{3} \left (x \right ) \\ y_{2}^{\prime }\left (x \right )=-y_{1} \left (x \right )+4 y_{2} \left (x \right )+2 y_{3} \left (x \right ) \\ y_{3}^{\prime }\left (x \right )=3 y_{1} \left (x \right )-5 y_{2} \left (x \right )-3 y_{3} \left (x \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.776 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )=4 y_{1} \left (x \right )+6 y_{2} \left (x \right )+6 y_{3} \left (x \right ) \\ y_{2}^{\prime }\left (x \right )=y_{1} \left (x \right )+3 y_{2} \left (x \right )+2 y_{3} \left (x \right ) \\ y_{3}^{\prime }\left (x \right )=-y_{1} \left (x \right )-4 y_{2} \left (x \right )-3 y_{3} \left (x \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.554 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )=y_{1} \left (x \right )+2 y_{2} \left (x \right )-3 y_{3} \left (x \right ) \\ y_{2}^{\prime }\left (x \right )=-3 y_{1} \left (x \right )+4 y_{2} \left (x \right )-2 y_{3} \left (x \right ) \\ y_{3}^{\prime }\left (x \right )=2 y_{1} \left (x \right )+y_{3} \left (x \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.921 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )=-2 y_{1} \left (x \right )-y_{2} \left (x \right )+y_{3} \left (x \right ) \\ y_{2}^{\prime }\left (x \right )=-y_{1} \left (x \right )-2 y_{2} \left (x \right )-y_{3} \left (x \right ) \\ y_{3}^{\prime }\left (x \right )=y_{1} \left (x \right )-y_{2} \left (x \right )-2 y_{3} \left (x \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.466 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )=y_{1} \left (x \right )+y_{2} \left (x \right )+2 y_{3} \left (x \right ) \\ y_{2}^{\prime }\left (x \right )=y_{1} \left (x \right )+y_{2} \left (x \right )+2 y_{3} \left (x \right ) \\ y_{3}^{\prime }\left (x \right )=2 y_{1} \left (x \right )+2 y_{2} \left (x \right )+4 y_{3} \left (x \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.419 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )=2 y_{1} \left (x \right )+y_{2} \left (x \right ) \\ y_{2}^{\prime }\left (x \right )=-y_{1} \left (x \right )+2 y_{2} \left (x \right ) \\ y_{3}^{\prime }\left (x \right )=3 y_{3} \left (x \right )-4 y_{4} \left (x \right ) \\ y_{4}^{\prime }\left (x \right )=4 y_{3} \left (x \right )+3 y_{4} \left (x \right ) \end {array}\right ] \] |
1 |
1 |
4 |
system of linear ODEs |
✓ |
✓ |
0.944 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )=y_{2} \left (x \right ) \\ y_{2}^{\prime }\left (x \right )=-3 y_{1} \left (x \right )+2 y_{3} \left (x \right ) \\ y_{3}^{\prime }\left (x \right )=y_{4} \left (x \right ) \\ y_{4}^{\prime }\left (x \right )=2 y_{1} \left (x \right )-5 y_{3} \left (x \right ) \end {array}\right ] \] |
1 |
1 |
4 |
system of linear ODEs |
✓ |
✓ |
4.61 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )=3 y_{1} \left (x \right )+2 y_{2} \left (x \right ) \\ y_{2}^{\prime }\left (x \right )=-2 y_{1} \left (x \right )+3 y_{2} \left (x \right ) \\ y_{3}^{\prime }\left (x \right )=y_{3} \left (x \right ) \\ y_{4}^{\prime }\left (x \right )=2 y_{4} \left (x \right ) \end {array}\right ] \] |
1 |
1 |
4 |
system of linear ODEs |
✓ |
✓ |
0.71 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )=y_{2} \left (x \right )+y_{4} \left (x \right ) \\ y_{2}^{\prime }\left (x \right )=y_{1} \left (x \right )-y_{3} \left (x \right ) \\ y_{3}^{\prime }\left (x \right )=y_{4} \left (x \right ) \\ y_{4}^{\prime }\left (x \right )=y_{3} \left (x \right ) \end {array}\right ] \] |
1 |
1 |
4 |
system of linear ODEs |
✓ |
✓ |
0.611 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-2 x \left (t \right )+3 y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )+2 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.319 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-x \left (t \right )-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )-3 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.873 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-x \left (t \right )-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=5 x \left (t \right )+y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.493 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-x \left (t \right )+2 y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right )-y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.454 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )+y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.426 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-5 x \left (t \right )-y \left (t \right )+2 \\ y^{\prime }\left (t \right )=3 x \left (t \right )-y \left (t \right )-3 \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.754 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right )-2 y \left (t \right )-6 \\ y^{\prime }\left (t \right )=4 x \left (t \right )-y \left (t \right )+2 \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
1.625 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )-y \left (t \right ) \\ y^{\prime }\left (t \right )=0 \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.503 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-x \left (t \right )+2 y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )-y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.563 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.87 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 y \left (t \right ) \\ y^{\prime }\left (t \right )=3 \pi y \left (t \right )-\frac {x \left (t \right )}{3} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
1.186 |
|
|
\[ {}\left [\begin {array}{c} p^{\prime }\left (t \right )=3 p \left (t \right )-2 q \left (t \right )-7 r \left (t \right ) \\ q^{\prime }\left (t \right )=-2 p \left (t \right )+6 r \left (t \right ) \\ r^{\prime }\left (t \right )=\frac {73 q \left (t \right )}{100}+2 r \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
