| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=4 x+y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= 3 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.402 |
|
| \begin{align*}
x^{\prime }&=x-3 y \\
y^{\prime }&=-2 x+2 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 5 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.398 |
|
| \begin{align*}
x^{\prime }&=x-y \\
y^{\prime }&=5 x-3 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.533 |
|
| \begin{align*}
x^{\prime }&=3 x-2 y \\
y^{\prime }&=4 x-y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 5 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.538 |
|
| \begin{align*}
x^{\prime }&=4 x+5 y+4 \,{\mathrm e}^{t} \cos \left (t \right ) \\
y^{\prime }&=-2 x-2 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.999 |
|
| \begin{align*}
x^{\prime }&=3 x-4 y+{\mathrm e}^{t} \\
y^{\prime }&=x-y+{\mathrm e}^{t} \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.575 |
|
| \begin{align*}
x^{\prime }&=2 x-5 y+\sin \left (t \right ) \\
y^{\prime }&=x-2 y+\tan \left (t \right ) \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.304 |
|
| \begin{align*}
x^{\prime }&=y+\textit {f\_1} \left (t \right ) \\
y^{\prime }&=-x+f_{2} \left (t \right ) \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.800 |
|
| \begin{align*}
y^{\prime \prime \prime }-2 y^{\prime \prime }-y^{\prime }+2 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.046 |
|
| \begin{align*}
y^{\prime \prime \prime }-6 y^{\prime \prime }+5 y^{\prime }+12 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.050 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+6 y^{\prime \prime }+4 y^{\prime }-8 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.056 |
|
| \begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.049 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+14 y^{\prime \prime }-20 y^{\prime }+25 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.605 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= -1 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.097 |
|
| \begin{align*}
y^{\left (5\right )}-2 y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime \prime }\left (0\right ) &= -1 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.095 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+y^{\prime \prime }+2 y^{\prime }-2 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.066 |
|
| \begin{align*}
y^{\prime \prime \prime }+y^{\prime }&=\tan \left (t \right ) \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.447 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-y&=g \left (t \right ) \\
\end{align*} | [[_high_order, _linear, _nonhomogeneous]] | ✓ | ✓ | ✓ | ✓ | 0.398 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+y&=g \left (t \right ) \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.740 |
|
| \begin{align*}
y^{\prime \prime \prime }+y^{\prime }&=2 t^{2}+4 \sin \left (t \right ) \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.503 |
|
| \begin{align*}
y^{\prime \prime \prime }-4 y^{\prime }&=t +\cos \left (t \right )+2 \,{\mathrm e}^{-2 t} \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.198 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-y&=t +\sin \left (t \right ) \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.474 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y&=t^{2} \sin \left (t \right ) \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.737 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+y^{\prime \prime }&=t^{2} \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.113 |
|
| \begin{align*}
y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+y&=t +{\mathrm e}^{-t} \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.130 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+6 y^{\prime \prime }+4 y^{\prime }+y&=t^{3} {\mathrm e}^{-t} \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.178 |
|
| \begin{align*}
x_{1}^{\prime }&=6 x_{1}-3 x_{2} \\
x_{2}^{\prime }&=2 x_{1}+x_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.374 |
|
| \begin{align*}
x_{1}^{\prime }&=-2 x_{1}+x_{2} \\
x_{2}^{\prime }&=-4 x_{1}+3 x_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.388 |
|
| \begin{align*}
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{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.615 |
|
| \begin{align*}
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{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.762 |
|
| \begin{align*}
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{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.552 |
|
| \begin{align*}
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{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.866 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}+x_{2} \\
x_{2}^{\prime }&=4 x_{1}+x_{2} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 2 \\
x_{2} \left (0\right ) &= 3 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.410 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}-3 x_{2} \\
x_{2}^{\prime }&=-2 x_{1}+2 x_{2} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= 5 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.407 |
|
| \begin{align*}
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{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= -2 \\
x_{3} \left (0\right ) &= -1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.587 |
|
| \begin{align*}
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{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= -1 \\
x_{2} \left (0\right ) &= -4 \\
x_{3} \left (0\right ) &= 13 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.759 |
