| # |
ODE |
Solved |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
x^{\prime }&=2 x+y \\
y^{\prime }&=6 x+3 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.363 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.336 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.290 |
|
| \begin{align*}
x^{\prime }&=-2 y \\
y^{\prime }&=2 x \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.365 |
|
| \begin{align*}
x^{\prime }&=10 y \\
y^{\prime }&=-10 x \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 3 \\
y \left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.392 |
|
| \begin{align*}
x^{\prime }&=\frac {y}{2} \\
y^{\prime }&=-8 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.361 |
|
| \begin{align*}
x^{\prime }&=8 y \\
y^{\prime }&=-2 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.339 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=6 x-y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.388 |
|
| \begin{align*}
x^{\prime }&=-y \\
y^{\prime }&=10 x-7 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= -7 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.405 |
|
| \begin{align*}
x^{\prime }&=-y \\
y^{\prime }&=13 x+4 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-9 x+6 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.306 |
|
| \begin{align*}
10 x_{1}^{\prime }&=-x_{1}+x_{3} \\
10 x_{2}^{\prime }&=x_{1}-x_{2} \\
10 x_{3}^{\prime }&=x_{2}-x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.143 |
|
| \begin{align*}
x^{\prime }&=-x+3 y \\
y^{\prime }&=2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.296 |
|
| \begin{align*}
x^{\prime }&=x-2 y \\
y^{\prime }&=2 x-3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.289 |
|
| \begin{align*}
x^{\prime }&=-3 x+2 y \\
y^{\prime }&=-3 x+4 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.392 |
|
| \begin{align*}
x^{\prime }&=3 x-y \\
y^{\prime }&=5 x-3 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.391 |
|
| \begin{align*}
x^{\prime }&=-3 x-4 y \\
y^{\prime }&=2 x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.469 |
|
| \begin{align*}
x^{\prime }&=x+9 y \\
y^{\prime }&=-2 x-5 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 3 \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.529 |
|
| \begin{align*}
x^{\prime }&=4 x+y+2 t \\
y^{\prime }&=-2 x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.605 |
|
| \begin{align*}
x^{\prime }&=2 x+y \\
y^{\prime }&=x+2 y-{\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.517 |
|
| \begin{align*}
x^{\prime }&=2 x-3 y+2 \sin \left (2 t \right ) \\
y^{\prime }&=x-2 y-\cos \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.891 |
|
| \begin{align*}
x^{\prime }+2 y^{\prime }&=4 x+5 y \\
2 x^{\prime }-y^{\prime }&=3 x \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| \begin{align*}
-x^{\prime }+2 y^{\prime }&=x+3 y+{\mathrm e}^{t} \\
3 x^{\prime }-4 y^{\prime }&=x-15 y+{\mathrm e}^{-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.859 |
|
| \begin{align*}
x^{\prime }&=x+2 y+z \\
y^{\prime }&=6 x-y \\
z^{\prime }&=-x-2 y-z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| \begin{align*}
x^{\prime }&=x-2 y \\
y^{\prime }&=-4 x+4 y-2 z \\
z^{\prime }&=-4 y+4 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
49.079 |
|
| \begin{align*}
x^{\prime }&=y+z+{\mathrm e}^{-t} \\
y^{\prime }&=x+z \\
z^{\prime }&=x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.792 |
|
| \begin{align*}
x^{\prime }&=-3 y \\
y^{\prime }&=3 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.336 |
|
| \begin{align*}
x^{\prime }&=3 x-2 y \\
y^{\prime }&=2 x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.750 |
|
| \begin{align*}
x^{\prime }&=2 x+4 y+3 \,{\mathrm e}^{t} \\
y^{\prime }&=5 x-y-t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.349 |
|
| \begin{align*}
x^{\prime }&=t x-{\mathrm e}^{t} y+\cos \left (t \right ) \\
y^{\prime }&={\mathrm e}^{-t} x+t^{2} y-\sin \left (t \right ) \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
0.031 |
|
| \begin{align*}
x^{\prime }&=y+z \\
y^{\prime }&=x+z \\
z^{\prime }&=x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.484 |
|
| \begin{align*}
x^{\prime }&=2 x-3 y \\
y^{\prime }&=x+y+2 z \\
z^{\prime }&=5 y-7 z \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.174 |
|
| \begin{align*}
x^{\prime }&=3 x-4 y+z+t \\
y^{\prime }&=x-3 z+t^{2} \\
z^{\prime }&=6 y-7 z+t^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
103.830 |
|
| \begin{align*}
x^{\prime }&=t x-y+{\mathrm e}^{t} z \\
y^{\prime }&=2 x+t^{2} y-z \\
z^{\prime }&={\mathrm e}^{-t} x+3 t y+t^{3} z \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.038 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{2} \\
x_{2}^{\prime }&=2 x_{3} \\
x_{3}^{\prime }&=3 x_{4} \\
x_{4}^{\prime }&=4 x_{1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.823 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{2}+x_{3}+1 \\
x_{2}^{\prime }&=x_{3}+x_{4}+t \\
x_{3}^{\prime }&=x_{1}+x_{4}+t^{2} \\
x_{4}^{\prime }&=x_{1}+x_{2}+t^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.112 |
|
| \begin{align*}
x_{1}^{\prime }&=4 x_{1}+2 x_{2} \\
x_{2}^{\prime }&=-3 x_{1}-x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.335 |
|
| \begin{align*}
x_{1}^{\prime }&=-3 x_{1}+2 x_{2} \\
x_{2}^{\prime }&=-3 x_{1}+4 x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.401 |
|
| \begin{align*}
x_{1}^{\prime }&=3 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 ) &= 5 \\
x_{2} \left (0\right ) &= -3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.400 |
|
| \begin{align*}
x_{1}^{\prime }&=4 x_{1}+x_{2} \\
x_{2}^{\prime }&=-2 x_{1}+x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 11 \\
x_{2} \left (0\right ) &= -7 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.416 |
|
| \begin{align*}
x_{1}^{\prime }&=4 x_{1}-3 x_{2} \\
x_{2}^{\prime }&=6 x_{1}-7 x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 8 \\
x_{2} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.435 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}-2 x_{2} \\
x_{2}^{\prime }&=-x_{1}+3 x_{2}-2 x_{3} \\
x_{3}^{\prime }&=-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 ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.674 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{2}+x_{3} \\
x_{2}^{\prime }&=x_{1}+x_{3} \\
x_{3}^{\prime }&=x_{1}+x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 10 \\
x_{2} \left (0\right ) &= 12 \\
x_{3} \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}+2 x_{2}+x_{3} \\
x_{2}^{\prime }&=6 x_{1}-x_{2} \\
x_{3}^{\prime }&=-x_{1}-2 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 ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.655 |
|
| \begin{align*}
x_{1}^{\prime }&=-8 x_{1}-11 x_{2}-2 x_{3} \\
x_{2}^{\prime }&=6 x_{1}+9 x_{2}+2 x_{3} \\
x_{3}^{\prime }&=-6 x_{1}-6 x_{2}+x_{3} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 5 \\
x_{2} \left (0\right ) &= -7 \\
x_{3} \left (0\right ) &= 11 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.711 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}-4 x_{2}-2 x_{4} \\
x_{2}^{\prime }&=x_{2} \\
x_{3}^{\prime }&=6 x_{1}-12 x_{2}-x_{3}-6 x_{4} \\
x_{4}^{\prime }&=-4 x_{2}-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*} |
✓ |
✓ |
✓ |
✓ |
0.792 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}+2 x_{2} \\
x_{2}^{\prime }&=2 x_{1}+x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.340 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}+3 x_{2} \\
x_{2}^{\prime }&=2 x_{1}+x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.376 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}+4 x_{2} \\
x_{2}^{\prime }&=3 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*} |
✓ |
✓ |
✓ |
✓ |
0.410 |
|
| \begin{align*}
x_{1}^{\prime }&=4 x_{1}+x_{2} \\
x_{2}^{\prime }&=6 x_{1}-x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.385 |
|
| \begin{align*}
x_{1}^{\prime }&=6 x_{1}-7 x_{2} \\
x_{2}^{\prime }&=x_{1}-2 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.372 |
|
| \begin{align*}
x_{1}^{\prime }&=9 x_{1}+5 x_{2} \\
x_{2}^{\prime }&=-6 x_{1}-2 x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.415 |
|
| \begin{align*}
x_{1}^{\prime }&=-3 x_{1}+4 x_{2} \\
x_{2}^{\prime }&=6 x_{1}-5 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.386 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}-5 x_{2} \\
x_{2}^{\prime }&=x_{1}-x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.395 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}-5 x_{2} \\
x_{2}^{\prime }&=4 x_{1}-2 x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 2 \\
x_{2} \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.437 |
|
| \begin{align*}
x_{1}^{\prime }&=-3 x_{1}-2 x_{2} \\
x_{2}^{\prime }&=9 x_{1}+3 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.406 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}-2 x_{2} \\
x_{2}^{\prime }&=2 x_{1}+x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.395 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}-5 x_{2} \\
x_{2}^{\prime }&=x_{1}+3 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.505 |
|
| \begin{align*}
x_{1}^{\prime }&=5 x_{1}-9 x_{2} \\
x_{2}^{\prime }&=2 x_{1}-x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.522 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}-4 x_{2} \\
x_{2}^{\prime }&=4 x_{1}+3 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.386 |
|
| \begin{align*}
x_{1}^{\prime }&=7 x_{1}-5 x_{2} \\
x_{2}^{\prime }&=4 x_{1}+3 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.533 |
|
| \begin{align*}
x_{1}^{\prime }&=-50 x_{1}+20 x_{2} \\
x_{2}^{\prime }&=100 x_{1}-60 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.398 |
|
| \begin{align*}
x_{1}^{\prime }&=4 x_{1}+x_{2}+4 x_{3} \\
x_{2}^{\prime }&=x_{1}+7 x_{2}+x_{3} \\
x_{3}^{\prime }&=4 x_{1}+x_{2}+4 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.625 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}+2 x_{2}+2 x_{3} \\
x_{2}^{\prime }&=2 x_{1}+7 x_{2}+x_{3} \\
x_{3}^{\prime }&=2 x_{1}+x_{2}+7 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.644 |
|
| \begin{align*}
x_{1}^{\prime }&=4 x_{1}+x_{2}+x_{3} \\
x_{2}^{\prime }&=x_{1}+4 x_{2}+x_{3} \\
x_{3}^{\prime }&=x_{1}+x_{2}+4 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.526 |
|
| \begin{align*}
x_{1}^{\prime }&=5 x_{1}+x_{2}+3 x_{3} \\
x_{2}^{\prime }&=x_{1}+7 x_{2}+x_{3} \\
x_{3}^{\prime }&=3 x_{1}+x_{2}+5 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.653 |
|
| \begin{align*}
x_{1}^{\prime }&=5 x_{1}-6 x_{3} \\
x_{2}^{\prime }&=2 x_{1}-x_{2}-2 x_{3} \\
x_{3}^{\prime }&=4 x_{1}-2 x_{2}-4 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.692 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}+2 x_{2}+2 x_{3} \\
x_{2}^{\prime }&=-5 x_{1}-4 x_{2}-2 x_{3} \\
x_{3}^{\prime }&=5 x_{1}+5 x_{2}+3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.635 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}+x_{2}+x_{3} \\
x_{2}^{\prime }&=-5 x_{1}-3 x_{2}-x_{3} \\
x_{3}^{\prime }&=5 x_{1}+5 x_{2}+3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.638 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}+x_{2}-x_{3} \\
x_{2}^{\prime }&=-4 x_{1}-3 x_{2}-x_{3} \\
x_{3}^{\prime }&=4 x_{1}+4 x_{2}+2 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.809 |
|
| \begin{align*}
x_{1}^{\prime }&=5 x_{1}+5 x_{2}+2 x_{3} \\
x_{2}^{\prime }&=-6 x_{1}-6 x_{2}-5 x_{3} \\
x_{3}^{\prime }&=6 x_{1}+6 x_{2}+5 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.900 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}+x_{3} \\
x_{2}^{\prime }&=9 x_{1}-x_{2}+2 x_{3} \\
x_{3}^{\prime }&=-9 x_{1}+4 x_{2}-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 ) &= 17 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.971 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1} \\
x_{2}^{\prime }&=2 x_{1}+2 x_{2} \\
x_{3}^{\prime }&=3 x_{2}+3 x_{3} \\
x_{4}^{\prime }&=4 x_{3}+4 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.053 |
|
| \begin{align*}
x_{1}^{\prime }&=-2 x_{1}+9 x_{4} \\
x_{2}^{\prime }&=4 x_{1}+2 x_{2}-10 x_{4} \\
x_{3}^{\prime }&=-x_{3}+8 x_{4} \\
x_{4}^{\prime }&=x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.071 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1} \\
x_{2}^{\prime }&=-21 x_{1}-5 x_{2}-27 x_{3}-9 x_{4} \\
x_{3}^{\prime }&=5 x_{3} \\
x_{4}^{\prime }&=-21 x_{3}-2 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.152 |
|
| \begin{align*}
x_{1}^{\prime }&=4 x_{1}+x_{2}+x_{3}+7 x_{4} \\
x_{2}^{\prime }&=x_{1}+4 x_{2}+10 x_{3}+x_{4} \\
x_{3}^{\prime }&=x_{1}+10 x_{2}+4 x_{3}+x_{4} \\
x_{4}^{\prime }&=7 x_{1}+x_{2}+x_{3}+4 x_{4} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 3 \\
x_{2} \left (0\right ) &= 1 \\
x_{3} \left (0\right ) &= 1 \\
x_{4} \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.098 |
|
| \begin{align*}
x^{\prime }&=-3 y \\
y^{\prime }&=3 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.377 |
|
| \begin{align*}
x^{\prime }&=3 x-2 y \\
y^{\prime }&=2 x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.836 |
|
| \begin{align*}
x^{\prime }&=2 x+4 y+3 \,{\mathrm e}^{t} \\
y^{\prime }&=5 x-y-t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.342 |
|
| \begin{align*}
x^{\prime }&=y+z \\
y^{\prime }&=x+z \\
z^{\prime }&=x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.524 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{2} \\
x_{2}^{\prime }&=2 x_{3} \\
x_{3}^{\prime }&=3 x_{4} \\
x_{4}^{\prime }&=4 x_{1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.928 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{2}+x_{3}+1 \\
x_{2}^{\prime }&=x_{3}+x_{4}+t \\
x_{3}^{\prime }&=x_{1}+x_{4}+t^{2} \\
x_{4}^{\prime }&=x_{1}+x_{2}+t^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.143 |
|
| \begin{align*}
x_{1}^{\prime }&=6 x_{1} \\
x_{2}^{\prime }&=-3 x_{1}-x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.382 |
|
| \begin{align*}
x_{1}^{\prime }&=-3 x_{1}+2 x_{2} \\
x_{2}^{\prime }&=-3 x_{1}+4 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.404 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}+2 x_{2} \\
x_{2}^{\prime }&=2 x_{1}+x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.366 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}+3 x_{2} \\