99.342 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-3 x \left (t \right )+2 \pi y \left (t \right ) \\ y^{\prime }\left (t \right )=4 x \left (t \right )-y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
1.168 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=\beta y \left (t \right ) \\ y^{\prime }\left (t \right )=\gamma x \left (t \right )-y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.895 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.556 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-2 x \left (t \right )-y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )-5 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.583 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-2 x \left (t \right )-3 y \left (t \right ) \\ y^{\prime }\left (t \right )=3 x \left (t \right )-2 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.656 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )+3 y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.556 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right ) \\ y^{\prime }\left (t \right )=-2 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.435 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-4 x \left (t \right )-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )-3 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.615 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-5 x \left (t \right )-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )-4 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.62 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=5 x \left (t \right )+4 y \left (t \right ) \\ y^{\prime }\left (t \right )=9 x \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.654 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right )+4 y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.605 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )-y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )+y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.829 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.771 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-x \left (t \right )-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )-4 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.605 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-2 x \left (t \right )-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right )+y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.667 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-2 x \left (t \right )-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right )+y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.595 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-2 x \left (t \right )-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right )+y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.534 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )-2 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.509 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )-2 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.471 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )-2 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.525 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-4 x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )-3 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.565 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-4 x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )-3 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.559 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-4 x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )-3 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.513 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=4 x \left (t \right )-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.546 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=4 x \left (t \right )-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.467 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=4 x \left (t \right )-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.522 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.575 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )+2 y \left (t \right ) \\ y^{\prime }\left (t \right )=-4 x \left (t \right )+6 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.708 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-3 x \left (t \right )-5 y \left (t \right ) \\ y^{\prime }\left (t \right )=3 x \left (t \right )+y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
1.311 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right )-y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
1.381 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )-6 y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )+y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
1.375 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+4 y \left (t \right ) \\ y^{\prime }\left (t \right )=-3 x \left (t \right )+2 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.855 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.562 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )+2 y \left (t \right ) \\ y^{\prime }\left (t \right )=-4 x \left (t \right )+6 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.626 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-3 x \left (t \right )-5 y \left (t \right ) \\ y^{\prime }\left (t \right )=3 x \left (t \right )+y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.742 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right )-y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.76 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )-6 y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )+y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.741 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+4 y \left (t \right ) \\ y^{\prime }\left (t \right )=-3 x \left (t \right )+2 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.732 