Column notations: A is ODE degree. B is Program Number of solutions generated. C is CAS Number of solutions generated.
|
# |
ODE |
A |
B |
C |
Program classification |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=6 x_{1}-3 x_{2} \\ x_{2}^{\prime }=2 x_{1}+x_{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.634 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}+x_{2} \\ x_{2}^{\prime }=-4 x_{1}+3 x_{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.577 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}+2 x_{2}+4 x_{3} \\ x_{2}^{\prime }=2 x_{1}+2 x_{3} \\ x_{3}^{\prime }=4 x_{1}+2 x_{2}+3 x_{3} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.983 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=7 x_{1}-x_{2}+6 x_{3} \\ x_{2}^{\prime }=-10 x_{1}+4 x_{2}-12 x_{3} \\ x_{3}^{\prime }=-2 x_{1}+x_{2}-x_{3} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.043 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-7 x_{1}+6 x_{3} \\ x_{2}^{\prime }=5 x_{2} \\ x_{3}^{\prime }=6 x_{1}+2 x_{3} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.905 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+2 x_{2}+3 x_{3}+6 x_{4} \\ x_{2}^{\prime }=3 x_{1}+6 x_{2}+9 x_{3}+18 x_{4} \\ x_{3}^{\prime }=5 x_{1}+10 x_{2}+15 x_{3}+30 x_{4} \\ x_{4}^{\prime }=7 x_{1}+14 x_{2}+21 x_{3}+42 x_{4} \end {array}\right ] \] |
1 |
1 |
4 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.295 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2} \\ x_{2}^{\prime }=4 x_{1}+x_{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.558 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-3 x_{2} \\ x_{2}^{\prime }=-2 x_{1}+2 x_{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.553 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}+x_{2}-x_{3} \\ x_{2}^{\prime }=x_{1}+3 x_{2}-x_{3} \\ x_{3}^{\prime }=3 x_{1}+3 x_{2}-x_{3} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.707 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-x_{2} \\ x_{2}^{\prime }=x_{1}+2 x_{2}+x_{3} \\ x_{3}^{\prime }=x_{1}+10 x_{2}+2 x_{3} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.896 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-3 x_{2}+2 x_{3} \\ x_{2}^{\prime }=-x_{2} \\ x_{3}^{\prime }=-x_{2}-2 x_{3} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.775 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}+x_{2}-2 x_{3} \\ x_{2}^{\prime }=-x_{1}+2 x_{2}+x_{3} \\ x_{3}^{\prime }=4 x_{1}+x_{2}-3 x_{3} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.901 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}+2 x_{2} \\ x_{2}^{\prime }=-x_{1}-x_{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.837 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-5 x_{2} \\ x_{2}^{\prime }=x_{1}-3 x_{2} \\ x_{3}^{\prime }=x_{3} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.045 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1} \\ x_{2}^{\prime }=3 x_{1}+x_{2}-2 x_{3} \\ x_{3}^{\prime }=2 x_{1}+2 x_{2}+x_{3} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.143 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{3} \\ x_{2}^{\prime }=x_{2}-x_{3} \\ x_{3}^{\prime }=-2 x_{1}-x_{3} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.194 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-x_{2} \\ x_{2}^{\prime }=5 x_{1}-3 x_{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.64 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-2 x_{2} \\ x_{2}^{\prime }=4 x_{1}-x_{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.652 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}+2 x_{3} \\ x_{2}^{\prime }=x_{1}-x_{2} \\ x_{3}^{\prime }=-2 x_{1}-x_{2} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
2.155 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{2} \\ x_{2}^{\prime }=-2 x_{1} \\ x_{3}^{\prime }=-3 x_{4} \\ x_{4}^{\prime }=3 x_{3} \end {array}\right ] \] |
1 |
1 |
4 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
3.183 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2} \\ x_{2}^{\prime }=x_{2} \\ x_{3}^{\prime }=2 x_{3} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.459 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+x_{2}+3 x_{3} \\ x_{2}^{\prime }=2 x_{2}-x_{3} \\ x_{3}^{\prime }=2 x_{3} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.698 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-x_{2}+x_{3} \\ x_{2}^{\prime }=2 x_{1}-3 x_{2}+x_{3} \\ x_{3}^{\prime }=x_{1}-x_{2}-x_{3} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.903 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}+x_{3} \\ x_{2}^{\prime }=2 x_{1}+x_{2}-x_{3} \\ x_{3}^{\prime }=-3 x_{1}+2 x_{2}+4 x_{3} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.668 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}-x_{2} \\ x_{2}^{\prime }=-x_{2} \\ x_{3}^{\prime }=-2 x_{3} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.471 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-x_{3} \\ x_{2}^{\prime }=2 x_{2}+x_{3} \\ x_{3}^{\prime }=2 x_{3} \\ x_{4}^{\prime }=-x_{3}+2 x_{4} \end {array}\right ] \] |