x_{2}^{\prime }&=2 x_{1}+x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.398 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}+4 x_{2} \\
x_{2}^{\prime }&=3 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*} |
✓ |
✓ |
✓ |
✓ |
0.430 |
|
| \begin{align*}
x_{1}^{\prime }&=4 x_{1}+x_{2} \\
x_{2}^{\prime }&=6 x_{1}-x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.393 |
|
| \begin{align*}
x_{1}^{\prime }&=6 x_{1}-7 x_{2} \\
x_{2}^{\prime }&=x_{1}-2 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.379 |
|
| \begin{align*}
x_{1}^{\prime }&=9 x_{1}+5 x_{2} \\
x_{2}^{\prime }&=-6 x_{1}-2 x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.416 |
|
| \begin{align*}
x_{1}^{\prime }&=-3 x_{1}+4 x_{2} \\
x_{2}^{\prime }&=6 x_{1}-5 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.394 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}-5 x_{2} \\
x_{2}^{\prime }&=x_{1}-x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.429 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}-5 x_{2} \\
x_{2}^{\prime }&=4 x_{1}-2 x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 2 \\
x_{2} \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.458 |
|
| \begin{align*}
x_{1}^{\prime }&=-3 x_{1}-2 x_{2} \\
x_{2}^{\prime }&=9 x_{1}+3 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.432 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}-2 x_{2} \\
x_{2}^{\prime }&=2 x_{1}+x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.422 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}-5 x_{2} \\
x_{2}^{\prime }&=x_{1}+3 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.530 |
|
| \begin{align*}
x_{1}^{\prime }&=5 x_{1}-9 x_{2} \\
x_{2}^{\prime }&=2 x_{1}-x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.553 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}-4 x_{2} \\
x_{2}^{\prime }&=4 x_{1}+3 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.414 |
|
| \begin{align*}
x_{1}^{\prime }&=7 x_{1}-5 x_{2} \\
x_{2}^{\prime }&=4 x_{1}+3 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.552 |
|
| \begin{align*}
x_{1}^{\prime }&=-50 x_{1}+20 x_{2} \\
x_{2}^{\prime }&=100 x_{1}-60 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.404 |
|
| \begin{align*}
x_{1}^{\prime }&=4 x_{1}+x_{2}+4 x_{3} \\
x_{2}^{\prime }&=x_{1}+7 x_{2}+x_{3} \\
x_{3}^{\prime }&=4 x_{1}+x_{2}+4 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.672 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}+2 x_{2}+2 x_{3} \\
x_{2}^{\prime }&=2 x_{1}+7 x_{2}+x_{3} \\
x_{3}^{\prime }&=2 x_{1}+x_{2}+7 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.668 |
|
| \begin{align*}
x_{1}^{\prime }&=4 x_{1}+x_{2}+x_{3} \\
x_{2}^{\prime }&=x_{1}+4 x_{2}+x_{3} \\
x_{3}^{\prime }&=x_{1}+x_{2}+4 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.539 |
|
| \begin{align*}
x_{1}^{\prime }&=5 x_{1}+x_{2}+3 x_{3} \\
x_{2}^{\prime }&=x_{1}+7 x_{2}+x_{3} \\
x_{3}^{\prime }&=3 x_{1}+x_{2}+5 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.662 |
|
| \begin{align*}
x_{1}^{\prime }&=5 x_{1}-6 x_{3} \\
x_{2}^{\prime }&=2 x_{1}-x_{2}-2 x_{3} \\
x_{3}^{\prime }&=4 x_{1}-2 x_{2}-4 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.714 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}+2 x_{2}+2 x_{3} \\
x_{2}^{\prime }&=-5 x_{1}-4 x_{2}-2 x_{3} \\
x_{3}^{\prime }&=5 x_{1}+5 x_{2}+3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.662 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}+x_{2}+x_{3} \\
x_{2}^{\prime }&=-5 x_{1}-3 x_{2}-x_{3} \\
x_{3}^{\prime }&=5 x_{1}+5 x_{2}+3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.641 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}+x_{2}-x_{3} \\
x_{2}^{\prime }&=-4 x_{1}-3 x_{2}-x_{3} \\
x_{3}^{\prime }&=4 x_{1}+4 x_{2}+2 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.815 |
|
| \begin{align*}
x_{1}^{\prime }&=5 x_{1}+5 x_{2}+2 x_{3} \\
x_{2}^{\prime }&=-6 x_{1}-6 x_{2}-5 x_{3} \\
x_{3}^{\prime }&=6 x_{1}+6 x_{2}+5 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.876 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}+x_{3} \\
x_{2}^{\prime }&=9 x_{1}-x_{2}+2 x_{3} \\
x_{3}^{\prime }&=-9 x_{1}+4 x_{2}-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 ) &= 17 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.897 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1} \\
x_{2}^{\prime }&=2 x_{1}+2 x_{2} \\
x_{3}^{\prime }&=3 x_{2}+3 x_{3} \\
x_{4}^{\prime }&=4 x_{3}+4 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.050 |
|
| \begin{align*}
x_{1}^{\prime }&=-2 x_{1}+9 x_{4} \\
x_{2}^{\prime }&=4 x_{1}+2 x_{2}-10 x_{4} \\
x_{3}^{\prime }&=-x_{3}+8 x_{4} \\
x_{4}^{\prime }&=x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.046 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1} \\
x_{2}^{\prime }&=-21 x_{1}-5 x_{2}-27 x_{3}-9 x_{4} \\
x_{3}^{\prime }&=5 x_{3} \\
x_{4}^{\prime }&=-21 x_{3}-2 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.193 |
|
| \begin{align*}
x_{1}^{\prime }&=4 x_{1}+x_{2}+x_{3}+7 x_{4} \\
x_{2}^{\prime }&=x_{1}+4 x_{2}+10 x_{3}+x_{4} \\
x_{3}^{\prime }&=x_{1}+10 x_{2}+4 x_{3}+x_{4} \\
x_{4}^{\prime }&=7 x_{1}+x_{2}+x_{3}+4 x_{4} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 3 \\
x_{2} \left (0\right ) &= 1 \\
x_{3} \left (0\right ) &= 1 \\
x_{4} \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.114 |
|
| \begin{align*}
x_{1}^{\prime }&=-40 x_{1}-12 x_{2}+54 x_{3} \\
x_{2}^{\prime }&=35 x_{1}+13 x_{2}-46 x_{3} \\
x_{3}^{\prime }&=-25 x_{1}-7 x_{2}+34 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.757 |
|
| \begin{align*}
x_{1}^{\prime }&=-20 x_{1}+11 x_{2}+13 x_{3} \\
x_{2}^{\prime }&=12 x_{1}-x_{2}-7 x_{3} \\
x_{3}^{\prime }&=-48 x_{1}+21 x_{2}+31 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.800 |
|
| \begin{align*}
x_{1}^{\prime }&=147 x_{1}+23 x_{2}-202 x_{3} \\
x_{2}^{\prime }&=-90 x_{1}-9 x_{2}+129 x_{3} \\
x_{3}^{\prime }&=90 x_{1}+15 x_{2}-123 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.833 |
|
| \begin{align*}
x_{1}^{\prime }&=9 x_{1}-7 x_{2}-5 x_{3} \\
x_{2}^{\prime }&=-12 x_{1}+7 x_{2}+11 x_{3}+9 x_{4} \\
x_{3}^{\prime }&=24 x_{1}-17 x_{2}-19 x_{3}-9 x_{4} \\
x_{4}^{\prime }&=-18 x_{1}+13 x_{2}+17 x_{3}+9 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.185 |
|
| \begin{align*}
x_{1}^{\prime }&=13 x_{1}-42 x_{2}+106 x_{3}+139 x_{4} \\
x_{2}^{\prime }&=2 x_{1}-16 x_{2}+52 x_{3}+70 x_{4} \\
x_{3}^{\prime }&=x_{1}+6 x_{2}-20 x_{3}-31 x_{4} \\
x_{4}^{\prime }&=-x_{1}-6 x_{2}+22 x_{3}+33 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.575 |
|
| \begin{align*}
x_{1}^{\prime }&=23 x_{1}-18 x_{2}-16 x_{3} \\
x_{2}^{\prime }&=-8 x_{1}+6 x_{2}+7 x_{3}+9 x_{4} \\
x_{3}^{\prime }&=34 x_{1}-27 x_{2}-26 x_{3}-9 x_{4} \\
x_{4}^{\prime }&=-26 x_{1}+21 x_{2}+25 x_{3}+12 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.430 |
|
| \begin{align*}
x_{1}^{\prime }&=47 x_{1}-8 x_{2}+5 x_{3}-5 x_{4} \\
x_{2}^{\prime }&=-10 x_{1}+32 x_{2}+18 x_{3}-2 x_{4} \\
x_{3}^{\prime }&=139 x_{1}-40 x_{2}-167 x_{3}-121 x_{4} \\
x_{4}^{\prime }&=-232 x_{1}+64 x_{2}+360 x_{3}+248 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.654 |
|
| \begin{align*}
x_{1}^{\prime }&=139 x_{1}-14 x_{2}-52 x_{3}-14 x_{4}+28 x_{5} \\
x_{2}^{\prime }&=-22 x_{1}+5 x_{2}+7 x_{3}+8 x_{4}-7 x_{5} \\
x_{3}^{\prime }&=370 x_{1}-38 x_{2}-139 x_{3}-38 x_{4}+76 x_{5} \\
x_{4}^{\prime }&=152 x_{1}-16 x_{2}-59 x_{3}-13 x_{4}+35 x_{5} \\
x_{5}^{\prime }&=95 x_{1}-10 x_{2}-38 x_{3}-7 x_{4}+23 x_{5} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.257 |
|
| \begin{align*}
x_{1}^{\prime }&=9 x_{1}+13 x_{2}-13 x_{6} \\
x_{2}^{\prime }&=-14 x_{1}+19 x_{2}-10 x_{3}-20 x_{4}+10 x_{5}+4 x_{6} \\
x_{3}^{\prime }&=-30 x_{1}+12 x_{2}-7 x_{3}-30 x_{4}+12 x_{5}+18 x_{6} \\
x_{4}^{\prime }&=-12 x_{1}+10 x_{2}-10 x_{3}-9 x_{4}+10 x_{5}+2 x_{6} \\
x_{5}^{\prime }&=6 x_{1}+9 x_{2}+6 x_{4}+5 x_{5}-15 x_{6} \\
x_{6}^{\prime }&=-14 x_{1}+23 x_{2}-10 x_{3}-20 x_{4}+10 x_{5} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.504 |
|
| \begin{align*}
x_{1}^{\prime }&=9 x_{1}+4 x_{2} \\
x_{2}^{\prime }&=-6 x_{1}-x_{2} \\
x_{3}^{\prime }&=6 x_{1}+4 x_{2}+3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.616 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}-3 x_{2} \\
x_{2}^{\prime }&=3 x_{1}+7 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.356 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{2}+2 x_{3} \\
x_{2}^{\prime }&=-5 x_{1}-3 x_{2}-7 x_{3} \\
x_{3}^{\prime }&=x_{1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.638 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{3} \\
x_{2}^{\prime }&=x_{4} \\
x_{3}^{\prime }&=-2 x_{1}+2 x_{2}-3 x_{3}+x_{4} \\
x_{4}^{\prime }&=2 x_{1}-2 x_{2}+x_{3}-3 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.979 |
|
| \begin{align*}
x_{1}^{\prime }&=-2 x_{1}+x_{2} \\
x_{2}^{\prime }&=-x_{1}-4 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.353 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}-x_{2} \\
x_{2}^{\prime }&=x_{1}+x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.345 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}-2 x_{2} \\
x_{2}^{\prime }&=2 x_{1}+5 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.352 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}-x_{2} \\
x_{2}^{\prime }&=x_{1}+5 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.335 |
|
| \begin{align*}
x_{1}^{\prime }&=7 x_{1}+x_{2} \\
x_{2}^{\prime }&=-4 x_{1}+3 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.366 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}-4 x_{2} \\
x_{2}^{\prime }&=4 x_{1}+9 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.362 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1} \\
x_{2}^{\prime }&=-7 x_{1}+9 x_{2}+7 x_{3} \\
x_{3}^{\prime }&=2 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.524 |
|
| \begin{align*}
x_{1}^{\prime }&=25 x_{1}+12 x_{2} \\
x_{2}^{\prime }&=-18 x_{1}-5 x_{2} \\
x_{3}^{\prime }&=6 x_{1}+6 x_{2}+13 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.652 |
|
| \begin{align*}
x_{1}^{\prime }&=-19 x_{1}+12 x_{2}+84 x_{3} \\
x_{2}^{\prime }&=5 x_{2} \\
x_{3}^{\prime }&=-8 x_{1}+4 x_{2}+33 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.641 |
|
| \begin{align*}
x_{1}^{\prime }&=-13 x_{1}+40 x_{2}-48 x_{3} \\
x_{2}^{\prime }&=-8 x_{1}+23 x_{2}-24 x_{3} \\
x_{3}^{\prime }&=3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.647 |
|
| \begin{align*}
x_{1}^{\prime }&=-3 x_{1}-4 x_{3} \\
x_{2}^{\prime }&=-x_{1}-x_{2}-x_{3} \\
x_{3}^{\prime }&=x_{1}+x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.546 |
|
| \begin{align*}
x_{1}^{\prime }&=-x_{1}+x_{3} \\
x_{2}^{\prime }&=-x_{2}+x_{3} \\
x_{3}^{\prime }&=x_{1}-x_{2}-x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.530 |
|
| \begin{align*}
x_{1}^{\prime }&=-x_{1}+x_{3} \\
x_{2}^{\prime }&=x_{2}-4 x_{3} \\
x_{3}^{\prime }&=x_{2}-3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.514 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{3} \\
x_{2}^{\prime }&=-5 x_{1}-x_{2}-5 x_{3} \\
x_{3}^{\prime }&=4 x_{1}+x_{2}-2 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.635 |
|
| \begin{align*}
x_{1}^{\prime }&=-2 x_{1}-9 x_{2} \\
x_{2}^{\prime }&=x_{1}+4 x_{2} \\
x_{3}^{\prime }&=x_{1}+3 x_{2}+x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.579 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1} \\
x_{2}^{\prime }&=-2 x_{1}-2 x_{2}-3 x_{3} \\
x_{3}^{\prime }&=2 x_{1}+3 x_{2}+4 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.602 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1} \\
x_{2}^{\prime }&=18 x_{1}+7 x_{2}+4 x_{3} \\
x_{3}^{\prime }&=-27 x_{1}-9 x_{2}-5 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.628 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1} \\
x_{2}^{\prime }&=x_{1}+3 x_{2}+x_{3} \\
x_{3}^{\prime }&=-2 x_{1}-4 x_{2}-x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.574 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}-4 x_{2}-2 x_{4} \\
x_{2}^{\prime }&=x_{2} \\
x_{3}^{\prime }&=6 x_{1}-12 x_{2}-x_{3}-6 x_{4} \\
x_{4}^{\prime }&=-4 x_{2}-x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.769 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}+x_{2}+x_{4} \\
x_{2}^{\prime }&=2 x_{2}+x_{3} \\
x_{3}^{\prime }&=2 x_{3}+x_{4} \\
x_{4}^{\prime }&=2 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.758 |
|
| \begin{align*}
x_{1}^{\prime }&=-x_{1}-4 x_{2} \\
x_{2}^{\prime }&=x_{1}+3 x_{2} \\
x_{3}^{\prime }&=x_{1}+2 x_{2}+x_{3} \\
x_{4}^{\prime }&=x_{2}+x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.651 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}+3 x_{2}+7 x_{3} \\
x_{2}^{\prime }&=-x_{2}-4 x_{3} \\
x_{3}^{\prime }&=x_{2}+3 x_{3} \\
x_{4}^{\prime }&=-6 x_{2}-14 x_{3}+x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.704 |
|
| \begin{align*}
x_{1}^{\prime }&=39 x_{1}+8 x_{2}-16 x_{3} \\
x_{2}^{\prime }&=-36 x_{1}-5 x_{2}+16 x_{3} \\
x_{3}^{\prime }&=72 x_{1}+16 x_{2}-29 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.710 |
|
| \begin{align*}
x_{1}^{\prime }&=28 x_{1}+50 x_{2}+100 x_{3} \\
x_{2}^{\prime }&=15 x_{1}+33 x_{2}+60 x_{3} \\
x_{3}^{\prime }&=-15 x_{1}-30 x_{2}-57 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.701 |
|
| \begin{align*}
x_{1}^{\prime }&=-2 x_{1}+17 x_{2}+4 x_{3} \\
x_{2}^{\prime }&=-x_{1}+6 x_{2}+x_{3} \\
x_{3}^{\prime }&=x_{2}+2 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.577 |
|
| \begin{align*}
x_{1}^{\prime }&=5 x_{1}-x_{2}+x_{3} \\
x_{2}^{\prime }&=x_{1}+3 x_{2} \\
x_{3}^{\prime }&=-3 x_{1}+2 x_{2}+x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.590 |
|
| \begin{align*}
x_{1}^{\prime }&=-3 x_{1}+5 x_{2}-5 x_{3} \\
x_{2}^{\prime }&=3 x_{1}-x_{2}+3 x_{3} \\
x_{3}^{\prime }&=8 x_{1}-8 x_{2}+10 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.632 |
|
| \begin{align*}
x_{1}^{\prime }&=-15 x_{1}-7 x_{2}+4 x_{3} \\
x_{2}^{\prime }&=34 x_{1}+16 x_{2}-11 x_{3} \\
x_{3}^{\prime }&=17 x_{1}+7 x_{2}+5 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| \begin{align*}
x_{1}^{\prime }&=-x_{1}+x_{2}+x_{3}-2 x_{4} \\
x_{2}^{\prime }&=7 x_{1}-4 x_{2}-6 x_{3}+11 x_{4} \\
x_{3}^{\prime }&=5 x_{1}-x_{2}+x_{3}+3 x_{4} \\
x_{4}^{\prime }&=6 x_{1}-2 x_{2}-2 x_{3}+6 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.208 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}+x_{2}-2 x_{3}+x_{4} \\
x_{2}^{\prime }&=3 x_{2}-5 x_{3}+3 x_{4} \\
x_{3}^{\prime }&=-13 x_{2}+22 x_{3}-12 x_{4} \\