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-\frac {9 x \left (t \right )}{10}-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+\frac {11 y \left (t \right )}{10} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.708 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-3 x \left (t \right )+10 y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )+3 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.776 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )-2 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.933 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 y \left (t \right ) \\ y^{\prime }\left (t \right )=-y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.437 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )+4 y \left (t \right ) \\ y^{\prime }\left (t \right )=3 x \left (t \right )+6 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.518 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=4 x \left (t \right )+2 y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )+y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.499 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=\frac {y \left (t \right )}{10} \\ y^{\prime }\left (t \right )=\frac {z \left (t \right )}{5} \\ z^{\prime }\left (t \right )=\frac {2 x \left (t \right )}{5} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
2.663 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right ) \\ z^{\prime }\left (t \right )=2 z \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.908 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-2 x \left (t \right )+3 y \left (t \right ) \\ y^{\prime }\left (t \right )=3 x \left (t \right )-2 y \left (t \right ) \\ z^{\prime }\left (t \right )=-z \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.783 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+3 z \left (t \right ) \\ y^{\prime }\left (t \right )=-y \left (t \right ) \\ z^{\prime }\left (t \right )=-3 x \left (t \right )+z \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.997 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right ) \\ y^{\prime }\left (t \right )=2 y \left (t \right )-z \left (t \right ) \\ z^{\prime }\left (t \right )=-y \left (t \right )+2 z \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.53 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-x \left (t \right )+2 y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )-4 y \left (t \right ) \\ z^{\prime }\left (t \right )=-z \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.754 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-x \left (t \right )+2 y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )-4 y \left (t \right ) \\ z^{\prime }\left (t \right )=0 \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.657 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )-y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 y \left (t \right )+3 z \left (t \right ) \\ z^{\prime }\left (t \right )=-x \left (t \right )+3 y \left (t \right )-z \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
1.845 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-4 x \left (t \right )+3 y \left (t \right ) \\ y^{\prime }\left (t \right )=-y \left (t \right )+z \left (t \right ) \\ z^{\prime }\left (t \right )=5 x \left (t \right )-5 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
1.633 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-10 x \left (t \right )+10 y \left (t \right ) \\ y^{\prime }\left (t \right )=28 x \left (t \right )-y \left (t \right ) \\ z^{\prime }\left (t \right )=-\frac {8 z \left (t \right )}{3} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
1.366 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-y \left (t \right )+z \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )+z \left (t \right ) \\ z^{\prime }\left (t \right )=z \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.792 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right ) \\ y^{\prime }\left (t \right )=-2 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.433 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=0 \\ y^{\prime }\left (t \right )=x \left (t \right )-y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.46 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=\pi ^{2} x \left (t \right )+\frac {187 y \left (t \right )}{5} \\ y^{\prime }\left (t \right )=\sqrt {555}\, x \left (t \right )+\frac {400617 y \left (t \right )}{5000} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
1.509 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right )-y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.754 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-3 x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )+y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.854 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-3 x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.878 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right )+y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.735 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )-y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.3 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.468 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-3 x \left (t \right )-3 y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )+y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.933 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 y \left (t \right ) \\ y^{\prime }\left (t \right )=1-2 x \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
1.827 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=4 x \left (t \right )-3 y \left (t \right ) \\ y^{\prime }\left (t \right )=6 x \left (t \right )-7 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.719 |
|
|
\[ {}\left [\begin {array}{c} t x^{\prime }\left (t \right )+2 x \left (t \right )=15 y \left (t \right ) \\ t y^{\prime }\left (t \right )=x \left (t \right ) \end {array}\right ] \] |
