|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=\frac {x_{1}}{2}-x_{2}-\frac {3 x_{3}}{2} \\ x_{2}^{\prime }=\frac {3 x_{1}}{2}-2 x_{2}-\frac {3 x_{3}}{2} \\ x_{3}^{\prime }=-2 x_{1}+2 x_{2}+x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.527 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+5 x_{2}+3 x_{3}-5 x_{4} \\ x_{2}^{\prime }=2 x_{1}+3 x_{2}+2 x_{3}-4 x_{4} \\ x_{3}^{\prime }=-x_{2}-2 x_{3}+x_{4} \\ x_{4}^{\prime }=2 x_{1}+4 x_{2}+2 x_{3}-5 x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.706 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-5 x_{1}+x_{2}-4 x_{3}-x_{4} \\ x_{2}^{\prime }=-3 x_{2} \\ x_{3}^{\prime }=x_{1}-x_{2}+x_{4} \\ x_{4}^{\prime }=2 x_{1}-x_{2}+2 x_{3}-2 x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.724 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+2 x_{2}-x_{4} \\ x_{2}^{\prime }=2 x_{1}-x_{2}+2 x_{4} \\ x_{3}^{\prime }=3 x_{3} \\ x_{4}^{\prime }=-x_{1}+2 x_{2}+2 x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.513 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+8 x_{2}+5 x_{3}+3 x_{4} \\ x_{2}^{\prime }=2 x_{1}+16 x_{2}+10 x_{3}+6 x_{4} \\ x_{3}^{\prime }=5 x_{1}-14 x_{2}-11 x_{3}-3 x_{4} \\ x_{4}^{\prime }=-x_{1}-8 x_{2}-5 x_{3}-3 x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.865 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}+2 x_{2}-2 x_{4} \\ x_{2}^{\prime }=-x_{1}+3 x_{2}-x_{3}+x_{4} \\ x_{3}^{\prime }=-2 x_{1}-2 x_{2}-4 x_{3}+2 x_{4} \\ x_{4}^{\prime }=-7 x_{1}+x_{2}-7 x_{3}+3 x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.852 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-5 x_{1}-2 x_{2}-x_{3}+2 x_{4}+3 x_{5} \\ x_{2}^{\prime }=-3 x_{2} \\ x_{3}^{\prime }=x_{1}-x_{3}-x_{5} \\ x_{4}^{\prime }=2 x_{1}+x_{2}-4 x_{4}-2 x_{5} \\ x_{5}^{\prime }=-3 x_{1}-2 x_{2}-x_{3}+2 x_{4}+x_{5} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.079 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{2}-2 x_{3}+3 x_{4}+2 x_{5} \\ x_{2}^{\prime }=8 x_{1}+6 x_{2}+4 x_{3}-8 x_{4}-16 x_{5} \\ x_{3}^{\prime }=-8 x_{1}-8 x_{2}-6 x_{3}+8 x_{4}-16 x_{5} \\ x_{4}^{\prime }=8 x_{1}+7 x_{2}+4 x_{3}-9 x_{4}-16 x_{5} \\ x_{5}^{\prime }=-3 x_{1}-5 x_{2}-3 x_{3}+5 x_{4}+7 x_{5} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
3.681 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}+2 x_{2}+x_{3} \\ x_{2}^{\prime }=-2 x_{1}+2 x_{2}+2 x_{3} \\ x_{3}^{\prime }=2 x_{1}-3 x_{2}-3 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.632 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-4 x_{2}-x_{3} \\ x_{2}^{\prime }=x_{1}+x_{2}+3 x_{3} \\ x_{3}^{\prime }=3 x_{1}-4 x_{2}-2 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.666 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{2}-x_{3} \\ x_{2}^{\prime }=x_{1}-x_{2}+x_{3} \\ x_{3}^{\prime }=x_{1}-2 x_{2}-2 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.628 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-4 x_{1}+2 x_{2}-x_{3} \\ x_{2}^{\prime }=-6 x_{1}-3 x_{3} \\ x_{3}^{\prime }=\frac {8 x_{2}}{3}-2 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.684 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-7 x_{1}+6 x_{2}-6 x_{3} \\ x_{2}^{\prime }=-9 x_{1}+5 x_{2}-9 x_{3} \\ x_{3}^{\prime }=-x_{2}-x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.646 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=\frac {4 x_{1}}{3}+\frac {4 x_{2}}{3}-\frac {11 x_{3}}{3} \\ x_{2}^{\prime }=-\frac {16 x_{1}}{3}-\frac {x_{2}}{3}+\frac {14 x_{3}}{3} \\ x_{3}^{\prime }=3 x_{1}-2 x_{2}-2 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.682 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}+x_{3} \\ x_{2}^{\prime }=2 x_{1}+x_{2}-x_{3} \\ x_{3}^{\prime }=-8 x_{1}-5 x_{2}-3 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.554 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-x_{2}+4 x_{3} \\ x_{2}^{\prime }=3 x_{1}+2 x_{2}-x_{3} \\ x_{3}^{\prime }=2 x_{1}+x_{2}-x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.533 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=\frac {3 x_{1}}{4}+\frac {29 x_{2}}{4}-\frac {11 x_{3}}{2} \\ x_{2}^{\prime }=-\frac {3 x_{1}}{4}+\frac {3 x_{2}}{4}-\frac {5 x_{3}}{2} \\ x_{3}^{\prime }=\frac {5 x_{1}}{4}+\frac {11 x_{2}}{4}-\frac {5 x_{3}}{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.674 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}-x_{2}+4 x_{3}+2 x_{4} \\ x_{2}^{\prime }=-19 x_{1}-6 x_{2}+6 x_{3}+16 x_{4} \\ x_{3}^{\prime }=-9 x_{1}-x_{2}+x_{3}+6 x_{4} \\ x_{4}^{\prime }=-5 x_{1}-3 x_{2}+6 x_{3}+5 x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
4.119 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}+6 x_{2}+2 x_{3}-2 x_{4} \\ x_{2}^{\prime }=2 x_{1}-3 x_{2}-6 x_{3}+2 x_{4} \\ x_{3}^{\prime }=-4 x_{1}+8 x_{2}+3 x_{3}-4 x_{4} \\ x_{4}^{\prime }=2 x_{1}-2 x_{2}-6 x_{3}+x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.123 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}-4 x_{2}+5 x_{3}+9 x_{4} \\ x_{2}^{\prime }=-2 x_{1}-5 x_{2}+4 x_{3}+12 x_{4} \\ x_{3}^{\prime }=-2 x_{1}-x_{3}+2 x_{4} \\ x_{4}^{\prime }=-2 x_{2}+2 x_{3}+3 x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.499 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}-5 x_{2}+8 x_{3}+14 x_{4} \\ x_{2}^{\prime }=-6 x_{1}-8 x_{2}+11 x_{3}+27 x_{4} \\ x_{3}^{\prime }=-6 x_{1}-4 x_{2}+7 x_{3}+17 x_{4} \\ x_{4}^{\prime }=-2 x_{2}+2 x_{3}+4 x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
2.528 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{2}-2 x_{4} \\ x_{2}^{\prime }=-\frac {x_{1}}{2}+x_{2}-3 x_{3}-\frac {5 x_{4}}{2} \\ x_{3}^{\prime }=3 x_{2}-5 x_{3}-3 x_{4} \\ x_{4}^{\prime }=x_{1}+3 x_{2}-3 x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.132 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-2 x_{2} \\ x_{2}^{\prime }=2 x_{1}-2 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.338 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}+2 x_{2} \\ x_{2}^{\prime }=\frac {x_{1}}{2}-3 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.330 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-4 x_{2} \\ x_{2}^{\prime }=x_{1}-x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.312 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=\frac {x_{1}}{2}-\frac {x_{2}}{4} \\ x_{2}^{\prime }=x_{1}-\frac {x_{2}}{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.269 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-\frac {5 x_{2}}{2} \\ x_{2}^{\prime }=\frac {x_{1}}{2}-x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.399 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}-4 x_{2} \\ x_{2}^{\prime }=x_{1}-x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.392 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=5 x_{1}-x_{2} \\ x_{2}^{\prime }=3 x_{1}+x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.339 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-x_{2} \\ x_{2}^{\prime }=5 x_{1}-3 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.428 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-x_{2} \\ x_{2}^{\prime }=3 x_{1}-2 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.327 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=\frac {x_{1}}{2}+\frac {x_{2}}{2} \\ x_{2}^{\prime }=2 x_{1}-x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.355 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}+4 x_{2} \\ x_{2}^{\prime }=-x_{1}-2 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.626 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}+\frac {5 x_{2}}{2} \\ x_{2}^{\prime }=-\frac {5 x_{1}}{2}+2 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.313 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}+x_{3} \\ x_{2}^{\prime }=2 x_{1}+x_{2}-x_{3} \\ x_{3}^{\prime }=-8 x_{1}-5 x_{2}-3 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.569 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-x_{2}+4 x_{3} \\ x_{2}^{\prime }=3 x_{1}+2 x_{2}-x_{3} \\ x_{3}^{\prime }=2 x_{1}+x_{2}-x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.543 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}-9 x_{2} \\ x_{2}^{\prime }=x_{1}-3 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.520 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-x_{2} \\ x_{2}^{\prime }=3 x_{1}-2 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.442 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-4 x_{1}-x_{2} \\ x_{2}^{\prime }=x_{1}-2 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.223 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=5 x_{1}-x_{2} \\ x_{2}^{\prime }=x_{1}+3 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.217 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}-5 x_{2} \\ x_{2}^{\prime }=x_{1}+3 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.236 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{2}-x_{3} \\ x_{2}^{\prime }=x_{1}+x_{3} \\ x_{3}^{\prime }=x_{1}+x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.218 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-k_{1} x_{1} \\ x_{2}^{\prime }=k_{1} x_{1}-k_{2} x_{2} \\ x_{3}^{\prime }=k_{2} x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.568 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-x_{2}+{\mathrm e}^{t} \\ x_{2}^{\prime }=3 x_{1}-2 x_{2}+t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.505 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+\sqrt {3}\, x_{2}+{\mathrm e}^{t} \\ x_{2}^{\prime }=\sqrt {3}\, x_{1}-x_{2}+\sqrt {3}\, {\mathrm e}^{-t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.633 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-5 x_{2}-\cos \left (t \right ) \\ x_{2}^{\prime }=x_{1}-2 x_{2}+\sin \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.843 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}+{\mathrm e}^{-2 t} \\ x_{2}^{\prime }=4 x_{1}-2 x_{2}-2 \,{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.555 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=1-x_{2}+x_{3} \\ x_{2}^{\prime }=2 x_{2}+t \\ x_{3}^{\prime }=-2 x_{1}-x_{2}+3 x_{3}+{\mathrm e}^{-t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.625 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-\frac {x_{1}}{2}+\frac {x_{2}}{2}-\frac {x_{3}}{2}+1 \\ x_{2}^{\prime }=-x_{1}-2 x_{2}+x_{3}+t \\ x_{3}^{\prime }=\frac {x_{1}}{2}+\frac {x_{2}}{2}-\frac {3 x_{3}}{2}+11 \,{\mathrm e}^{-3 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.703 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-4 x_{1}+x_{2}+3 x_{3}+3 t \\ x_{2}^{\prime }=-2 x_{2} \\ x_{3}^{\prime }=-2 x_{1}+x_{2}+x_{3}+3 \cos \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.799 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-\frac {x_{1}}{2}+x_{2}+\frac {x_{3}}{2} \\ x_{2}^{\prime }=x_{1}-x_{2}+x_{3}-\sin \left (t \right ) \\ x_{3}^{\prime }=\frac {x_{1}}{2}+x_{2}-\frac {x_{3}}{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.918 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+x_{2}+1 \\ x_{2}^{\prime }=x_{1}-2 x_{2}+x_{3} \\ x_{3}^{\prime }=x_{2}-x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
230.934 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{1}-9 x_{2} \\ x_{2}^{\prime }=x_{1}-2 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.325 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-9 x_{2} \\ x_{2}^{\prime }=x_{1}-3 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.271 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}+x_{3} \\ x_{2}^{\prime }=2 x_{1}+x_{2}-x_{3} \\ x_{3}^{\prime }=-3 x_{1}+2 x_{2}+4 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.388 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=5 x_{1}-3 x_{2}-2 x_{3} \\ x_{2}^{\prime }=8 x_{1}-5 x_{2}-4 x_{3} \\ x_{3}^{\prime }=-4 x_{1}+3 x_{2}+3 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.477 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-7 x_{1}+9 x_{2}-6 x_{3} \\ x_{2}^{\prime }=-8 x_{1}+11 x_{2}-7 x_{3} \\ x_{3}^{\prime }=-2 x_{1}+3 x_{2}-x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.518 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=5 x_{1}+6 x_{2}+2 x_{3} \\ x_{2}^{\prime }=-2 x_{1}-2 x_{2}-x_{3} \\ x_{3}^{\prime }=-2 x_{1}-3 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.459 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-8 x_{1}-16 x_{2}-16 x_{3}-17 x_{4} \\ x_{2}^{\prime }=-2 x_{1}-10 x_{2}-8 x_{3}-7 x_{4} \\ x_{3}^{\prime }=-2 x_{1}-2 x_{3}-3 x_{4} \\ x_{4}^{\prime }=6 x_{1}+14 x_{2}+14 x_{3}+14 x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.307 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-x_{2}-2 x_{3}+3 x_{4} \\ x_{2}^{\prime }=2 x_{1}-\frac {3 x_{2}}{2}-x_{3}+\frac {7 x_{4}}{2} \\ x_{3}^{\prime }=-x_{1}+\frac {x_{2}}{2}-\frac {3 x_{4}}{2} \\ x_{4}^{\prime }=-2 x_{1}+\frac {3 x_{2}}{2}+3 x_{3}-\frac {7 x_{4}}{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.595 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-4 x_{2} \\ x_{2}^{\prime }=4 x_{1}-7 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.449 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-4 x_{2} \\ x_{2}^{\prime }=x_{1}-x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.447 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{1}+x_{2}+3 x_{3} \\ x_{2}^{\prime }=6 x_{1}+4 x_{2}+6 x_{3} \\ x_{3}^{\prime }=-5 x_{1}-2 x_{2}-4 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.495 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2} \\ x_{2}^{\prime }=-14 x_{1}-5 x_{2}+x_{3} \\ x_{3}^{\prime }=15 x_{1}+5 x_{2}-2 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.505 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 y+x y \\ y^{\prime }=x+4 x y \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.050 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=1+5 y \\ y^{\prime }=1-6 x^{2} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.050 |
|
|
\[
{}y^{\prime } = 2
\] |
[_quadrature] |
✓ |
0.484 |
|
|
\[
{}y^{\prime } = -x^{3}
\] |
[_quadrature] |
✓ |
0.263 |
|
|
\[
{}y^{\prime \prime } = \sin \left (x \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.503 |