x_{4}^{\prime }&=-27 x_{2}+45 x_{3}-25 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.134 |
|
| \begin{align*}
x_{1}^{\prime }&=35 x_{1}-12 x_{2}+4 x_{3}+30 x_{4} \\
x_{2}^{\prime }&=22 x_{1}-8 x_{2}+3 x_{3}+19 x_{4} \\
x_{3}^{\prime }&=-10 x_{1}+3 x_{2}-9 x_{4} \\
x_{4}^{\prime }&=-27 x_{1}+9 x_{2}-3 x_{3}-23 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.970 |
|
| \begin{align*}
x_{1}^{\prime }&=11 x_{1}-x_{2}+26 x_{3}+6 x_{4}-3 x_{5} \\
x_{2}^{\prime }&=3 x_{2} \\
x_{3}^{\prime }&=-9 x_{1}-24 x_{3}-6 x_{4}+3 x_{5} \\
x_{4}^{\prime }&=3 x_{1}+9 x_{3}+5 x_{4}-x_{5} \\
x_{5}^{\prime }&=-48 x_{1}-3 x_{2}-138 x_{3}-30 x_{4}+18 x_{5} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.459 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}-4 x_{2}+x_{3} \\
x_{2}^{\prime }&=4 x_{1}+3 x_{2}+x_{4} \\
x_{3}^{\prime }&=3 x_{3}-4 x_{4} \\
x_{4}^{\prime }&=4 x_{3}+3 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.836 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}-8 x_{3}-3 x_{4} \\
x_{2}^{\prime }&=-18 x_{1}-x_{2} \\
x_{3}^{\prime }&=-9 x_{1}-3 x_{2}-25 x_{3}-9 x_{4} \\
x_{4}^{\prime }&=33 x_{1}+10 x_{2}+90 x_{3}+32 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.504 |
|
| \begin{align*}
x_{1}^{\prime }&=-\frac {x_{1}}{10}+\frac {3 x_{2}}{40} \\
x_{2}^{\prime }&=\frac {x_{1}}{10}-\frac {x_{2}}{5} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= -17 \\
x_{2} \left (0\right ) &= -21 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.507 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}-2 x_{2} \\
x_{2}^{\prime }&=4 x_{1}-x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.602 |
|
| \begin{align*}
x_{1}^{\prime }&=-x_{1}-4 x_{2} \\
x_{2}^{\prime }&=x_{1}-x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.475 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}-5 x_{2} \\
x_{2}^{\prime }&=x_{1}-2 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.453 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}-\frac {5 x_{2}}{2} \\
x_{2}^{\prime }&=\frac {9 x_{1}}{5}-x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.604 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}-x_{2} \\
x_{2}^{\prime }&=5 x_{1}-3 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.602 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}+2 x_{2} \\
x_{2}^{\prime }&=-5 x_{1}-x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.494 |
|
| \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} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.852 |
|
| \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*} |
✓ |
✓ |
✓ |
✓ |
2.468 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}-5 x_{2} \\
x_{2}^{\prime }&=x_{1}-3 x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.582 |
|
| \begin{align*}
x_{1}^{\prime }&=-3 x_{1}+2 x_{2} \\
x_{2}^{\prime }&=-x_{1}-x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.595 |
|
| \begin{align*}
x_{1}^{\prime }&=\frac {3 x_{1}}{4}-2 x_{2} \\
x_{2}^{\prime }&=x_{1}-\frac {5 x_{2}}{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.569 |
|
| \begin{align*}
x_{1}^{\prime }&=-\frac {4 x_{1}}{5}+2 x_{2} \\
x_{2}^{\prime }&=-x_{1}+\frac {6 x_{2}}{5} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.572 |
|
| \begin{align*}
x_{1}^{\prime }&=-\frac {x_{1}}{4}+x_{2} \\
x_{2}^{\prime }&=-x_{1}-\frac {x_{2}}{4} \\
x_{3}^{\prime }&=-\frac {x_{3}}{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.688 |
|
| \begin{align*}
x_{1}^{\prime }&=-\frac {x_{1}}{4}+x_{2} \\
x_{2}^{\prime }&=-x_{1}-\frac {x_{2}}{4} \\
x_{3}^{\prime }&=\frac {x_{3}}{10} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.715 |
|
| \begin{align*}
x_{1}^{\prime }&=-\frac {x_{1}}{2}-\frac {x_{2}}{8} \\
x_{2}^{\prime }&=2 x_{1}-\frac {x_{2}}{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.496 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}-4 x_{2} \\
x_{2}^{\prime }&=x_{1}-x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.379 |
|
| \begin{align*}
x_{1}^{\prime }&=4 x_{1}-2 x_{2} \\
x_{2}^{\prime }&=8 x_{1}-4 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.362 |
|
| \begin{align*}
x_{1}^{\prime }&=-\frac {3 x_{1}}{2}+x_{2} \\
x_{2}^{\prime }&=-\frac {x_{1}}{4}-\frac {x_{2}}{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.385 |
|
| \begin{align*}
x_{1}^{\prime }&=-3 x_{1}+\frac {5 x_{2}}{2} \\
x_{2}^{\prime }&=-\frac {5 x_{1}}{2}+2 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.388 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}+x_{2}+x_{3} \\
x_{2}^{\prime }&=2 x_{1}+x_{2}-x_{3} \\
x_{3}^{\prime }&=-x_{2}+x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.801 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{2}+x_{3} \\
x_{2}^{\prime }&=x_{1}+x_{3} \\
x_{3}^{\prime }&=x_{1}+x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.598 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}-4 x_{2} \\
x_{2}^{\prime }&=4 x_{1}-7 x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 3 \\
x_{2} \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.418 |
|
| \begin{align*}
x_{1}^{\prime }&=-\frac {5 x_{1}}{2}+\frac {3 x_{2}}{2} \\
x_{2}^{\prime }&=-\frac {3 x_{1}}{2}+\frac {x_{2}}{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 3 \\
x_{2} \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.417 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}+\frac {3 x_{2}}{2} \\
x_{2}^{\prime }&=-\frac {3 x_{1}}{2}-x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 3 \\
x_{2} \left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.440 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}+9 x_{2} \\
x_{2}^{\prime }&=-x_{1}-3 x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 2 \\
x_{2} \left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.375 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1} \\
x_{2}^{\prime }&=-4 x_{1}+x_{2} \\
x_{3}^{\prime }&=3 x_{1}+6 x_{2}+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 ) &= -30 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.682 |
|
| \begin{align*}
x_{1}^{\prime }&=-\frac {5 x_{1}}{2}+x_{2}+x_{3} \\
x_{2}^{\prime }&=x_{1}-\frac {5 x_{2}}{2}+x_{3} \\
x_{3}^{\prime }&=x_{1}+x_{2}-\frac {5 x_{3}}{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 2 \\
x_{2} \left (0\right ) &= 3 \\
x_{3} \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.661 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}-x_{2}+{\mathrm e}^{t} \\
x_{2}^{\prime }&=3 x_{1}-2 x_{2}+t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.912 |
|
| \begin{align*}
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{align*} |
✓ |
✓ |
✓ |
✓ |
0.966 |
|
| \begin{align*}
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{align*} |
✓ |
✓ |
✓ |
✓ |
0.967 |
|
| \begin{align*}
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{align*} |
✓ |
✓ |
✓ |
✓ |
0.771 |
|
| \begin{align*}
x_{1}^{\prime }&=4 x_{1}-2 x_{2}+\frac {1}{t^{3}} \\
x_{2}^{\prime }&=8 x_{1}-4 x_{2}-\frac {1}{t^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.625 |
|
| \begin{align*}
x_{1}^{\prime }&=-4 x_{1}+2 x_{2}+\frac {1}{t} \\
x_{2}^{\prime }&=2 x_{1}-x_{2}+\frac {2}{t}+4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.740 |
|
| \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*} |
✓ |
✓ |
✓ |
✓ |
0.746 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}-x_{2}+{\mathrm e}^{t} \\
x_{2}^{\prime }&=3 x_{1}-2 x_{2}-{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.758 |
|
| \begin{align*}
x_{1}^{\prime }&=-\frac {5 x_{1}}{4}+\frac {3 x_{2}}{4}+2 t \\
x_{2}^{\prime }&=\frac {3 x_{1}}{4}-\frac {5 x_{2}}{4}+{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.790 |
|
| \begin{align*}
x_{1}^{\prime }&=-3 x_{1}+\sqrt {2}\, x_{2}+{\mathrm e}^{-t} \\
x_{2}^{\prime }&=\sqrt {2}\, x_{1}-2 x_{2}-{\mathrm e}^{-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.944 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}-5 x_{2} \\
x_{2}^{\prime }&=x_{1}-2 x_{2}+\cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.918 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}-5 x_{2}+\csc \left (t \right ) \\
x_{2}^{\prime }&=x_{1}-2 x_{2}+\sec \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.313 |
|
| \begin{align*}
x_{1}^{\prime }&=-\frac {x_{1}}{2}-\frac {x_{2}}{8}+\frac {{\mathrm e}^{-\frac {t}{2}}}{2} \\
x_{2}^{\prime }&=2 x_{1}-\frac {x_{2}}{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| \begin{align*}
x_{1}^{\prime }&=-2 x_{1}+x_{2}+2 \,{\mathrm e}^{-t} \\
x_{2}^{\prime }&=x_{1}-2 x_{2}+3 t \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= \alpha _{1} \\
x_{2} \left (0\right ) &= \alpha _{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.792 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}-2 x_{2} \\
x_{2}^{\prime }&=2 x_{1}-2 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.444 |
|
| \begin{align*}
x_{1}^{\prime }&=5 x_{1}-x_{2} \\
x_{2}^{\prime }&=3 x_{1}+x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.463 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}-x_{2} \\
x_{2}^{\prime }&=3 x_{1}-2 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.428 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}-4 x_{2} \\
x_{2}^{\prime }&=4 x_{1}-7 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.361 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}-5 x_{2} \\
x_{2}^{\prime }&=x_{1}-3 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.530 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}-5 x_{2} \\
x_{2}^{\prime }&=x_{1}-2 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.429 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}-2 x_{2} \\
x_{2}^{\prime }&=4 x_{1}-x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.571 |
|
| \begin{align*}
x_{1}^{\prime }&=-x_{1}-x_{2} \\
x_{2}^{\prime }&=-\frac {5 x_{2}}{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.408 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}-4 x_{2} \\
x_{2}^{\prime }&=x_{1}-x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.363 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}+2 x_{2} \\
x_{2}^{\prime }&=-5 x_{1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.034 |
|
| \begin{align*}
x_{1}^{\prime }&=-x_{1} \\
x_{2}^{\prime }&=-x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.273 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}-\frac {5 x_{2}}{2} \\
x_{2}^{\prime }&=\frac {9 x_{1}}{5}-x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.598 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}+x_{2}-2 \\
x_{2}^{\prime }&=x_{1}-x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.908 |
|
| \begin{align*}
x_{1}^{\prime }&=-2 x_{1}+x_{2}-2 \\
x_{2}^{\prime }&=x_{1}-2 x_{2}+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.647 |
|
| \begin{align*}
x_{1}^{\prime }&=-x_{1}-x_{2}-1 \\
x_{2}^{\prime }&=2 x_{1}-x_{2}+5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.938 |
|
| \begin{align*}
x^{\prime }&=-x \\
y^{\prime }&=-2 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 4 \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.352 |
|
| \begin{align*}
x^{\prime }&=-x \\
y^{\prime }&=2 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 4 \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| \begin{align*}
x^{\prime }&=-x \\
y^{\prime }&=2 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 4 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.339 |
|
| \begin{align*}
x^{\prime }&=-y \\
y^{\prime }&=x \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 4 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.417 |
|
| \begin{align*}
x^{\prime }&=-y \\
y^{\prime }&=x \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.398 |
|
| \begin{align*}
y_{1}^{\prime }&=y_{1}+2 y_{2} \\
y_{2}^{\prime }&=2 y_{1}+y_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.438 |
|
| \begin{align*}
y_{1}^{\prime }&=-\frac {5 y_{1}}{4}+\frac {3 y_{2}}{4} \\
y_{2}^{\prime }&=\frac {3 y_{1}}{4}-\frac {5 y_{2}}{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.434 |
|
| \begin{align*}
y_{1}^{\prime }&=-\frac {4 y_{1}}{5}+\frac {3 y_{2}}{5} \\
y_{2}^{\prime }&=-\frac {2 y_{1}}{5}-\frac {11 y_{2}}{5} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.472 |
|
| \begin{align*}
y_{1}^{\prime }&=-y_{1}-4 y_{2} \\
y_{2}^{\prime }&=-y_{1}-y_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.442 |
|
| \begin{align*}
y_{1}^{\prime }&=2 y_{1}-4 y_{2} \\
y_{2}^{\prime }&=-y_{1}-y_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.447 |
|
| \begin{align*}
y_{1}^{\prime }&=4 y_{1}-3 y_{2} \\
y_{2}^{\prime }&=2 y_{1}-y_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.440 |
|
| \begin{align*}
y_{1}^{\prime }&=-6 y_{1}-3 y_{2} \\
y_{2}^{\prime }&=y_{1}-2 y_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.449 |
|
| \begin{align*}
y_{1}^{\prime }&=y_{1}-y_{2}-2 y_{3} \\
y_{2}^{\prime }&=y_{1}-2 y_{2}-3 y_{3} \\
y_{3}^{\prime }&=-4 y_{1}+y_{2}-y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.879 |
|
| \begin{align*}
y_{1}^{\prime }&=-6 y_{1}-4 y_{2}-8 y_{3} \\
y_{2}^{\prime }&=-4 y_{1}-4 y_{3} \\
y_{3}^{\prime }&=-8 y_{1}-4 y_{2}-6 y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.771 |
|
| \begin{align*}
y_{1}^{\prime }&=3 y_{1}+5 y_{2}+8 y_{3} \\
y_{2}^{\prime }&=y_{1}-y_{2}-2 y_{3} \\
y_{3}^{\prime }&=-y_{1}-y_{2}-y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.860 |
|
| \begin{align*}
y_{1}^{\prime }&=y_{1}-y_{2}+2 y_{3} \\
y_{2}^{\prime }&=12 y_{1}-4 y_{2}+10 y_{3} \\
y_{3}^{\prime }&=-6 y_{1}+y_{2}-7 y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.877 |
|
| \begin{align*}
y_{1}^{\prime }&=4 y_{1}-y_{2}-4 y_{3} \\
y_{2}^{\prime }&=4 y_{1}-3 y_{2}-2 y_{3} \\
y_{3}^{\prime }&=y_{1}-y_{2}-y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.855 |
|
| \begin{align*}
y_{1}^{\prime }&=-2 y_{1}+2 y_{2}-6 y_{3} \\
y_{2}^{\prime }&=2 y_{1}+6 y_{2}+2 y_{3} \\
y_{3}^{\prime }&=-2 y_{1}-2 y_{2}+2 y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.842 |
|
| \begin{align*}
y_{1}^{\prime }&=3 y_{1}+2 y_{2}-2 y_{3} \\
y_{2}^{\prime }&=-2 y_{1}+7 y_{2}-2 y_{3} \\
y_{3}^{\prime }&=-10 y_{1}+10 y_{2}-5 y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.743 |
|
| \begin{align*}
y_{1}^{\prime }&=3 y_{1}+y_{2}-y_{3} \\
y_{2}^{\prime }&=3 y_{1}+5 y_{2}+y_{3} \\
y_{3}^{\prime }&=-6 y_{1}+2 y_{2}+4 y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.720 |