1 |
0 |
2 |
system of linear ODEs |
✗ |
N/A |
0.042 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+2 y \left (t \right ) \\ y^{\prime }\left (t \right )=5 x \left (t \right )-2 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.712 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=5 x \left (t \right )+4 y \left (t \right ) \\ y^{\prime }\left (t \right )=8 x \left (t \right )+y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.627 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=4 x \left (t \right )+2 y \left (t \right ) \\ y^{\prime }\left (t \right )=3 x \left (t \right )-y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.734 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+2 y \left (t \right ) \\ y^{\prime }\left (t \right )=5 x \left (t \right )-2 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.668 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.605 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.75 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=8 x \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.816 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=4 x \left (t \right )-13 y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.793 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right )+2 y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right )+3 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.695 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=8 x \left (t \right )+2 y \left (t \right )-17 \\ y^{\prime }\left (t \right )=4 x \left (t \right )+y \left (t \right )-13 \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
1.019 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=8 x \left (t \right )+2 y \left (t \right )+7 \,{\mathrm e}^{2 t} \\ y^{\prime }\left (t \right )=4 x \left (t \right )+y \left (t \right )-7 \,{\mathrm e}^{2 t} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
1.035 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=4 x \left (t \right )+3 y \left (t \right )-6 \,{\mathrm e}^{3 t} \\ y^{\prime }\left (t \right )=x \left (t \right )+6 y \left (t \right )+2 \,{\mathrm e}^{3 t} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
1.15 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-y \left (t \right ) \\ y^{\prime }\left (t \right )=4 x \left (t \right )+24 t \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
1.218 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=4 x \left (t \right )-13 y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+19 \cos \left (4 t \right )-13 \sin \left (4 t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
3.619 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=4 x \left (t \right )+3 y \left (t \right )+5 \operatorname {Heaviside}\left (t -2\right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+6 y \left (t \right )+17 \operatorname {Heaviside}\left (t -2\right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
1.465 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=5 x \left (t \right )+4 y \left (t \right ) \\ y^{\prime }\left (t \right )=8 x \left (t \right )+y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.64 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )-5 y \left (t \right ) \\ y^{\prime }\left (t \right )=3 x \left (t \right )-7 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
1.059 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )-5 y \left (t \right )+4 \\ y^{\prime }\left (t \right )=3 x \left (t \right )-7 y \left (t \right )+5 \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
2.147 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=6 x \left (t \right )+2 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.67 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right ) y \left (t \right )-6 y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )-y \left (t \right )-5 \end {array}\right ] \] |
1 |
0 |
2 |
system of linear ODEs |
✗ |
N/A |
0.257 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-x \left (t \right )+2 y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )-y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.6 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=4 y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )-2 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
1.799 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=4 y \left (t \right ) \\ y^{\prime }\left (t \right )=-4 x \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.619 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-5 x \left (t \right )+4 y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )+2 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.734 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=6 \\ y^{\prime }\left (t \right )=\cos \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.715 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right ) \\ y^{\prime }\left (t \right )=1 \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.76 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=0 \\ y^{\prime }\left (t \right )=-2 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.281 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )^{2} \\ y^{\prime }\left (t \right )={\mathrm e}^{t} \end {array}\right ] \] |
1 |
0 |
2 |
system of linear ODEs |
✗ |
N/A |
0.339 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-3 x_{1} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=1 \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.663 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-x_{1} \left (t \right )+1 \\ x_{2}^{\prime }\left (t \right )=x_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.655 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-3 x \left (t \right )+6 y \left (t \right ) \\ y^{\prime }\left (t \right )=4 x \left (t \right )-y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.449 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-x \left (t \right )-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.577 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=4 x \left (t \right )+2 y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )+2 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.635 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )+1 \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