|
| \begin{align*}
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{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= -2 \\
x_{2} \left (0\right ) &= 0 \\
x_{3} \left (0\right ) &= 3 \\
\end{align*} | system_of_ODEs | ✓ | ✓ | ✓ | ✓ | 0.655 |
|
| \begin{align*}
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{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 4 \\
x_{3} \left (0\right ) &= -7 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.725 |
|
| \begin{align*}
x_{1}^{\prime }&=-3 x_{1}+2 x_{2} \\
x_{2}^{\prime }&=-x_{1}-x_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.516 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}-5 x_{2} \\
x_{2}^{\prime }&=x_{1}-3 x_{2} \\
x_{3}^{\prime }&=x_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.746 |
|
| \begin{align*}
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{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.761 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}+x_{3} \\
x_{2}^{\prime }&=x_{2}-x_{3} \\
x_{3}^{\prime }&=-2 x_{1}-x_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.566 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}-x_{2} \\
x_{2}^{\prime }&=5 x_{1}-3 x_{2} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.408 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}-2 x_{2} \\
x_{2}^{\prime }&=4 x_{1}-x_{2} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 5 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.463 |
|
| \begin{align*}
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{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= -1 \\
x_{3} \left (0\right ) &= -2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.343 |
|
| \begin{align*}
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{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 1 \\
x_{3} \left (0\right ) &= 1 \\
x_{4} \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.188 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}+x_{2} \\
x_{2}^{\prime }&=x_{2} \\
x_{3}^{\prime }&=2 x_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.379 |
|
| \begin{align*}
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{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 2 \\
x_{3} \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.441 |
|
| \begin{align*}
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{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.507 |
|
| \begin{align*}
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{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.468 |
|
| \begin{align*}
x_{1}^{\prime }&=-x_{1}-x_{2} \\
x_{2}^{\prime }&=-x_{2} \\
x_{3}^{\prime }&=-2 x_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.411 |
|
| \begin{align*}
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{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.535 |
|
| \begin{align*}
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{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 0 \\
x_{3} \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.459 |
|
| \begin{align*}
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{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 2 \\
x_{2} \left (0\right ) &= 1 \\
x_{3} \left (0\right ) &= -1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.519 |
|
| \begin{align*}
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{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 0 \\
x_{3} \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.428 |
|
| \begin{align*}
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{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 1 \\
x_{3} \left (0\right ) &= 1 \\
x_{4} \left (0\right ) &= 1 \\
\end{align*} | system_of_ODEs | ✓ | ✓ | ✓ | ✓ | 0.477 |
|
| \begin{align*}
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{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.111 |
|
| \begin{align*}
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{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.270 |
|
| \begin{align*}
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{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.731 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}-4 x_{2}+{\mathrm e}^{t} \\
x_{2}^{\prime }&=x_{1}-x_{2}+{\mathrm e}^{t} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.471 |
|
| \begin{align*}
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{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.766 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{2}+f_{1} \left (t \right ) \\
x_{2}^{\prime }&=-x_{1}+f_{2} \left (t \right ) \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.697 |
|
| \begin{align*}
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{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 1 \\
x_{3} \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.719 |
|
| \begin{align*}
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{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= 0 \\
x_{3} \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.710 |
|
| \begin{align*}
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{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.851 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}-x_{2}-t^{2} \\
x_{2}^{\prime }&=x_{1}+3 x_{2}+2 t \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.550 |
|
| \begin{align*}
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{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.250 |
|
| \begin{align*}
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{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.899 |