1 |
1 |
4 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.6 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}+x_{2}+2 x_{3} \\ x_{2}^{\prime }=-x_{1}+x_{2}+x_{3} \\ x_{3}^{\prime }=-2 x_{1}+x_{2}+3 x_{3} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.634 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-4 x_{1}-4 x_{2} \\ x_{2}^{\prime }=10 x_{1}+9 x_{2}+x_{3} \\ x_{3}^{\prime }=-4 x_{1}-3 x_{2}+x_{3} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.067 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+2 x_{2}-3 x_{3} \\ x_{2}^{\prime }=x_{1}+x_{2}+2 x_{3} \\ x_{3}^{\prime }=x_{1}-x_{2}+4 x_{3} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.681 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1} \\ x_{2}^{\prime }=x_{1}+3 x_{2} \\ x_{3}^{\prime }=3 x_{3} \\ x_{4}^{\prime }=2 x_{3}+3 x_{4} \end {array}\right ] \] |
1 |
1 |
4 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.817 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1} \\ x_{2}^{\prime }=2 x_{1}+x_{2}-2 x_{3} \\ x_{3}^{\prime }=3 x_{1}+2 x_{2}+x_{3}+{\mathrm e}^{t} \cos \left (2 t \right ) \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
3.177 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+{\mathrm e}^{c t} \\ x_{2}^{\prime }=2 x_{1}+x_{2}-2 x_{3} \\ x_{3}^{\prime }=3 x_{1}+2 x_{2}+x_{3} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
4.136 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{1}+5 x_{2}+4 \,{\mathrm e}^{t} \cos \left (t \right ) \\ x_{2}^{\prime }=-2 x_{1}-2 x_{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.867 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-4 x_{2}+{\mathrm e}^{t} \\ x_{2}^{\prime }=x_{1}-x_{2}+{\mathrm e}^{t} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.023 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-5 x_{2}+\sin \left (t \right ) \\ x_{2}^{\prime }=x_{1}-2 x_{2}+\tan \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
3.764 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{2}+f_{1} \left (t \right ) \\ x_{2}^{\prime }=-x_{1}+f_{2} \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
2.004 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+x_{3}+{\mathrm e}^{2 t} \\ x_{2}^{\prime }=2 x_{2} \\ x_{3}^{\prime }=x_{2}+3 x_{3}+{\mathrm e}^{2 t} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.121 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}-x_{2}-2 x_{3}+{\mathrm e}^{t} \\ x_{2}^{\prime }=x_{1}+x_{2}+x_{3} \\ x_{3}^{\prime }=2 x_{1}+x_{2}+3 x_{3} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.353 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+x_{2}+{\mathrm e}^{3 t} \\ x_{2}^{\prime }=3 x_{1}-2 x_{2}+{\mathrm e}^{3 t} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
2.088 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-x_{2}-t^{2} \\ x_{2}^{\prime }=x_{1}+3 x_{2}+2 t \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.409 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+3 x_{2}+2 x_{3}+\sin \left (t \right ) \\ x_{2}^{\prime }=-x_{1}+2 x_{2}+x_{3} \\ x_{3}^{\prime }=4 x_{1}-x_{2}-x_{3} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
2.861 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+2 x_{2}-3 x_{3}+{\mathrm e}^{t} \\ x_{2}^{\prime }=x_{1}+x_{2}+2 x_{3} \\ x_{3}^{\prime }=x_{1}-x_{2}+4 x_{3}-{\mathrm e}^{t} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.233 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}-x_{2}+1 \\ x_{2}^{\prime }=-4 x_{2}-x_{3}+t \\ x_{3}^{\prime }=5 x_{2}+{\mathrm e}^{t} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
4.827 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}-x_{3}+{\mathrm e}^{2 t} \\ x_{2}^{\prime }=2 x_{1}+3 x_{2}-4 x_{3}+2 \,{\mathrm e}^{2 t} \\ x_{3}^{\prime }=4 x_{1}+x_{2}-4 x_{3}+{\mathrm e}^{2 t} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
2.149 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-x_{2}-x_{3}+{\mathrm e}^{3 t} \\ x_{2}^{\prime }=x_{1}+3 x_{2}+x_{3}-{\mathrm e}^{3 t} \\ x_{3}^{\prime }=-3 x_{1}+x_{2}-x_{3}-{\mathrm e}^{3 t} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.863 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}+2 x_{2}+4 x_{3}+2 \,{\mathrm e}^{8 t} \\ x_{2}^{\prime }=2 x_{1}+2 x_{3}+{\mathrm e}^{8 t} \\ x_{3}^{\prime }=4 x_{1}+2 x_{2}+3 x_{3}+2 \,{\mathrm e}^{8 t} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.789 |
|
|
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