1.323 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )+\sin \left (2 t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
1.405 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-2 t x_{1} \left (t \right )^{2} \\ x_{2}^{\prime }\left (t \right )=\frac {x_{2} \left (t \right )+t}{t} \end {array}\right ] \] |
1 |
0 |
2 |
system of linear ODEs |
✗ |
N/A |
0.119 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )={\mathrm e}^{t -x_{1} \left (t \right )} \\ x_{2}^{\prime }\left (t \right )=2 \,{\mathrm e}^{x_{1} \left (t \right )} \end {array}\right ] \] |
1 |
0 |
2 |
system of linear ODEs |
✗ |
N/A |
0.246 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=y \left (t \right ) \\ y^{\prime }\left (t \right )=\frac {y \left (t \right )^{2}}{x \left (t \right )} \end {array}\right ] \] |
1 |
0 |
2 |
system of linear ODEs |
✗ |
N/A |
0.122 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=\frac {x_{1} \left (t \right )^{2}}{x_{2} \left (t \right )} \\ x_{2}^{\prime }\left (t \right )=x_{2} \left (t \right )-x_{1} \left (t \right ) \end {array}\right ] \] |
1 |
0 |
2 |
system of linear ODEs |
✗ |
N/A |
0.129 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=\frac {{\mathrm e}^{-x \left (t \right )}}{t} \\ y^{\prime }\left (t \right )=\frac {x \left (t \right ) {\mathrm e}^{-y \left (t \right )}}{t} \end {array}\right ] \] |
1 |
0 |
2 |
system of linear ODEs |
✗ |
N/A |
0.267 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=\frac {t +y \left (t \right )}{x \left (t \right )+y \left (t \right )} \\ y^{\prime }\left (t \right )=\frac {x \left (t \right )-t}{x \left (t \right )+y \left (t \right )} \end {array}\right ] \] |
1 |
0 |
2 |
system of linear ODEs |
✗ |
N/A |
0.262 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=\frac {t -y \left (t \right )}{-x \left (t \right )+y \left (t \right )} \\ y^{\prime }\left (t \right )=\frac {x \left (t \right )-t}{-x \left (t \right )+y \left (t \right )} \end {array}\right ] \] |
1 |
0 |
2 |
system of linear ODEs |
✗ |
N/A |
0.257 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=\frac {t +y \left (t \right )}{x \left (t \right )+y \left (t \right )} \\ y^{\prime }\left (t \right )=\frac {t +x \left (t \right )}{x \left (t \right )+y \left (t \right )} \end {array}\right ] \] |
1 |
0 |
2 |
system of linear ODEs |
✗ |
N/A |
0.237 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-9 y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.349 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=t +y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )-t \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.595 |
|
|
|
||||||||
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )+3 x \left (t \right )+4 y \left (t \right )=0 \\ y^{\prime }\left (t \right )+2 x \left (t \right )+5 y \left (t \right )=0 \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.286 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+5 y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )-3 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.332 |
|
|
\[ {}\left [\begin {array}{c} 4 x^{\prime }\left (t \right )-y^{\prime }\left (t \right )+3 x \left (t \right )=\sin \left (t \right ) \\ x^{\prime }\left (t \right )+y \left (t \right )=\cos \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.878 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-y \left (t \right )+z \left (t \right ) \\ y^{\prime }\left (t \right )=z \left (t \right ) \\ z^{\prime }\left (t \right )=-x \left (t \right )+z \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.589 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=y \left (t \right )+z \left (t \right ) \\ y^{\prime }\left (t \right )=z \left (t \right )+x \left (t \right ) \\ z^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.402 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )^{2}+y \left (t \right )^{2} \\ y^{\prime }\left (t \right )=2 x \left (t \right ) y \left (t \right ) \end {array}\right ] \] |
1 |
0 |
2 |
system of linear ODEs |
✗ |
N/A |
0.244 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-\frac {1}{y \left (t \right )} \\ y^{\prime }\left (t \right )=\frac {1}{x \left (t \right )} \end {array}\right ] \] |
1 |
0 |
2 |
system of linear ODEs |
✗ |
N/A |
0.251 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=\frac {x \left (t \right )}{y \left (t \right )} \\ y^{\prime }\left (t \right )=\frac {y \left (t \right )}{x \left (t \right )} \end {array}\right ] \] |
1 |
0 |
2 |
system of linear ODEs |
✗ |
N/A |
0.242 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=\frac {y \left (t \right )}{x \left (t \right )-y \left (t \right )} \\ y^{\prime }\left (t \right )=\frac {x \left (t \right )}{x \left (t \right )-y \left (t \right )} \end {array}\right ] \] |
1 |
0 |
2 |
system of linear ODEs |
✗ |
N/A |
0.267 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=\sin \left (x \left (t \right )\right ) \cos \left (y \left (t \right )\right ) \\ y^{\prime }\left (t \right )=\cos \left (x \left (t \right )\right ) \sin \left (y \left (t \right )\right ) \end {array}\right ] \] |
1 |
0 |
2 |
system of linear ODEs |
✗ |
N/A |
0.266 |
|
|
\[ {}\left [\begin {array}{c} {\mathrm e}^{t} x^{\prime }\left (t \right )=\frac {1}{y \left (t \right )} \\ {\mathrm e}^{t} y^{\prime }\left (t \right )=\frac {1}{x \left (t \right )} \end {array}\right ] \] |
1 |
0 |
2 |
system of linear ODEs |
✗ |
N/A |