|
| \begin{align*}
y_{1}^{\prime }&=3 y_{1}+4 y_{2} \\
y_{2}^{\prime }&=-y_{1}+7 y_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.411 |
|
| \begin{align*}
y_{1}^{\prime }&=-y_{2} \\
y_{2}^{\prime }&=y_{1}-2 y_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.392 |
|
| \begin{align*}
y_{1}^{\prime }&=-7 y_{1}+4 y_{2} \\
y_{2}^{\prime }&=-y_{1}-11 y_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.419 |
|
| \begin{align*}
y_{1}^{\prime }&=3 y_{1}+y_{2} \\
y_{2}^{\prime }&=-y_{1}+y_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.388 |
|
| \begin{align*}
y_{1}^{\prime }&=4 y_{1}+12 y_{2} \\
y_{2}^{\prime }&=-3 y_{1}-8 y_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.407 |
|
| \begin{align*}
y_{1}^{\prime }&=-10 y_{1}+9 y_{2} \\
y_{2}^{\prime }&=-4 y_{1}+2 y_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.421 |
|
| \begin{align*}
y_{1}^{\prime }&=-13 y_{1}+16 y_{2} \\
y_{2}^{\prime }&=-9 y_{1}+11 y_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.406 |
|
| \begin{align*}
y_{1}^{\prime }&=2 y_{2}+y_{3} \\
y_{2}^{\prime }&=-4 y_{1}+6 y_{2}+y_{3} \\
y_{3}^{\prime }&=4 y_{2}+2 y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.755 |
|
| \begin{align*}
y_{1}^{\prime }&=\frac {y_{1}}{3}+\frac {y_{2}}{3}-y_{3} \\
y_{2}^{\prime }&=-\frac {4 y_{1}}{3}-\frac {4 y_{2}}{3}+y_{3} \\
y_{3}^{\prime }&=-\frac {2 y_{1}}{3}+\frac {y_{2}}{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.787 |
|
| \begin{align*}
y_{1}^{\prime }&=-y_{1}+y_{2}-y_{3} \\
y_{2}^{\prime }&=-2 y_{1}+2 y_{3} \\
y_{3}^{\prime }&=-y_{1}+3 y_{2}-y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.757 |
|
| \begin{align*}
y_{1}^{\prime }&=4 y_{1}-2 y_{2}-2 y_{3} \\
y_{2}^{\prime }&=-2 y_{1}+3 y_{2}-y_{3} \\
y_{3}^{\prime }&=2 y_{1}-y_{2}+3 y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.802 |
|
| \begin{align*}
y_{1}^{\prime }&=6 y_{1}-5 y_{2}+3 y_{3} \\
y_{2}^{\prime }&=2 y_{1}-y_{2}+3 y_{3} \\
y_{3}^{\prime }&=2 y_{1}+y_{2}+y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.813 |
|
| \begin{align*}
y_{1}^{\prime }&=-11 y_{1}+8 y_{2} \\
y_{2}^{\prime }&=-2 y_{1}-3 y_{2} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 6 \\
y_{2} \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.480 |
|
| \begin{align*}
y_{1}^{\prime }&=15 y_{1}-9 y_{2} \\
y_{2}^{\prime }&=16 y_{1}-9 y_{2} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 5 \\
y_{2} \left (0\right ) &= 8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.439 |
|
| \begin{align*}
y_{1}^{\prime }&=-3 y_{1}-4 y_{2} \\
y_{2}^{\prime }&=y_{1}-7 y_{2} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 2 \\
y_{2} \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.427 |
|
| \begin{align*}
y_{1}^{\prime }&=-7 y_{1}+24 y_{2} \\
y_{2}^{\prime }&=-6 y_{1}+17 y_{2} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 3 \\
y_{2} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.435 |
|
| \begin{align*}
y_{1}^{\prime }&=-7 y_{1}+3 y_{2} \\
y_{2}^{\prime }&=-3 y_{1}-y_{2} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 0 \\
y_{2} \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.415 |
|
| \begin{align*}
y_{1}^{\prime }&=-y_{1}+y_{2} \\
y_{2}^{\prime }&=y_{1}-y_{2}-2 y_{3} \\
y_{3}^{\prime }&=-y_{1}-y_{2}-y_{3} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 6 \\
y_{2} \left (0\right ) &= 5 \\
y_{3} \left (0\right ) &= -7 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.810 |
|
| \begin{align*}
y_{1}^{\prime }&=-2 y_{1}+2 y_{2}+y_{3} \\
y_{2}^{\prime }&=-2 y_{1}+2 y_{2}+y_{3} \\
y_{3}^{\prime }&=-3 y_{1}+3 y_{2}+2 y_{3} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= -6 \\
y_{2} \left (0\right ) &= -2 \\
y_{3} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.724 |
|
| \begin{align*}
y_{1}^{\prime }&=-7 y_{1}-4 y_{2}+4 y_{3} \\
y_{2}^{\prime }&=y_{1}+y_{3} \\
y_{3}^{\prime }&=-9 y_{1}-5 y_{2}+6 y_{3} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= -6 \\
y_{2} \left (0\right ) &= 9 \\
y_{3} \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.265 |
|
| \begin{align*}
y_{1}^{\prime }&=-y_{1}-4 y_{2}-y_{3} \\
y_{2}^{\prime }&=3 y_{1}+6 y_{2}+y_{3} \\
y_{3}^{\prime }&=-3 y_{1}-2 y_{2}+3 y_{3} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= -2 \\
y_{2} \left (0\right ) &= 1 \\
y_{3} \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| \begin{align*}
y_{1}^{\prime }&=4 y_{1}-8 y_{2}-4 y_{3} \\
y_{2}^{\prime }&=-3 y_{1}-y_{2}-4 y_{3} \\
y_{3}^{\prime }&=y_{1}-y_{2}+9 y_{3} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= -4 \\
y_{2} \left (0\right ) &= 1 \\
y_{3} \left (0\right ) &= -3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.893 |
|
| \begin{align*}
y_{1}^{\prime }&=-5 y_{1}-y_{2}+11 y_{3} \\
y_{2}^{\prime }&=-7 y_{1}+y_{2}+13 y_{3} \\
y_{3}^{\prime }&=-4 y_{1}+8 y_{3} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 0 \\
y_{2} \left (0\right ) &= 2 \\
y_{3} \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.762 |
|
| \begin{align*}
y_{1}^{\prime }&=5 y_{1}-y_{2}+y_{3} \\
y_{2}^{\prime }&=-y_{1}+9 y_{2}-3 y_{3} \\
y_{3}^{\prime }&=-2 y_{1}+2 y_{2}+4 y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.749 |
|
| \begin{align*}
y_{1}^{\prime }&=y_{1}+10 y_{2}-12 y_{3} \\
y_{2}^{\prime }&=2 y_{1}+2 y_{2}+3 y_{3} \\
y_{3}^{\prime }&=2 y_{1}-y_{2}+6 y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.752 |
|
| \begin{align*}
y_{1}^{\prime }&=-6 y_{1}-4 y_{2}-4 y_{3} \\
y_{2}^{\prime }&=2 y_{1}-y_{2}+y_{3} \\
y_{3}^{\prime }&=2 y_{1}+3 y_{2}+y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.712 |
|
| \begin{align*}
y_{1}^{\prime }&=2 y_{2}-2 y_{3} \\
y_{2}^{\prime }&=-y_{1}+5 y_{2}-3 y_{3} \\
y_{3}^{\prime }&=y_{1}+y_{2}+y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.731 |
|
| \begin{align*}
y_{1}^{\prime }&=-2 y_{1}-12 y_{2}+10 y_{3} \\
y_{2}^{\prime }&=2 y_{1}-24 y_{2}+11 y_{3} \\
y_{3}^{\prime }&=2 y_{1}-24 y_{2}+8 y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| \begin{align*}
y_{1}^{\prime }&=-y_{1}-12 y_{2}+8 y_{3} \\
y_{2}^{\prime }&=y_{1}-9 y_{2}+4 y_{3} \\
y_{3}^{\prime }&=y_{1}-6 y_{2}+y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.744 |
|
| \begin{align*}
y_{1}^{\prime }&=-4 y_{1}-y_{3} \\
y_{2}^{\prime }&=-y_{1}-3 y_{2}-y_{3} \\
y_{3}^{\prime }&=y_{1}-2 y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.673 |
|
| \begin{align*}
y_{1}^{\prime }&=-3 y_{1}-3 y_{2}+4 y_{3} \\
y_{2}^{\prime }&=4 y_{1}+5 y_{2}-8 y_{3} \\
y_{3}^{\prime }&=2 y_{1}+3 y_{2}-5 y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.751 |
|
| \begin{align*}
y_{1}^{\prime }&=-3 y_{1}-y_{2} \\
y_{2}^{\prime }&=y_{1}-y_{2} \\
y_{3}^{\prime }&=-y_{1}-y_{2}-2 y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.595 |
|
| \begin{align*}
y_{1}^{\prime }&=-y_{1}+2 y_{2} \\
y_{2}^{\prime }&=-5 y_{1}+5 y_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.581 |
|
| \begin{align*}
y_{1}^{\prime }&=-11 y_{1}+4 y_{2} \\
y_{2}^{\prime }&=-26 y_{1}+9 y_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.565 |
|
| \begin{align*}
y_{1}^{\prime }&=y_{1}+2 y_{2} \\
y_{2}^{\prime }&=-4 y_{1}+5 y_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.572 |
|
| \begin{align*}
y_{1}^{\prime }&=5 y_{1}-6 y_{2} \\
y_{2}^{\prime }&=3 y_{1}-y_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.563 |
|
| \begin{align*}
y_{1}^{\prime }&=-3 y_{1}-3 y_{2}+y_{3} \\
y_{2}^{\prime }&=2 y_{2}+2 y_{3} \\
y_{3}^{\prime }&=5 y_{1}+y_{2}+y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.978 |
|
| \begin{align*}
y_{1}^{\prime }&=-3 y_{1}+3 y_{2}+y_{3} \\
y_{2}^{\prime }&=y_{1}-5 y_{2}-3 y_{3} \\
y_{3}^{\prime }&=-3 y_{1}+7 y_{2}+3 y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.235 |
|
| \begin{align*}
y_{1}^{\prime }&=2 y_{1}+y_{2}-y_{3} \\
y_{2}^{\prime }&=y_{2}+y_{3} \\
y_{3}^{\prime }&=y_{1}+y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.173 |
|
| \begin{align*}
y_{1}^{\prime }&=-3 y_{1}+y_{2}-3 y_{3} \\
y_{2}^{\prime }&=4 y_{1}-y_{2}+2 y_{3} \\
y_{3}^{\prime }&=4 y_{1}-2 y_{2}+3 y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.204 |
|
| \begin{align*}
x^{\prime }&=6 x-3 y \\
y^{\prime }&=2 x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.315 |
|
| \begin{align*}
x^{\prime }&=-2 x+y+t \\
y^{\prime }&=-4 x+3 y-1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.533 |
|
| \begin{align*}
x^{\prime }&=6 x-3 y \\
y^{\prime }&=2 x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.286 |
|
| \begin{align*}
x^{\prime }&=x+y+{\mathrm e}^{t} \\
y^{\prime }&=x-y-{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.755 |
|
| \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*} |
✓ |
✓ |
✓ |
✓ |
0.338 |
|
| \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*} |
✓ |
✓ |
✓ |
✓ |
0.341 |
|
| \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*} |
✓ |
✓ |
✓ |
✓ |
0.464 |
|
| \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*} |
✓ |
✓ |
✓ |
✓ |
0.479 |
|
| \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*} |
✓ |
✓ |
✓ |
✓ |
0.868 |
|
| \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*} |
✓ |
✓ |
✓ |
✓ |
0.514 |
|
| \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*} |
✓ |
✓ |
✓ |
✓ |
1.194 |
|
| \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*} |
✓ |
✓ |
✓ |
✓ |
0.713 |
|
| \begin{align*}
x_{1}^{\prime }&=6 x_{1}-3 x_{2} \\
x_{2}^{\prime }&=2 x_{1}+x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.319 |
|
| \begin{align*}
x_{1}^{\prime }&=-2 x_{1}+x_{2} \\
x_{2}^{\prime }&=-4 x_{1}+3 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.319 |
|
| \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*} |
✓ |
✓ |
✓ |
✓ |
0.519 |
|
| \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*} |
✓ |
✓ |
✓ |
✓ |
0.642 |
|
| \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*} |
✓ |
✓ |
✓ |
✓ |
0.470 |
|
| \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*} |
✓ |
✓ |
✓ |
✓ |
0.750 |
|
| \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*} |
✓ |
✓ |
✓ |
✓ |
0.355 |
|
| \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*} |
✓ |
✓ |
✓ |
✓ |
0.332 |
|
| \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*} |
✓ |
✓ |
✓ |
✓ |
0.485 |
|
| \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*} |
✓ |
✓ |
✓ |
✓ |
0.603 |
|
| \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*} |
✓ |
✓ |
✓ |
✓ |
0.539 |
|
| \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*} |
✓ |
✓ |
✓ |
✓ |
0.579 |
|
| \begin{align*}
x_{1}^{\prime }&=-3 x_{1}+2 x_{2} \\
x_{2}^{\prime }&=-x_{1}-x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.458 |
|
| \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*} |
✓ |
✓ |
✓ |
✓ |
0.617 |
|
| \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*} |
✓ |
✓ |
✓ |
✓ |
0.643 |
|
| \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*} |
✓ |
✓ |
✓ |
✓ |
0.592 |
|
| \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*} |
✓ |
✓ |
✓ |
✓ |
0.416 |
|
| \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*} |
✓ |
✓ |
✓ |
✓ |
0.447 |
|
| \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*} |
✓ |
✓ |
✓ |
✓ |
1.416 |
|
| \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*} |
✓ |
✓ |
✓ |
✓ |
1.248 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}+x_{2} \\
x_{2}^{\prime }&=x_{2} \\
x_{3}^{\prime }&=2 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.388 |
|
| \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*} |
✓ |
✓ |
✓ |
✓ |
0.422 |
|
| \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*} |
✓ |
✓ |
✓ |
✓ |
0.498 |
|
| \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*} |
✓ |
✓ |
✓ |
✓ |
0.480 |
|
| \begin{align*}
x_{1}^{\prime }&=-x_{1}-x_{2} \\
x_{2}^{\prime }&=-x_{2} \\
x_{3}^{\prime }&=-2 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.392 |
|
| \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*} |
✓ |
✓ |
✓ |
✓ |
0.544 |
|
| \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*} |
✓ |
✓ |
✓ |
✓ |
0.462 |
|
| \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*} |
✓ |
✓ |
✓ |
✓ |
0.540 |
|
| \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*} |
✓ |
✓ |
✓ |
✓ |
0.454 |
|
| \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*} |
✓ |
✓ |
✓ |
✓ |
0.499 |
|
| \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*} |
✓ |
✓ |
✓ |
✓ |
1.241 |
|
| \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*} |
✓ |
✓ |
✓ |
✓ |
1.332 |
|
| \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*} |
✓ |
✓ |
✓ |
✓ |
0.717 |
|
| \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*} |
✓ |
✓ |
✓ |
✓ |
0.487 |
|
| \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*} |
✓ |
✓ |
✓ |
✓ |
0.805 |
|
| \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*} |
✓ |
✓ |
✓ |
✓ |
0.705 |
|
| \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*} |
✓ |
✓ |
✓ |
✓ |
0.680 |
|
| \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*} |
✓ |
✓ |
✓ |
✓ |
0.721 |
|
| \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*} |
✓ |
✓ |
✓ |
✓ |
0.839 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}-x_{2}-t^{2} \\
x_{2}^{\prime }&=x_{1}+3 x_{2}+2 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.494 |
|
| \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*} |
✓ |
✓ |
✓ |
✓ |
1.142 |
|
| \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*} |
✓ |
✓ |
✓ |
✓ |
0.809 |
|
| \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*} |
✓ |
✓ |
✓ |
✓ |
1.638 |
|
| \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*} |
✓ |
✓ |
✓ |
✓ |
22.217 |
|
| \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*} |
✓ |
✓ |
✓ |
✓ |
22.299 |
|
| \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*} |
✓ |
✓ |
✓ |
✓ |
0.803 |
|
| \begin{align*}
x^{\prime }&=x-x^{2}-2 x y \\
y^{\prime }&=2 y-2 y^{2}-3 x y \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.036 |
|
| \begin{align*}
x^{\prime }&=-b x y+m \\
y^{\prime }&=b x y-g y \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.033 |
|
| \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*} |
✗ |
✓ |
✓ |
✗ |
0.053 |
|
| \begin{align*}
x^{\prime }&=-x-x \,y^{2} \\
y^{\prime }&=-y-y \,x^{2} \\
z^{\prime }&=1-z+x^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.042 |
|
| \begin{align*}
x^{\prime }&=x \,y^{2}-x \\
y^{\prime }&=x \sin \left (\pi y\right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.032 |
|
| \begin{align*}