|
| \begin{align*}
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{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.710 |
|
| \begin{align*}
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{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
21.969 |
|
| \begin{align*}
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{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
22.717 |
|
| \begin{align*}
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{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.917 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}-3 x_{2} \\
x_{2}^{\prime }&=-2 x_{1}+2 x_{2} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= 5 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.211 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}-x_{2} \\
x_{2}^{\prime }&=5 x_{1}-3 x_{2} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.207 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}-2 x_{2}+t \\
x_{2}^{\prime }&=2 x_{1}-2 x_{2}+3 \,{\mathrm e}^{t} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 2 \\
x_{2} \left (0\right ) &= 1 \\
\end{align*} | system_of_ODEs | ✓ | ✓ | ✓ | ✓ | 0.214 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}+x_{2}+2 \,{\mathrm e}^{t} \\
x_{2}^{\prime }&=4 x_{1}+x_{2}-{\mathrm e}^{t} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.195 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}-4 x_{2}+{\mathrm e}^{t} \\
x_{2}^{\prime }&=x_{1}-x_{2}+{\mathrm e}^{t} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.183 |
|
| \begin{align*}
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{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= -1 \\
x_{2} \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
147.855 |
|
| \begin{align*}
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{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.300 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{2}+f_{1} \left (t \right ) \\
x_{2}^{\prime }&=-x_{1}+f_{2} \left (t \right ) \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.200 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}-2 x_{2} \\
x_{2}^{\prime }&=4 x_{1}-2 x_{2}+\delta \left (t -\pi \right ) \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.377 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}-2 x_{2}+1-\operatorname {Heaviside}\left (t -\pi \right ) \\
x_{2}^{\prime }&=2 x_{1}-2 x_{2} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.368 |
|
| \begin{align*}
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{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 0 \\
x_{3} \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.331 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}+x_{3}+{\mathrm e}^{2 t} \\
x_{2}^{\prime }&=2 x_{2} \\
x_{3}^{\prime }&=3 x_{3}+{\mathrm e}^{2 t} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 1 \\
x_{3} \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.283 |
|
| \begin{align*}
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{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= 0 \\
x_{3} \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✗ |
0.376 |
|
| \begin{align*}
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{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= 1 \\
x_{3} \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.325 |
|
| \begin{align*}
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{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 1 \\
x_{3} \left (0\right ) &= 1 \\
x_{4} \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.375 |
|
| \begin{align*}
x^{\prime }&=x-x^{2}-2 x y \\
y^{\prime }&=2 y-2 y^{2}-3 x y \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
✗ |
0.040 |
|
| \begin{align*}
x^{\prime }&=-b x y+m \\
y^{\prime }&=b x y-g y \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
✗ |
0.036 |
|
| \begin{align*}
x^{\prime }&=a x-b x y \\
y^{\prime }&=-c y+d x y \\
z^{\prime }&=z+x^{2}+y^{2} \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✗ |
0.046 |
|
| \begin{align*}
x^{\prime }&=-x-x \,y^{2} \\
y^{\prime }&=-y-y \,x^{2} \\
z^{\prime }&=1-z+x^{2} \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✗ |
0.056 |
|
| \begin{align*}
x^{\prime }&=x \,y^{2}-x \\
y^{\prime }&=x \sin \left (\pi y\right ) \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✗ |
0.036 |
|
| \begin{align*}
x^{\prime }&=\cos \left (y\right ) \\
y^{\prime }&=\sin \left (x\right )-1 \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✗ |
0.036 |
|
| \begin{align*}
x^{\prime }&=-1-y-{\mathrm e}^{x} \\
y^{\prime }&=x^{2}+y \left ({\mathrm e}^{x}-1\right ) \\
z^{\prime }&=x+\sin \left (z\right ) \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
✗ |
0.047 |
|
| \begin{align*}
x^{\prime }&=x-y^{2} \\
y^{\prime }&=x^{2}-y \\
z^{\prime }&={\mathrm e}^{z}-x \\
\end{align*} | system_of_ODEs | ✗ | ✓ | ✓ | ✗ | 0.060 |
|
| \begin{align*}
x^{\prime }&=x-y \\
y^{\prime }&=2 x-y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.425 |
|
| \begin{align*}
x^{\prime }&=x+y+z-2 \,{\mathrm e}^{-t} \\
y^{\prime }&=2 x+y-z-2 \,{\mathrm e}^{-t} \\
z^{\prime }&=-3 x+2 y+4 z+3 \,{\mathrm e}^{-t} \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
z \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.942 |
|
| \begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=-2 x-2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.362 |
|
| \begin{align*}
x^{\prime }&=-3 x-4 y \\
y^{\prime }&=2 x+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.528 |
|
| \begin{align*}
x^{\prime }&=-5 x+3 y \\
y^{\prime }&=-x+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.559 |
|