0.269 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=\cos \left (x \left (t \right )\right )^{2} \cos \left (y \left (t \right )\right )^{2}+\sin \left (x \left (t \right )\right )^{2} \cos \left (y \left (t \right )\right )^{2} \\ y^{\prime }\left (t \right )=-\frac {\sin \left (2 x \left (t \right )\right ) \sin \left (2 y \left (t \right )\right )}{2} \end {array}\right ] \] |
1 |
0 |
0 |
system of linear ODEs |
✗ |
N/A |
0.259 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=8 y \left (t \right )-x \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.293 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )-y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )+y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.247 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )-3 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.373 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right )+4 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.274 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=4 x \left (t \right )-5 y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.301 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=y \left (t \right )+z \left (t \right )-x \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )-y \left (t \right )+z \left (t \right ) \\ z^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right )-z \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.412 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )-y \left (t \right )+z \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+2 y \left (t \right )-z \left (t \right ) \\ z^{\prime }\left (t \right )=x \left (t \right )-y \left (t \right )+2 z \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.385 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )-y \left (t \right )+z \left (t \right ) \\ y^{\prime }\left (t \right )=z \left (t \right )+x \left (t \right ) \\ z^{\prime }\left (t \right )=y \left (t \right )-2 z \left (t \right )-3 x \left (t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
0.353 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )+2 x \left (t \right )-y \left (t \right )=-{\mathrm e}^{2 t} \\ y^{\prime }\left (t \right )+3 x \left (t \right )-2 y \left (t \right )=6 \,{\mathrm e}^{2 t} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.626 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right )-\cos \left (t \right ) \\ y^{\prime }\left (t \right )=-y \left (t \right )-2 x \left (t \right )+\cos \left (t \right )+\sin \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.777 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=y \left (t \right )+\tan \left (t \right )^{2}-1 \\ y^{\prime }\left (t \right )=\tan \left (t \right )-x \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
2.716 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-4 x \left (t \right )-2 y \left (t \right )+\frac {2}{{\mathrm e}^{t}-1} \\ y^{\prime }\left (t \right )=6 x \left (t \right )+3 y \left (t \right )-\frac {3}{{\mathrm e}^{t}-1} \end {array}\right ] \] |
1 |
0 |
2 |
system of linear ODEs |
✗ |
N/A |
0.033 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )+\frac {1}{\cos \left (t \right )} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.616 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )+1 \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.65 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=3-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )-2 t \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.899 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-y \left (t \right )+\sin \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+\cos \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.75 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right )+{\mathrm e}^{t} \\ y^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right )-{\mathrm e}^{t} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.556 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=4 x \left (t \right )-5 y \left (t \right )+4 t -1 \\ y^{\prime }\left (t \right )=x \left (t \right )-2 y \left (t \right )+t \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.471 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=y \left (t \right )-x \left (t \right )+{\mathrm e}^{t} \\ y^{\prime }\left (t \right )=x \left (t \right )-y \left (t \right )+{\mathrm e}^{t} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.476 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )+y \left (t \right )=t^{2} \\ y^{\prime }\left (t \right )-x \left (t \right )=t \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.76 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )+y \left (t \right )-2 z \left (t \right )+2-t \\ y^{\prime }\left (t \right )=-x \left (t \right )+1 \\ z^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right )-z \left (t \right )+1-t \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
✓ |
✓ |
1.952 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=5 x \left (t \right )+4 y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+2 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.283 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=6 x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=4 x \left (t \right )+3 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.282 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )-4 y \left (t \right )+1 \\ y^{\prime }\left (t \right )=-x \left (t \right )+5 y \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.615 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right )+y \left (t \right )+{\mathrm e}^{t} \\ y^{\prime }\left (t \right )=x \left (t \right )+3 y \left (t \right )-{\mathrm e}^{t} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✓ |
✓ |
0.546 |
|
|
|
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|
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|
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