x^{\prime }&=\cos \left (y\right ) \\
y^{\prime }&=\sin \left (x\right )-1 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.033 |
|
| \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*} |
✗ |
✗ |
✗ |
✗ |
0.042 |
|
| \begin{align*}
x^{\prime }&=x-y^{2} \\
y^{\prime }&=x^{2}-y \\
z^{\prime }&={\mathrm e}^{z}-x \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.051 |
|
| \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*} |
✓ |
✓ |
✓ |
✓ |
0.366 |
|
| \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*} |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| \begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=-2 x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.312 |
|
| \begin{align*}
x^{\prime }&=-3 x-4 y \\
y^{\prime }&=2 x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.447 |
|
| \begin{align*}
x^{\prime }&=-5 x+3 y \\
y^{\prime }&=-x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.501 |
|
| \begin{align*}
x^{\prime }&=x-4 y \\
y^{\prime }&=4 x-7 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.286 |
|
| \begin{align*}
x^{\prime }&=-7 x+y-6 z \\
y^{\prime }&=10 x-4 y+12 z \\
z^{\prime }&=2 x-y+z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.619 |
|
| \begin{align*}
x^{\prime }&=3 x+2 y+4 z \\
y^{\prime }&=2 x+2 z \\
z^{\prime }&=4 x+2 y+3 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.497 |
|
| \begin{align*}
x^{\prime }&=2 y+z \\
y^{\prime }&=-x-3 y-z \\
z^{\prime }&=x+y-z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.508 |
|
| \begin{align*}
x^{\prime }&=-2 x+y+z \\
y^{\prime }&=-3 x+2 y+3 z \\
z^{\prime }&=x-y-2 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.463 |
|
| \begin{align*}
x^{\prime }&=2 y \\
y^{\prime }&=-2 x \\
z^{\prime }&=2 h \\
h^{\prime }&=-2 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.653 |
|
| \begin{align*}
x^{\prime }&=2 y+z \\
y^{\prime }&=-2 x+h \\
z^{\prime }&=2 h \\
h^{\prime }&=-2 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.591 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{2} \\
x_{2}^{\prime }&=-\frac {\left (x_{1}^{2}+\sqrt {x_{1}^{2}+4 x_{2}^{2}}\right ) x_{1}}{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.033 |
|
| \begin{align*}
x_{1}^{\prime }&=-x_{1}-x_{2}+1 \\
x_{2}^{\prime }&=2 x_{1}-x_{2}+5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.772 |
|
| \begin{align*}
x^{\prime }&=x-x^{3}-x y \\
y^{\prime }&=2 y-y^{5}-y \,x^{4} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.033 |
|
| \begin{align*}
x^{\prime }&=x^{2}+y^{2}+1 \\
y^{\prime }&=x^{2}-y^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.051 |
|
| \begin{align*}
x^{\prime }&=x^{2}+y^{2}-1 \\
y^{\prime }&=2 x y \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.030 |
|
| \begin{align*}
x^{\prime }&=6 x-6 x^{2}-2 x y \\
y^{\prime }&=4 y-4 y^{2}-2 x y \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.048 |
|
| \begin{align*}
x^{\prime }&=\tan \left (x+y\right ) \\
y^{\prime }&=x+x^{3} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.033 |
|
| \begin{align*}
x^{\prime }&={\mathrm e}^{y}-x \\
y^{\prime }&={\mathrm e}^{x}+y \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.031 |
|
| \begin{align*}
x_{1}^{\prime }&=-5 x_{1}+x_{2} \\
x_{2}^{\prime }&=x_{1}-5 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.319 |
|
| \begin{align*}
x_{1}^{\prime }&=-x_{2} \\
x_{2}^{\prime }&=8 x_{1}-6 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.373 |
|
| \begin{align*}
x_{1}^{\prime }&=4 x_{1}-x_{2} \\
x_{2}^{\prime }&=-2 x_{1}+5 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.359 |
|
| \begin{align*}
x_{1}^{\prime }&=-4 x_{1}-x_{2} \\
x_{2}^{\prime }&=x_{1}-6 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.293 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}-4 x_{2} \\
x_{2}^{\prime }&=-8 x_{1}+4 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.550 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}-x_{2} \\
x_{2}^{\prime }&=5 x_{1}-3 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.356 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{2} \\
x_{2}^{\prime }&=-2 x_{1}-x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.883 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}-x_{2} \\
x_{2}^{\prime }&=5 x_{1}-3 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.473 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}+x_{2} \\
x_{2}^{\prime }&=-5 x_{1}-2 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.372 |
|
| \begin{align*}
x_{1}^{\prime }&=4 x_{2} \\
x_{2}^{\prime }&=-9 x_{1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.361 |
|
| \begin{align*}
x^{\prime }-x&=\cos \left (t \right ) \\
y+y^{\prime }&=4 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.509 |
|
| \begin{align*}
x^{\prime }+5 x&=3 t^{2} \\
y+y^{\prime }&={\mathrm e}^{3 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.474 |
|
| \begin{align*}
x^{\prime }+2 x&=3 t \\
x^{\prime }+2 y^{\prime }+y&=\cos \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.733 |
|
| \begin{align*}
x^{\prime }-x+y&=2 \sin \left (t \right ) \\
x^{\prime }+y^{\prime }&=3 y-3 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.671 |
|
| \begin{align*}
2 x^{\prime }+3 x-y&={\mathrm e}^{t} \\
5 x-3 y^{\prime }&=y+2 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.724 |
|
| \begin{align*}
5 y^{\prime }-3 x^{\prime }-5 y&=5 t \\
3 x^{\prime }-5 y^{\prime }-2 x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.385 |
|
| \begin{align*}
x^{\prime }&=3 x \\
y^{\prime }&=2 x+3 y \\
z^{\prime }&=3 y-2 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}+x_{2} \\
x_{2}^{\prime }&=2 x_{1}+3 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.471 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}-3 x_{2} \\
x_{2}^{\prime }&=x_{1}-2 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.474 |
|
| \begin{align*}
x_{1}^{\prime }&=4 x_{1}+2 x_{2} \\
x_{2}^{\prime }&=x_{2}-x_{1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.464 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}+4 x_{2} \\
x_{2}^{\prime }&=-4 x_{1}-6 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.390 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{2} \\
x_{2}^{\prime }&=-2 x_{1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.465 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}-3 x_{2} \\
x_{2}^{\prime }&=3 x_{1}+x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.500 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1} \\
x_{2}^{\prime }&=x_{2}-x_{3} \\
x_{3}^{\prime }&=x_{2}+x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| \begin{align*}
x_{1}^{\prime }&=-2 x_{1}+x_{2}+x_{3} \\
x_{2}^{\prime }&=x_{1}-x_{2}+3 x_{3} \\
x_{3}^{\prime }&=-x_{2}-3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.094 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{2} \\
x_{2}^{\prime }&=x_{1}+x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 3 \\
x_{2} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.460 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}+5 x_{2} \\
x_{2}^{\prime }&=-x_{1}-2 x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.481 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}+x_{2} \\
x_{2}^{\prime }&=-x_{1}+4 x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.395 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}+2 x_{2}+5 \,{\mathrm e}^{4 t} \\
x_{2}^{\prime }&=2 x_{1}+x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.691 |
|
| \begin{align*}
x_{1}^{\prime }&=-2 x_{1}+x_{2}+t \\
x_{2}^{\prime }&=-2 x_{1}+x_{2}+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.660 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}+x_{2}+{\mathrm e}^{2 t} \\
x_{2}^{\prime }&=3 x_{1}-x_{2}+5 \,{\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.792 |
|
| \begin{align*}
x_{1}^{\prime }&=-\tan \left (t \right ) x_{1}+3 \cos \left (t \right )^{2} \\
x_{2}^{\prime }&=x_{1}+\tan \left (t \right ) x_{2}+2 \sin \left (t \right ) \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 4 \\
x_{2} \left (0\right ) &= 0 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.057 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}-4 x_{2} \\
x_{2}^{\prime }&=x_{1}-3 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.453 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{2} \\
x_{2}^{\prime }&=-b x_{1}-a x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.993 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{2} \\
x_{2}^{\prime }&=-3 x_{1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.473 |
|
| \begin{align*}
x_{1}^{\prime }&=-2 x_{1}+3 x_{2} \\
x_{2}^{\prime }&=-2 x_{1}+5 x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= -2 \\
x_{2} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.506 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}-2 x_{2} \\
x_{2}^{\prime }&=2 x_{1}+x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.487 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}+x_{2} \\
x_{2}^{\prime }&=x_{2}-x_{1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.374 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}-x_{2}+3 x_{3} \\
x_{2}^{\prime }&=3 x_{1}+x_{2} \\
x_{3}^{\prime }&=2 x_{1}-x_{2}+3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.805 |
|
| \begin{align*}
x_{1}^{\prime }&=\frac {x_{1}}{t} \\
x_{2}^{\prime }&=x_{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.043 |
|
| \begin{align*}
x_{1}^{\prime }&=\frac {x_{1}}{t}+t x_{2} \\
x_{2}^{\prime }&=-\frac {x_{1}}{t} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.045 |
|
| \begin{align*}
x_{1}^{\prime }&=-x_{1}+2 x_{2} \\
x_{2}^{\prime }&=2 x_{1}+2 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.492 |
|
| \begin{align*}
x_{1}^{\prime }&=-2 x_{1}-7 x_{2} \\
x_{2}^{\prime }&=-x_{1}+4 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.476 |
|
| \begin{align*}
x_{1}^{\prime }&=-4 x_{2} \\
x_{2}^{\prime }&=4 x_{1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.931 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}-2 x_{2} \\
x_{2}^{\prime }&=5 x_{1}-5 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.639 |
|
| \begin{align*}
x_{1}^{\prime }&=-x_{1}+2 x_{2} \\
x_{2}^{\prime }&=-2 x_{1}-x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.490 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1} \\
x_{2}^{\prime }&=5 x_{2}-7 x_{3} \\
x_{3}^{\prime }&=2 x_{2}-4 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.704 |
|
| \begin{align*}
x_{1}^{\prime }&=-x_{1} \\
x_{2}^{\prime }&=x_{1}+5 x_{2}-x_{3} \\
x_{3}^{\prime }&=x_{1}+6 x_{2}-2 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.647 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{2} \\
x_{2}^{\prime }&=-x_{1} \\
x_{3}^{\prime }&=5 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.739 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}+3 x_{3} \\
x_{2}^{\prime }&=-4 x_{2} \\
x_{3}^{\prime }&=-3 x_{1}+2 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.813 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}+2 x_{2}+6 x_{3} \\
x_{2}^{\prime }&=-2 x_{1}+x_{2}-2 x_{3} \\
x_{3}^{\prime }&=-x_{1}-2 x_{2}-4 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.819 |
|
| \begin{align*}
x_{1}^{\prime }&=-3 x_{2}+x_{3} \\
x_{2}^{\prime }&=-2 x_{1}-x_{2}+x_{3} \\
x_{3}^{\prime }&=2 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.687 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}-x_{3} \\
x_{2}^{\prime }&=-3 x_{2}-x_{3} \\
x_{3}^{\prime }&=2 x_{2}-x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.997 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}+x_{2}-x_{3} \\
x_{2}^{\prime }&=x_{1}+x_{2}+x_{3} \\
x_{3}^{\prime }&=-x_{1}+x_{2}+x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.661 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}-x_{2}+3 x_{3} \\
x_{2}^{\prime }&=2 x_{1}-x_{2}+3 x_{3} \\
x_{3}^{\prime }&=2 x_{1}-x_{2}+3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.647 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}+2 x_{2}+3 x_{3}+4 x_{4} \\
x_{2}^{\prime }&=4 x_{1}+3 x_{2}+2 x_{3}+x_{4} \\
x_{3}^{\prime }&=4 x_{1}+5 x_{2}+6 x_{3}+7 x_{4} \\
x_{4}^{\prime }&=7 x_{1}+6 x_{2}+5 x_{3}+4 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.259 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{2} \\
x_{2}^{\prime }&=-x_{1} \\
x_{3}^{\prime }&=-x_{4} \\
x_{4}^{\prime }&=x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.848 |
|
| \begin{align*}
x_{1}^{\prime }&=-x_{1}+4 x_{2} \\
x_{2}^{\prime }&=2 x_{1}-3 x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 3 \\
x_{2} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.490 |
|
| \begin{align*}
x_{1}^{\prime }&=-x_{1}-6 x_{2} \\
x_{2}^{\prime }&=3 x_{1}+5 x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 2 \\
x_{2} \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.628 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}-x_{2}+3 x_{3} \\
x_{2}^{\prime }&=3 x_{1}+x_{2} \\
x_{3}^{\prime }&=2 x_{1}-x_{2}+3 x_{3} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= -4 \\
x_{2} \left (0\right ) &= 4 \\
x_{3} \left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.724 |
|
| \begin{align*}
x_{1}^{\prime }&=4 x_{2} \\
x_{2}^{\prime }&=-4 x_{1} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.474 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{2} \\
x_{2}^{\prime }&=-b x_{1}-a x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.643 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}+x_{2} \\
x_{2}^{\prime }&=-x_{1}+3 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.369 |
|
| \begin{align*}
x_{1}^{\prime }&=-2 x_{2} \\
x_{2}^{\prime }&=2 x_{1}+4 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.381 |
|
| \begin{align*}
x_{1}^{\prime }&=-3 x_{1}-2 x_{2} \\
x_{2}^{\prime }&=2 x_{1}+x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.386 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{2} \\
x_{2}^{\prime }&=x_{3} \\
x_{3}^{\prime }&=x_{1}+x_{2}-x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}+2 x_{2}-x_{3} \\
x_{2}^{\prime }&=2 x_{1}+x_{2}-x_{3} \\
x_{3}^{\prime }&=2 x_{1}+3 x_{2}-x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.704 |
|
| \begin{align*}
x_{1}^{\prime }&=-2 x_{1} \\
x_{2}^{\prime }&=x_{1}-3 x_{2}-x_{3} \\
x_{3}^{\prime }&=-x_{1}+x_{2}-x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.536 |