|
|
\[
{}x \sqrt {1+y^{2}}+y \sqrt {x^{2}+1}\, y^{\prime } = 0
\] |
[_separable] |
✓ |
6.337 |
|
|
\[
{}\sec \left (x \right )^{2} \tan \left (y\right )+\sec \left (y\right )^{2} \tan \left (x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
36.711 |
|
|
\[
{}\sqrt {-x^{2}+1}\, y^{\prime }+\sqrt {1-y^{2}} = 0
\] |
[_separable] |
✓ |
16.800 |
|
|
\[
{}y^{\prime } = \frac {2 x y}{y^{2}+x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
4.802 |
|
|
\[
{}y^{\prime } = \frac {y \left (1+\ln \left (y\right )-\ln \left (x \right )\right )}{x}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
4.046 |
|
|
\[
{}y^{2}+x^{2} y^{\prime } = x y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
37.229 |
|
|
\[
{}\left (x +y\right ) y^{\prime } = y-x
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.702 |
|
|
\[
{}x -y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
4.631 |
|
|
\[
{}3 y-7 x +7 = \left (3 x -7 y-3\right ) y^{\prime }
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.537 |
|
|
\[
{}\left (x +2 y+1\right ) y^{\prime } = 2 x +4 y+3
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.457 |
|
|
\[
{}y^{\prime } = \frac {2 \left (y+2\right )^{2}}{\left (y-1+x \right )^{2}}
\] |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
1.773 |
|
|
\[
{}\left (x +y\right )^{2} y^{\prime } = a^{2}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
4.456 |
|
|
\[
{}x y^{\prime }-4 y = x^{2} \sqrt {y}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
3.473 |
|
|
\[
{}\cos \left (x \right ) y^{\prime } = y \sin \left (x \right )+\cos \left (x \right )^{2}
\] |
[_linear] |
✓ |
2.212 |
|
|
\[
{}y^{\prime } = 2 x y-x^{3}+x
\] |
[_linear] |
✓ |
1.391 |
|
|
\[
{}y^{\prime }+\frac {x y}{x^{2}+1} = \frac {1}{x \left (x^{2}+1\right )}
\] |
[_linear] |
✓ |
1.146 |
|
|
\[
{}\left (x -2 x y-y^{2}\right ) y^{\prime }+y^{2} = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.801 |
|
|
\[
{}x y^{\prime }+y = x y^{2} \ln \left (x \right )
\] |
[_Bernoulli] |
✓ |
2.087 |
|
|
\[
{}y^{\prime }-\frac {x y}{2 x^{2}-2}-\frac {x}{2 y} = 0
\] |
[_rational, _Bernoulli] |
✓ |
1.681 |
|
|
\[
{}y^{\prime } \left (y^{3} x^{2}+x y\right ) = 1
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.473 |
|
|
\[
{}x -y^{2}+2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
1.606 |
|
|
\[
{}y^{\prime } = \frac {y^{2}}{3}+\frac {2}{3 x^{2}}
\] |
[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]] |
✓ |
1.670 |
|
|
\[
{}y^{\prime }+y^{2}+\frac {y}{x}-\frac {4}{x^{2}} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
1.931 |
|
|
\[
{}x y^{\prime }-3 y+y^{2} = 4 x^{2}-4 x
\] |
[_rational, _Riccati] |
✓ |
1.539 |
|
|
\[
{}y^{\prime } = y^{2}+\frac {1}{x^{4}}
\] |
[_rational, [_Riccati, _special]] |
✓ |
1.417 |
|
|
\[
{}\left (y-x \right ) \sqrt {x^{2}+1}\, y^{\prime } = \left (1+y^{2}\right )^{{3}/{2}}
\] |
[‘y=_G(x,y’)‘] |
✓ |
3.704 |
|
|
\[
{}y^{\prime } \left (x^{2}+y^{2}+3\right ) = 2 x \left (2 y-\frac {x^{2}}{y}\right )
\] |
[_rational] |
✗ |
2.862 |
|
|
\[
{}y^{\prime } = \frac {x -y^{2}}{2 y \left (x +y^{2}\right )}
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.629 |
|
|
\[
{}\left (\left (x +y\right ) x +a^{2}\right ) y^{\prime } = y \left (x +y\right )+b^{2}
\] |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.500 |
|
|
\[
{}y^{\prime } = k y+f \left (x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.224 |
|
|
\[
{}y^{\prime } = y^{2}-x^{2}
\] |
[_Riccati] |
✓ |
1.002 |
|