|
| \begin{align*}
x_{1}^{\prime }&=15 x_{1}-32 x_{2}+12 x_{3} \\
x_{2}^{\prime }&=8 x_{1}-17 x_{2}+6 x_{3} \\
x_{3}^{\prime }&=-x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.717 |
|
| \begin{align*}
x_{1}^{\prime }&=4 x_{1} \\
x_{2}^{\prime }&=x_{1}+4 x_{2} \\
x_{3}^{\prime }&=x_{2}+4 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.496 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1} \\
x_{2}^{\prime }&=3 x_{2}+2 x_{3} \\
x_{3}^{\prime }&=2 x_{1}-2 x_{2}-x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.566 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}+x_{2} \\
x_{2}^{\prime }&=-x_{1}+5 x_{2} \\
x_{3}^{\prime }&=4 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.567 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{2}-x_{1} \\
x_{2}^{\prime }&=-2 x_{1}-3 x_{2}+x_{3} \\
x_{3}^{\prime }&=x_{1}+x_{2}-2 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.621 |
|
| \begin{align*}
x_{1}^{\prime }&=-x_{2} \\
x_{2}^{\prime }&=x_{1} \\
x_{3}^{\prime }&=x_{1}+2 x_{3}+x_{4} \\
x_{4}^{\prime }&=x_{2}+2 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.229 |
|
| \begin{align*}
x_{1}^{\prime }&=-2 x_{1}+3 x_{2} \\
x_{2}^{\prime }&=3 x_{1}-2 x_{2} \\
x_{3}^{\prime }&=x_{1}+x_{3}+x_{4} \\
x_{4}^{\prime }&=x_{2}+x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.019 |
|
| \begin{align*}
x_{1}^{\prime }&=-x_{2} \\
x_{2}^{\prime }&=x_{1} \\
x_{3}^{\prime }&=x_{1}-x_{4} \\
x_{4}^{\prime }&=x_{2}+x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.761 |
|
| \begin{align*}
x_{1}^{\prime }&=-2 x_{1}-x_{2} \\
x_{2}^{\prime }&=x_{1}-4 x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.393 |
|
| \begin{align*}
x_{1}^{\prime }&=-2 x_{1}-x_{2}+4 x_{3} \\
x_{2}^{\prime }&=-x_{2} \\
x_{3}^{\prime }&=-x_{1}-3 x_{2}+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*} |
✓ |
✓ |
✓ |
✓ |
0.650 |
|
| \begin{align*}
x_{1}^{\prime }&=4 x_{1}-3 x_{2}+{\mathrm e}^{2 t} \\
x_{2}^{\prime }&=2 x_{1}-x_{2}+{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.759 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}-x_{2} \\
x_{2}^{\prime }&=-x_{1}+2 x_{2}+4 \,{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.690 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}+x_{2}+t \,{\mathrm e}^{3 t} \\
x_{2}^{\prime }&=3 x_{2}+{\mathrm e}^{3 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.526 |
|
| \begin{align*}
x_{1}^{\prime }&=-x_{1}+x_{2}+20 \,{\mathrm e}^{3 t} \\
x_{2}^{\prime }&=3 x_{1}+x_{2}+12 \,{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.827 |
|
| \begin{align*}
x_{1}^{\prime }&=-x_{1}+2 x_{2}+54 t \,{\mathrm e}^{3 t} \\
x_{2}^{\prime }&=-2 x_{1}+4 x_{2}+9 \,{\mathrm e}^{3 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.759 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}+4 x_{2}+8 \sin \left (2 t \right ) \\
x_{2}^{\prime }&=-2 x_{1}-2 x_{2}+8 \cos \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.230 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}+2 x_{2}-3 \,{\mathrm e}^{t} \\
x_{2}^{\prime }&=-2 x_{1}-x_{2}+6 \,{\mathrm e}^{t} t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.644 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}-{\mathrm e}^{t} \\
x_{2}^{\prime }&=2 x_{1}-3 x_{2}+2 x_{3}+6 \,{\mathrm e}^{-t} \\
x_{3}^{\prime }&=x_{1}-2 x_{2}+2 x_{3}+{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.032 |
|
| \begin{align*}
x_{1}^{\prime }&=-x_{1}-2 x_{2}+2 x_{3}-{\mathrm e}^{3 t} \\
x_{2}^{\prime }&=2 x_{1}+4 x_{2}-x_{3}+4 \,{\mathrm e}^{3 t} \\
x_{3}^{\prime }&=3 x_{3}+3 \,{\mathrm e}^{3 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.000 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}-3 x_{2}+34 \sin \left (t \right ) \\
x_{2}^{\prime }&=-4 x_{1}-2 x_{2}+17 \cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.006 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}+x_{2} \\
x_{2}^{\prime }&=2 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.329 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}+2 x_{2} \\
x_{2}^{\prime }&=-x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.375 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1} \\
x_{2}^{\prime }&=3 x_{2}-x_{3} \\
x_{3}^{\prime }&=x_{2}+x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.557 |
|
| \begin{align*}
x_{1}^{\prime }&=-3 x_{1}-2 x_{2} \\
x_{2}^{\prime }&=2 x_{1}+x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.373 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}-x_{2} \\
x_{2}^{\prime }&=4 x_{1}-x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.414 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1} \\
x_{2}^{\prime }&=x_{2}-8 x_{3} \\
x_{3}^{\prime }&=2 x_{2}-7 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.628 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{2}+3 x_{3} \\
x_{2}^{\prime }&=2 x_{1}+3 x_{2}-2 x_{3} \\
x_{3}^{\prime }&=2 x_{2}+2 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
14.824 |
|
| \begin{align*}
x_{1}^{\prime }&=-8 x_{1}+6 x_{2}-3 x_{3} \\
x_{2}^{\prime }&=-12 x_{1}+10 x_{2}-3 x_{3} \\
x_{3}^{\prime }&=-2 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.662 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1} \\
x_{2}^{\prime }&=6 x_{2}-7 x_{3}+3 x_{4} \\
x_{3}^{\prime }&=3 x_{3}-x_{4} \\
x_{4}^{\prime }&=-4 x_{2}+9 x_{3}-3 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.030 |
|
| \begin{align*}
x_{1}^{\prime }&=-x_{2} \\
x_{2}^{\prime }&=x_{1} \\
x_{3}^{\prime }&=x_{2}-x_{4} \\
x_{4}^{\prime }&=x_{2}+x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.889 |
|
| \begin{align*}
x_{1}^{\prime }&=\left (2 t -1\right ) x_{1} \\
x_{2}^{\prime }&={\mathrm e}^{-t^{2}+t} x_{1}+x_{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.051 |
|
| \begin{align*}
x_{1}^{\prime }&=t \cot \left (t^{2}\right ) x_{1}+\frac {t \cos \left (t^{2}\right ) x_{3}}{2} \\
x_{2}^{\prime }&=\frac {x_{2}}{t}-x_{3}+2-t \sin \left (t \right ) \\
x_{3}^{\prime }&=\csc \left (t^{2}\right ) x_{1}+x_{2}-x_{3}+1-t \cos \left (t \right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.073 |
|
| \begin{align*}
x_{1}^{\prime }&=-6 x_{1}+x_{2} \\
x_{2}^{\prime }&=6 x_{1}-5 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.513 |
|
| \begin{align*}
x_{1}^{\prime }&=9 x_{1}-2 x_{2} \\
x_{2}^{\prime }&=5 x_{1}-2 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.516 |
|
| \begin{align*}
x_{1}^{\prime }&=10 x_{1}-4 x_{2} \\
x_{2}^{\prime }&=4 x_{1}+2 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.395 |
|
| \begin{align*}
x_{1}^{\prime }&=-8 x_{1}+5 x_{2} \\
x_{2}^{\prime }&=-5 x_{1}+2 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.394 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}+4 x_{3} \\
x_{2}^{\prime }&=2 x_{2} \\
x_{3}^{\prime }&=-4 x_{1}-5 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.605 |
|
| \begin{align*}
x_{1}^{\prime }&=-3 x_{1}-x_{2} \\
x_{2}^{\prime }&=4 x_{1}-7 x_{2} \\
x_{3}^{\prime }&=6 x_{1}+6 x_{2}+4 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}+13 x_{2} \\
x_{2}^{\prime }&=-x_{1}-3 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.527 |
|
| \begin{align*}
x_{1}^{\prime }&=-3 x_{1}-10 x_{2} \\
x_{2}^{\prime }&=5 x_{1}+11 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.673 |
|
| \begin{align*}
x_{1}^{\prime }&=-x_{1}-5 x_{2}+x_{3} \\
x_{2}^{\prime }&=4 x_{1}-9 x_{2}-x_{3} \\
x_{3}^{\prime }&=3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.016 |
|
| \begin{align*}
x_{1}^{\prime }&=-4 x_{1} \\
x_{2}^{\prime }&=2 x_{1}+5 x_{2}-9 x_{3} \\
x_{3}^{\prime }&=5 x_{2}-x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.084 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}-2 x_{2}+x_{3} \\
x_{2}^{\prime }&=x_{1}-4 x_{2}+x_{3} \\
x_{3}^{\prime }&=2 x_{1}+2 x_{2}-3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.895 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}-4 x_{2}+3 x_{3} \\
x_{2}^{\prime }&=-9 x_{1}-3 x_{2}-9 x_{3} \\
x_{3}^{\prime }&=4 x_{1}+4 x_{2}+3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.833 |
|
| \begin{align*}
x_{1}^{\prime }&=-17 x_{1}-42 x_{3} \\
x_{2}^{\prime }&=-7 x_{1}+4 x_{2}-14 x_{3} \\
x_{3}^{\prime }&=7 x_{1}+18 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.695 |
|
| \begin{align*}
x_{1}^{\prime }&=-16 x_{1}+30 x_{2}-18 x_{3} \\
x_{2}^{\prime }&=-8 x_{1}+8 x_{2}+16 x_{3} \\
x_{3}^{\prime }&=8 x_{1}-15 x_{2}+9 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.649 |
|
| \begin{align*}
x_{1}^{\prime }&=-7 x_{1}-6 x_{2}-7 x_{3} \\
x_{2}^{\prime }&=-3 x_{1}-3 x_{2}-3 x_{3} \\
x_{3}^{\prime }&=7 x_{1}+6 x_{2}+7 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.688 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}-x_{2}-2 x_{3} \\
x_{2}^{\prime }&=x_{1}+6 x_{2}+x_{3} \\
x_{3}^{\prime }&=x_{1}+6 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.654 |
|
| \begin{align*}
x_{1}^{\prime }&=-x_{1}-4 x_{2}-2 x_{3} \\
x_{2}^{\prime }&=-4 x_{1}-5 x_{2}-6 x_{3} \\
x_{3}^{\prime }&=4 x_{1}+8 x_{2}+7 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.106 |
|
| \begin{align*}
x_{1}^{\prime }&=7 x_{1}-2 x_{2}+2 x_{3} \\
x_{2}^{\prime }&=4 x_{2}-x_{3} \\
x_{3}^{\prime }&=-x_{1}+x_{2}+4 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.653 |
|
| \begin{align*}
x_{1}^{\prime }&=-3 x_{1}-x_{2}-2 x_{3} \\
x_{2}^{\prime }&=x_{1}+x_{3} \\
x_{3}^{\prime }&=x_{1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.631 |
|
| \begin{align*}
x_{1}^{\prime }&=-2 x_{1}-x_{3} \\
x_{2}^{\prime }&=-x_{2} \\
x_{3}^{\prime }&=x_{1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.576 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}+13 x_{2} \\
x_{2}^{\prime }&=-x_{1}-2 x_{2} \\
x_{3}^{\prime }&=2 x_{3}+4 x_{4} \\
x_{4}^{\prime }&=2 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.062 |
|
| \begin{align*}
x_{1}^{\prime }&=7 x_{1}-x_{4} \\
x_{2}^{\prime }&=6 x_{2} \\
x_{3}^{\prime }&=-x_{3} \\
x_{4}^{\prime }&=2 x_{1}+5 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.262 |
|
| \begin{align*}
x_{1}^{\prime }&=-6 x_{1}+x_{2}+1 \\
x_{2}^{\prime }&=6 x_{1}-5 x_{2}+{\mathrm e}^{-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.835 |
|
| \begin{align*}
x_{1}^{\prime }&=9 x_{1}-2 x_{2}+9 t \\
x_{2}^{\prime }&=5 x_{1}-2 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| \begin{align*}
x_{1}^{\prime }&=10 x_{1}-4 x_{2} \\
x_{2}^{\prime }&=4 x_{1}+2 x_{2}+\frac {{\mathrm e}^{6 t}}{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.661 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}-4 x_{2}+3 x_{3}+{\mathrm e}^{6 t} \\
x_{2}^{\prime }&=-9 x_{1}-3 x_{2}-9 x_{3}+1 \\
x_{3}^{\prime }&=4 x_{1}+4 x_{2}+3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.222 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}-2 x_{2}+x_{3}+t \\
x_{2}^{\prime }&=x_{1}-4 x_{2}+x_{3} \\
x_{3}^{\prime }&=2 x_{1}+2 x_{2}-3 x_{3}+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.312 |
|
| \begin{align*}
x_{1}^{\prime }&=-3 x_{1}+4 x_{2} \\
x_{2}^{\prime }&=8 x_{1}+x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.484 |
|
| \begin{align*}
x_{1}^{\prime }&=-6 x_{2} \\
x_{2}^{\prime }&=x_{1}-5 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.491 |
|
| \begin{align*}
x_{1}^{\prime }&=5 x_{1}+9 x_{2} \\
x_{2}^{\prime }&=-2 x_{1}-x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.635 |
|
| \begin{align*}
x_{1}^{\prime }&=-4 x_{1} \\
x_{2}^{\prime }&=-4 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.293 |
|
| \begin{align*}
x_{1}^{\prime }&=7 x_{1}-2 x_{2} \\
x_{2}^{\prime }&=x_{1}+4 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.475 |
|
| \begin{align*}
x_{1}^{\prime }&=-3 x_{1}-5 x_{2} \\
x_{2}^{\prime }&=x_{1}-7 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.628 |
|
| \begin{align*}
x_{1}^{\prime }&=-2 x_{1}-x_{2} \\
x_{2}^{\prime }&=x_{1}-4 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.395 |
|
| \begin{align*}
x_{1}^{\prime }&=10 x_{1}-8 x_{2} \\
x_{2}^{\prime }&=2 x_{1}+2 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.412 |
|
| \begin{align*}
y_{1}^{\prime }&=y_{2} \\
y_{2}^{\prime }&=3 y_{2}-2 y_{1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.350 |
|
| \begin{align*}
y_{1}^{\prime }&=y_{1}+y_{2} \\
y_{2}^{\prime }&=3 y_{2}-y_{1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.289 |
|
| \begin{align*}
y_{1}^{\prime }&=y_{1}-y_{2} \\
y_{2}^{\prime }&=2 y_{1}+3 y_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.481 |
|
| \begin{align*}
y_{1}^{\prime }&=4 y_{2} \\
y_{2}^{\prime }&=4 y_{2}-y_{1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.295 |
|
| \begin{align*}
y_{1}^{\prime }&=y_{1}+y_{2} \\
y_{2}^{\prime }&=y_{1}-y_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.423 |
|
| \begin{align*}
y_{1}^{\prime }&=y_{2} \\
y_{2}^{\prime }&=y_{1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.293 |
|
| \begin{align*}
y_{1}^{\prime }&=y_{2}-y_{1} \\
y_{2}^{\prime }&=3 y_{1}-4 y_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.512 |
|
| \begin{align*}
2 y_{1}^{\prime }&=y_{1}+y_{2} \\
2 y_{2}^{\prime }&=5 y_{2}-3 y_{1} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 3 \\
y_{2} \left (0\right ) &= 7 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.390 |
|
| \begin{align*}
y_{1}^{\prime }&=-2 y_{2} \\
y_{2}^{\prime }&=y_{1}+2 y_{2} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= -1 \\
y_{2} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.455 |
|
| \begin{align*}
y_{1}^{\prime }&=1 \\
y_{2}^{\prime }&=2 y_{1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.399 |
|
| \begin{align*}
2 y_{1}^{\prime }+y_{2}^{\prime }-4 y_{1}-y_{2}&={\mathrm e}^{x} \\
y_{1}^{\prime }+3 y_{1}+y_{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.653 |
|
| \begin{align*}
y_{1}^{\prime }&=y_{2} \\
y_{2}^{\prime }&=-y_{1}+y_{3} \\
y_{3}^{\prime }&=-y_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.671 |
|
| \begin{align*}
x^{\prime }+2 x-y&=0 \\
x+y^{\prime }-2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.464 |
|
| \begin{align*}
2 x^{\prime }+x-5 y^{\prime }-4 y&=0 \\
-y^{\prime }-2 x+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.385 |
|
| \begin{align*}
x^{\prime }-x+3 y&=0 \\
3 x-y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.384 |
|
| \begin{align*}
x^{\prime \prime }+x^{\prime }+y^{\prime }-2 y&=0 \\
x^{\prime }+x-y^{\prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.038 |
|
| \begin{align*}
x^{\prime \prime }-3 x-4 y&=0 \\
x+y^{\prime \prime }+y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.035 |
|
| \begin{align*}
y_{1}^{\prime }-y_{2}&=0 \\
4 y_{1}+y_{2}^{\prime }-4 y_{2}-2 y_{3}&=0 \\
-2 y_{1}+y_{2}+y_{3}^{\prime }+y_{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.682 |
|
| \begin{align*}
y_{1}^{\prime }-2 y_{1}+3 y_{2}-3 y_{3}&=0 \\
-4 y_{1}+y_{2}^{\prime }+5 y_{2}-3 y_{3}&=0 \\
-4 y_{1}+4 y_{2}+y_{3}^{\prime }-2 y_{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.644 |
|
| \begin{align*}
x^{\prime }+x+2 y&=8 \\
2 x+y^{\prime }-2 y&=2 \,{\mathrm e}^{-t}-8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.658 |
|
| \begin{align*}
x^{\prime }&=2 x-3 y+t \,{\mathrm e}^{-t} \\
y^{\prime }&=2 x-3 y+{\mathrm e}^{-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.579 |
|
| \begin{align*}
x^{\prime }-x-2 y&={\mathrm e}^{t} \\
-4 x+y^{\prime }-3 y&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.665 |
|
| \begin{align*}
x^{\prime }-4 x+3 y&=\sin \left (t \right ) \\
-2 x+y^{\prime }+y&=-2 \cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.710 |
|
| \begin{align*}
x^{\prime }-y&=0 \\
-x+y^{\prime }&={\mathrm e}^{t}+{\mathrm e}^{-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.592 |
|
| \begin{align*}
x^{\prime }+2 x+5 y&=0 \\
-x+y^{\prime }-2 y&=\sin \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.724 |
|
| \begin{align*}
x^{\prime }-2 x+2 y^{\prime }&=-4 \,{\mathrm e}^{2 t} \\
2 x^{\prime }-3 x+3 y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.634 |
|
| \begin{align*}
3 x^{\prime }+2 x+y^{\prime }-6 y&=5 \,{\mathrm e}^{t} \\
4 x^{\prime }+2 x+y^{\prime }-8 y&=5 \,{\mathrm e}^{t}+2 t -3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.831 |
|
| \begin{align*}
x^{\prime }-5 x+3 y&=2 \,{\mathrm e}^{3 t} \\
-x+y^{\prime }-y&=5 \,{\mathrm e}^{-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.750 |
|
| \begin{align*}
x^{\prime }-2 x+y&=0 \\
x+y^{\prime }-2 y&=-5 \,{\mathrm e}^{t} \sin \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.691 |
|
| \begin{align*}
x^{\prime }+4 x+2 y&=\frac {2}{{\mathrm e}^{t}-1} \\
6 x-y^{\prime }+3 y&=\frac {3}{{\mathrm e}^{t}-1} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.036 |
|
| \begin{align*}
x^{\prime }-x+y&=\sec \left (t \right ) \\
-2 x+y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.787 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}-x_{2} \\
x_{2}^{\prime }&=-4 x_{1}+x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.391 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}-3 x_{2} \\
x_{2}^{\prime }&=3 x_{1}+x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.380 |
|
| \begin{align*}
x_{1}^{\prime }&=5 x_{1}+3 x_{2} \\
x_{2}^{\prime }&=-3 x_{1}-x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.387 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}-x_{2}+x_{3} \\
x_{2}^{\prime }&=x_{1}+2 x_{2}-x_{3} \\
x_{3}^{\prime }&=x_{1}-x_{2}+2 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.619 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}-x_{2}+x_{3} \\
x_{2}^{\prime }&=x_{1}+x_{2}+x_{3} \\
x_{3}^{\prime }&=4 x_{1}-x_{2}+4 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.736 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}+x_{2} \\
x_{2}^{\prime }&=x_{1}+3 x_{2}-x_{3} \\
x_{3}^{\prime }&=-x_{1}+2 x_{2}+3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.945 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}-2 x_{2}-x_{3} \\
x_{2}^{\prime }&=3 x_{1}-4 x_{2}-3 x_{3} \\
x_{3}^{\prime }&=2 x_{1}-4 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.661 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}-x_{2}+x_{3} \\
x_{2}^{\prime }&=x_{1}+x_{2}-x_{3} \\
x_{3}^{\prime }&=-2 x_{2}+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 ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.593 |
|
| \begin{align*}
x_{1}^{\prime }&=-x_{1}+x_{2}-2 x_{3} \\
x_{2}^{\prime }&=4 x_{1}+x_{2} \\
x_{3}^{\prime }&=2 x_{1}+x_{2}-x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.654 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}+x_{2}+26 \sin \left (t \right ) \\
x_{2}^{\prime }&=3 x_{1}+4 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.796 |
|
| \begin{align*}
x_{1}^{\prime }&=-x_{1}+8 x_{2}+9 t \\
x_{2}^{\prime }&=x_{1}+x_{2}+3 \,{\mathrm e}^{-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.833 |
|
| \begin{align*}
x_{1}^{\prime }&=-x_{1}+2 x_{2} \\
x_{2}^{\prime }&=-3 x_{1}+4 x_{2}+\frac {{\mathrm e}^{3 t}}{1+{\mathrm e}^{2 t}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.040 |
|
| \begin{align*}
x_{1}^{\prime }&=-4 x_{1}-2 x_{2}+\frac {2}{{\mathrm e}^{t}-1} \\
x_{2}^{\prime }&=6 x_{1}+3 x_{2}-\frac {3}{{\mathrm e}^{t}-1} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.053 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}+x_{2}+{\mathrm e}^{2 t} \\
x_{2}^{\prime }&=-2 x_{1}+3 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.914 |
|
| \begin{align*}
x_{1}^{\prime }&=-x_{1}-5 x_{2} \\
x_{2}^{\prime }&=x_{1}+x_{2}+\frac {4}{\sin \left (2 t \right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.046 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}+x_{2}+27 t \\
x_{2}^{\prime }&=-x_{1}+4 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.547 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}-x_{2}+{\mathrm e}^{t} \\
x_{2}^{\prime }&=4 x_{1}-x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.582 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}-2 x_{2} \\
x_{2}^{\prime }&=2 x_{1}-x_{2}+35 \,{\mathrm e}^{t} t^{{3}/{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.566 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}-x_{2}+x_{3} \\
x_{2}^{\prime }&=x_{1}+x_{2}-x_{3}+6 \,{\mathrm e}^{-t} \\
x_{3}^{\prime }&=2 x_{1}-x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.072 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}-2 x_{2}-x_{3} \\
x_{2}^{\prime }&=-x_{1}+x_{2}+x_{3}+12 t \\
x_{3}^{\prime }&=x_{1}-x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.037 |
|
| \begin{align*}
x_{1}^{\prime }&=-3 x_{1}+4 x_{2}-2 x_{3}+{\mathrm e}^{t} \\
x_{2}^{\prime }&=x_{1}+x_{2} \\
x_{3}^{\prime }&=6 x_{1}-6 x_{2}+5 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
119.389 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}-x_{2}-x_{3}+4 \,{\mathrm e}^{t} \\
x_{2}^{\prime }&=x_{1}+x_{2} \\
x_{3}^{\prime }&=3 x_{1}+x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.227 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}-x_{2}+2 x_{3} \\
x_{2}^{\prime }&=x_{1}+2 x_{3} \\
x_{3}^{\prime }&=-2 x_{1}+x_{2}-x_{3}+4 \sin \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.380 |
|
| \begin{align*}
x_{1}^{\prime }&=4 x_{1}-x_{2}-x_{3}+{\mathrm e}^{3 t} \\
x_{2}^{\prime }&=x_{1}+2 x_{2}-x_{3} \\
x_{3}^{\prime }&=x_{1}+x_{2}+2 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.744 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}-x_{2}-x_{3}+2 \,{\mathrm e}^{2 t} \\
x_{2}^{\prime }&=3 x_{1}-2 x_{2}-3 x_{3} \\
x_{3}^{\prime }&=-x_{1}+x_{2}+2 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.836 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}-x_{3}+24 t \\
x_{2}^{\prime }&=x_{1}-x_{2} \\
x_{3}^{\prime }&=3 x_{1}-x_{2}-x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.841 |
|
| \begin{align*}
y^{\prime }&=-4 x-y \\
x^{\prime }&=2 x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.516 |
|
| \begin{align*}
x^{\prime }-y^{\prime }+y&=-{\mathrm e}^{t} \\
x+y^{\prime }-y&={\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.638 |
|
| \begin{align*}
x^{\prime }+2 x+y^{\prime }+y&=t \\
5 x+y^{\prime }+3 y&=t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.763 |
|
| \begin{align*}
x^{\prime }+x+2 y^{\prime }+7 y&={\mathrm e}^{t}+2 \\
-2 x+y^{\prime }+3 y&={\mathrm e}^{t}-1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.113 |
|
| \begin{align*}
x^{\prime }-x+y^{\prime }+3 y&={\mathrm e}^{-t}-1 \\
x^{\prime }+2 x+y^{\prime }+3 y&=1+{\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.201 |
|
| \begin{align*}
x^{\prime }-x+y^{\prime }+2 y&=1+{\mathrm e}^{t} \\
y^{\prime }+2 y+z^{\prime }+z&={\mathrm e}^{t}+2 \\
x^{\prime }-x+z^{\prime }+z&=3+{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.717 |
|
| \begin{align*}
x^{\prime }&=x+3 y \\
y^{\prime }&=5 x+3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.357 |
|
| \begin{align*}
x^{\prime \prime }&=4 y+{\mathrm e}^{t} \\
y^{\prime \prime }&=4 x-{\mathrm e}^{t} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.052 |
|
| \begin{align*}
x^{\prime }&=-\lambda _{1} x \\
y^{\prime }&=\lambda _{1} x-\lambda _{2} y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.359 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}-18 x_{2} \\
x_{2}^{\prime }&=2 x_{1}-9 x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 2 \\
x_{2} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.409 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}+3 x_{2} \\
x_{2}^{\prime }&=5 x_{1}+3 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.392 |
|
| \begin{align*}
x_{1}^{\prime }&=-x_{1}+3 x_{2} \\
x_{2}^{\prime }&=-3 x_{1}+5 x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.366 |
|
| \begin{align*}
x_{1}^{\prime }&=4 x_{1}-x_{2} \\
x_{2}^{\prime }&=5 x_{1}+2 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.566 |
|
| \begin{align*}
x_{1}^{\prime }&=-2 x_{1}+x_{2} \\
x_{2}^{\prime }&=x_{1}-2 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.356 |
|
| \begin{align*}
x_{1}^{\prime }&=-2 x_{1}+x_{2}+2 \,{\mathrm e}^{-t} \\
x_{2}^{\prime }&=x_{1}-2 x_{2}+3 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.664 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}-x_{2} \\
x_{2}^{\prime }&=16 x_{1}-5 x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.384 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}-2 x_{2} \\
x_{2}^{\prime }&=3 x_{1}-4 x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.416 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}-18 x_{2} \\
x_{2}^{\prime }&=2 x_{1}-9 x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| \begin{align*}
x_{1}^{\prime }&=-x_{1}+3 x_{2} \\
x_{2}^{\prime }&=-3 x_{1}+5 x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.322 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}-18 x_{2} \\
x_{2}^{\prime }&=2 x_{1}-9 x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 2 \\
x_{2} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.343 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}-x_{2} \\
x_{2}^{\prime }&=4 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*} |
✓ |
✓ |
✓ |
✓ |
0.388 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}+x_{2}-8 \\
x_{2}^{\prime }&=x_{1}+x_{2}+3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.510 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}+x_{2}-8 \\
x_{2}^{\prime }&=x_{1}+x_{2}+3 \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.491 |
|
| \begin{align*}
y_{1}^{\prime }&=y_{1} \\
y_{2}^{\prime }&=y_{1}+y_{2} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.327 |
|
| \begin{align*}
y_{1}^{\prime }&=y_{2} \\
y_{2}^{\prime }&=6 y_{1}+y_{2} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.448 |
|
| \begin{align*}
y_{1}^{\prime }&=y_{1}+y_{2} \\
y_{2}^{\prime }&=y_{1}+y_{2}+{\mathrm e}^{3 x} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 0 \\
y_{2} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.535 |
|
| \begin{align*}
y_{1}^{\prime }&=3 y_{1}+x y_{3} \\
y_{2}^{\prime }&=y_{2}+x^{3} y_{3} \\
y_{3}^{\prime }&=2 x y_{1}-y_{2}+{\mathrm e}^{x} y_{3} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.050 |
|
| \begin{align*}
x^{\prime }&=x+3 y \\
y^{\prime }&=3 x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.414 |
|
| \begin{align*}
x^{\prime }&=x+3 y \\
y^{\prime }&=3 x+y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 5 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.428 |
|
| \begin{align*}
x^{\prime }&=x+2 y \\
y^{\prime }&=3 x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.450 |
|
| \begin{align*}
x^{\prime }&=x+2 y+t -1 \\
y^{\prime }&=3 x+2 y-5 t -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.738 |
|
| \begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.303 |
|
| \begin{align*}
x^{\prime }&=x \\
y^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.267 |
|
| \begin{align*}
x^{\prime }&=-3 x+4 y \\
y^{\prime }&=-2 x+3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.441 |
|
| \begin{align*}
x^{\prime }&=4 x-2 y \\
y^{\prime }&=5 x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.638 |
|
| \begin{align*}
x^{\prime }&=5 x+4 y \\
y^{\prime }&=-x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.392 |
|
| \begin{align*}
x^{\prime }&=4 x-3 y \\
y^{\prime }&=8 x-6 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.474 |
|
| \begin{align*}
x^{\prime }&=2 x \\
y^{\prime }&=3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.328 |
|
| \begin{align*}
x^{\prime }&=-4 x-y \\
y^{\prime }&=x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.354 |
|
| \begin{align*}
x^{\prime }&=7 x+6 y \\
y^{\prime }&=2 x+6 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.478 |
|
| \begin{align*}
x^{\prime }&=x-2 y \\
y^{\prime }&=4 x+5 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.621 |
|
| \begin{align*}
x^{\prime }&=x+y-5 t +2 \\
y^{\prime }&=4 x-2 y-8 t -8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.725 |
|
| \begin{align*}
x^{\prime }&=3 x-4 y \\
y^{\prime }&=4 x-7 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.474 |
|
| \begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=4 x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.459 |
|
| \begin{align*}
x^{\prime }&=-3 x+\sqrt {2}\, y \\
y^{\prime }&=\sqrt {2}\, x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.513 |
|
| \begin{align*}
x^{\prime }&=5 x+3 y \\
y^{\prime }&=-6 x-4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.439 |
|
| \begin{align*}
x^{\prime }&=3 x+2 y \\
y^{\prime }&=-2 x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.368 |
|
| \begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=-x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.458 |
|
| \begin{align*}
x^{\prime }&=3 x-5 y \\
y^{\prime }&=-x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.640 |
|
| \begin{align*}
x^{\prime }&=x+2 y \\
y^{\prime }&=-4 x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.555 |
|
| \begin{align*}
x^{\prime }&=3 x+2 y+z \\
y^{\prime }&=-2 x-y+3 z \\
z^{\prime }&=x+y+z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.832 |
|
| \begin{align*}
x^{\prime }&=-x+y-z \\
y^{\prime }&=2 x-y-4 z \\
z^{\prime }&=3 x-y+z \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
15.074 |
|
| \begin{align*}
x^{\prime }&=x+2 y-4 t +1 \\
y^{\prime }&=-x+2 y+3 t +4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.931 |
|
| \begin{align*}
x^{\prime }&=-2 x+y-t +3 \\
y^{\prime }&=x+4 y+t -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.322 |
|
| \begin{align*}
x^{\prime }&=-4 x+y-t +3 \\
y^{\prime }&=-x-5 y+t +1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.853 |
|
| \begin{align*}
x^{\prime }&=x y+1 \\
y^{\prime }&=-x+y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.043 |
|
| \begin{align*}
x^{\prime }&=t y+1 \\
y^{\prime }&=-t x+y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.037 |
|
| \begin{align*}
x^{\prime }&=3 x-5 y \\
y^{\prime }&=4 x+8 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.355 |
|
| \begin{align*}
x^{\prime }&=4 x-7 y \\
y^{\prime }&=5 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.369 |
|
| \begin{align*}
x^{\prime }&=-3 x+4 y-9 z \\
y^{\prime }&=6 x-y \\
z^{\prime }&=10 x+4 y+3 z \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
16.428 |
|
| \begin{align*}
x^{\prime }&=x-y \\
y^{\prime }&=x+2 z \\
z^{\prime }&=z-x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
12.296 |
|
| \begin{align*}
x^{\prime }&=x-y+z+t -1 \\
y^{\prime }&=2 x+y-z-3 t^{2} \\
z^{\prime }&=x+y+z+t^{2}-t +2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
5.254 |
|
| \begin{align*}
x^{\prime }&=-3 x+4 y+{\mathrm e}^{-t} \sin \left (2 t \right ) \\
y^{\prime }&=5 x+9 z+4 \,{\mathrm e}^{-t} \cos \left (2 t \right ) \\
z^{\prime }&=y+6 z-{\mathrm e}^{-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
177.561 |
|
| \begin{align*}
x^{\prime }&=4 x+2 y+{\mathrm e}^{t} \\
y^{\prime }&=-x+3 y-{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.072 |
|
| \begin{align*}
x^{\prime }&=7 x+5 y-9 z-8 \,{\mathrm e}^{-2 t} \\
y^{\prime }&=4 x+y+z+2 \,{\mathrm e}^{5 t} \\
z^{\prime }&=-2 y+3 z+{\mathrm e}^{5 t}-3 \,{\mathrm e}^{-2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
44.734 |
|
| \begin{align*}
x^{\prime }&=x-y+2 z+{\mathrm e}^{-t}-3 t \\
y^{\prime }&=3 x-4 y+z+2 \,{\mathrm e}^{-t}+t \\
z^{\prime }&=-2 x+5 y+6 z+2 \,{\mathrm e}^{-t}-t \\
\end{align*} |
✓ |
✗ |
✓ |
✗ |
204.309 |
|
| \begin{align*}
x^{\prime }&=3 x-7 y+4 \sin \left (t \right )+\left (t -4\right ) {\mathrm e}^{4 t} \\
y^{\prime }&=x+y+8 \sin \left (t \right )+\left (2 t +1\right ) {\mathrm e}^{4 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.573 |
|
| \begin{align*}
x^{\prime }&=3 x-4 y \\
y^{\prime }&=4 x-7 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.491 |
|
| \begin{align*}
x^{\prime }&=-2 x+5 y \\
y^{\prime }&=-2 x+4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.648 |
|
| \begin{align*}
x^{\prime }&=-x+\frac {y}{4} \\
y^{\prime }&=x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.490 |
|
| \begin{align*}
x^{\prime }&=2 x+y \\
y^{\prime }&=-x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.366 |
|
| \begin{align*}
x^{\prime }&=x+2 y+z \\
y^{\prime }&=6 x-y \\
z^{\prime }&=-x-2 y-z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.894 |
|
| \begin{align*}
x^{\prime }&=x+z \\
y^{\prime }&=x+y \\
z^{\prime }&=-2 x-z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.886 |
|
| \begin{align*}
x^{\prime }&=x+2 y \\
y^{\prime }&=4 x+3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.467 |
|
| \begin{align*}
x^{\prime }&=2 x+2 y \\
y^{\prime }&=x+3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.457 |
|
| \begin{align*}
x^{\prime }&=-4 x+2 y \\
y^{\prime }&=-\frac {5 x}{2}+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.491 |
|
| \begin{align*}
x^{\prime }&=-\frac {5 x}{2}+2 y \\
y^{\prime }&=\frac {3 x}{4}-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.515 |
|
| \begin{align*}
x^{\prime }&=10 x-5 y \\
y^{\prime }&=8 x-12 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.519 |
|
| \begin{align*}
x^{\prime }&=-6 x+2 y \\
y^{\prime }&=-3 x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.474 |
|
| \begin{align*}
x^{\prime }&=x+y-z \\
y^{\prime }&=2 y \\
z^{\prime }&=y-z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.715 |
|
| \begin{align*}
x^{\prime }&=2 x-7 y \\
y^{\prime }&=5 x+10 y+4 z \\
z^{\prime }&=5 y+2 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.917 |
|
| \begin{align*}
x^{\prime }&=-x+y \\
y^{\prime }&=x+2 y+z \\
z^{\prime }&=3 y-z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.842 |
|
| \begin{align*}
x^{\prime }&=x+z \\
y^{\prime }&=y \\
z^{\prime }&=x+z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.606 |
|
| \begin{align*}
x^{\prime }&=-x-y \\
y^{\prime }&=\frac {3 x}{4}-\frac {3 y}{2}+3 z \\
z^{\prime }&=\frac {x}{8}+\frac {y}{4}-\frac {z}{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.072 |
|
| \begin{align*}
x^{\prime }&=-x-y \\
y^{\prime }&=\frac {3 x}{4}-\frac {3 y}{2}+3 z \\
z^{\prime }&=\frac {x}{8}+\frac {y}{4}-\frac {z}{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.855 |
|
| \begin{align*}
x^{\prime }&=-x+4 y+2 z \\
y^{\prime }&=4 x-y-2 z \\
z^{\prime }&=6 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.757 |
|
| \begin{align*}
x^{\prime }&=\frac {x}{2} \\
y^{\prime }&=x-\frac {y}{2} \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 4 \\
y \left (0\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.422 |
|
| \begin{align*}
x^{\prime }&=x+y+4 z \\
y^{\prime }&=2 y \\
z^{\prime }&=x+y+z \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 3 \\
z \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.770 |
|
| \begin{align*}
x^{\prime }&=\frac {9 x}{10}+\frac {21 y}{10}+\frac {16 z}{5} \\
y^{\prime }&=\frac {7 x}{10}+\frac {13 y}{2}+\frac {21 z}{5} \\
z^{\prime }&=\frac {11 x}{10}+\frac {17 y}{10}+\frac {17 z}{5} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
88.783 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}+2 x_{3}-\frac {9 x_{4}}{5} \\
x_{2}^{\prime }&=\frac {51 x_{2}}{10}-x_{4}+3 x_{5} \\
x_{3}^{\prime }&=x_{1}+2 x_{2}-3 x_{3} \\
x_{4}^{\prime }&=x_{2}-\frac {31 x_{3}}{10}+4 x_{4} \\
x_{5}^{\prime }&=-\frac {14 x_{1}}{5}+\frac {3 x_{4}}{2}-x_{5} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
50.188 |
|
| \begin{align*}
x^{\prime }&=3 x-y \\
y^{\prime }&=9 x-3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.378 |
|
| \begin{align*}
x^{\prime }&=-6 x+5 y \\
y^{\prime }&=-5 x+4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.390 |
|
| \begin{align*}
x^{\prime }&=-x+3 y \\
y^{\prime }&=-3 x+5 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.369 |
|
| \begin{align*}
x^{\prime }&=12 x-9 y \\
y^{\prime }&=4 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.425 |
|
| \begin{align*}
x^{\prime }&=3 x-y-z \\
y^{\prime }&=x+y-z \\
z^{\prime }&=x-y+z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.619 |
|
| \begin{align*}
x^{\prime }&=3 x+2 y+4 z \\
y^{\prime }&=2 x+2 z \\
z^{\prime }&=4 x+2 y+3 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.728 |
|
| \begin{align*}
x^{\prime }&=5 x-4 y \\
y^{\prime }&=x+2 z \\
z^{\prime }&=2 y+5 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.753 |
|
| \begin{align*}
x^{\prime }&=x \\
y^{\prime }&=3 y+z \\
z^{\prime }&=z-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.601 |
|
| \begin{align*}
x^{\prime }&=x \\
y^{\prime }&=2 x+2 y-z \\
z^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.579 |
|
| \begin{align*}
x^{\prime }&=4 x+y \\
y^{\prime }&=4 y+z \\
z^{\prime }&=4 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.511 |
|
| \begin{align*}
x^{\prime }&=2 x+4 y \\
y^{\prime }&=-x+6 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= -1 \\
y \left (0\right ) &= 6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.451 |
|
| \begin{align*}
x^{\prime }&=z \\
y^{\prime }&=y \\
z^{\prime }&=x \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 2 \\
z \left (0\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.562 |
|
| \begin{align*}
x^{\prime }&=6 x-y \\
y^{\prime }&=5 x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.659 |
|
| \begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=-2 x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.496 |
|
| \begin{align*}
x^{\prime }&=5 x+y \\
y^{\prime }&=-2 x+3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.661 |
|
| \begin{align*}
x^{\prime }&=4 x+5 y \\
y^{\prime }&=-2 x+6 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.701 |
|
| \begin{align*}
x^{\prime }&=4 x-5 y \\
y^{\prime }&=5 x-4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.565 |
|
| \begin{align*}
x^{\prime }&=x-8 y \\
y^{\prime }&=x-3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.665 |
|
| \begin{align*}
x^{\prime }&=z \\
y^{\prime }&=-z \\
z^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.715 |
|
| \begin{align*}
x^{\prime }&=2 x+y+2 z \\
y^{\prime }&=3 x+6 z \\
z^{\prime }&=-4 x-3 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.292 |
|
| \begin{align*}
x^{\prime }&=x-12 y-14 z \\
y^{\prime }&=x+2 y-3 z \\
z^{\prime }&=x+y-2 z \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 4 \\
y \left (0\right ) &= 6 \\
z \left (0\right ) &= -7 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.134 |
|
| \begin{align*}
x^{\prime }&=2 x+3 y-7 \\
y^{\prime }&=-x-2 y+5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| \begin{align*}
x^{\prime }&=5 x+9 y+2 \\
y^{\prime }&=-x+11 y+6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.700 |
|
| \begin{align*}
x^{\prime }&=-2 x+3 y \\
y^{\prime }&=-2 x+5 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= -2 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.480 |
|
| \begin{align*}
x^{\prime }&=-x+4 y \\
y^{\prime }&=2 x-3 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 3 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.460 |
|
| \begin{align*}
x^{\prime }&=2 x-y \\
y^{\prime }&=-x+2 y+4 \,{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.671 |
|
| \begin{align*}
x^{\prime }&=6 x-7 y+10 \\
y^{\prime }&=x-2 y-2 \,{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.763 |
|
| \begin{align*}
x^{\prime }&=9 x+4 y \\
y^{\prime }&=-6 x-y \\
z^{\prime }&=6 x+4 y+3 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.445 |
|
| \begin{align*}
x^{\prime }&=x-3 y \\
y^{\prime }&=3 x+7 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.236 |
|
| \begin{align*}
x^{\prime }&=x-2 y \\
y^{\prime }&=2 x+5 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.236 |
|
| \begin{align*}
x^{\prime }&=7 x+y \\
y^{\prime }&=-4 x+3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.247 |
|
| \begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=y \\
z^{\prime }&=z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.353 |
|
| \begin{align*}
x^{\prime }&=2 x+y-z \\
y^{\prime }&=-x+2 z \\
z^{\prime }&=-x-2 y+4 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.404 |
|
| \begin{align*}
x^{\prime }&=x+2 y+2 t +1 \\
y^{\prime }&=5 x+y+3 t -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.820 |
|
| \begin{align*}
x^{\prime }+y^{\prime }-x&=y+t \\
x^{\prime }+y^{\prime }&=2 x+3 y+{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.151 |
|
| \begin{align*}
2 x^{\prime }+y^{\prime }-x&=y+t \\
x^{\prime }+y^{\prime }&=2 x+3 y+{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.190 |
|
| \begin{align*}
x^{\prime }+y^{\prime }-x&=y+t +\sin \left (t \right )+\cos \left (t \right ) \\
x^{\prime }+y^{\prime }&=2 x+3 y+{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.214 |
|
| \begin{align*}
x^{\prime }&=3 x+y \\
y^{\prime }&=-x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.305 |
|
| \begin{align*}
x^{\prime }&=a x \\
y^{\prime }&=b \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.733 |
|
| \begin{align*}
x^{\prime }&=a y \\
y^{\prime }&=-a x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.804 |
|
| \begin{align*}
x^{\prime }&=a y \\
y^{\prime }&=b x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.881 |
|
| \begin{align*}
x^{\prime }&=a x-y \\
y^{\prime }&=x+a y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.797 |
|
| \begin{align*}
x^{\prime }&=a x+b y \\
y^{\prime }&=c x+b y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.817 |
|
| \begin{align*}
a x^{\prime }+b y^{\prime }&=\alpha x+\beta y \\
b x^{\prime }-a y^{\prime }&=\beta x-\alpha y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.730 |
|
| \begin{align*}
x^{\prime }&=-y \\
y^{\prime }&=2 x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.960 |
|
| \begin{align*}
x^{\prime }+3 x+4 y&=0 \\
y^{\prime }+2 x+5 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.714 |
|
| \begin{align*}
x^{\prime }&=-5 x-2 y \\
y^{\prime }&=x-7 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.904 |
|
| \begin{align*}
x^{\prime }&=a_{1} x+b_{1} y+c_{1} \\
y^{\prime }&=a_{2} x+b_{2} y+c_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.923 |
|
| \begin{align*}
x^{\prime }+2 y&=3 t \\
y^{\prime }-2 x&=4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.083 |
|
| \begin{align*}
x^{\prime }+y-t^{2}+6 t +1&=0 \\
-x+y^{\prime }&=-3 t^{2}+3 t +1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.243 |
|
| \begin{align*}
x^{\prime }+3 x-y&={\mathrm e}^{2 t} \\
y^{\prime }+x+5 y&={\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.971 |
|
| \begin{align*}
x^{\prime }+2 x+y^{\prime }+y&={\mathrm e}^{2 t}+t \\
x^{\prime }-x+y^{\prime }+3 y&={\mathrm e}^{t}-1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.328 |
|
| \begin{align*}
x^{\prime }+y^{\prime }-y&={\mathrm e}^{t} \\
2 x^{\prime }+y^{\prime }+2 y&=\cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.086 |
|
| \begin{align*}
4 x^{\prime }+9 y^{\prime }+2 x+31 y&={\mathrm e}^{t} \\
3 x^{\prime }+7 y^{\prime }+x+24 y&=3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.725 |
|
| \begin{align*}
4 x^{\prime }+9 y^{\prime }+11 x+31 y&={\mathrm e}^{t} \\
3 x^{\prime }+7 y^{\prime }+8 x+24 y&={\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.989 |
|
| \begin{align*}
4 x^{\prime }+9 y^{\prime }+44 x+49 y&=t \\
3 x^{\prime }+7 y^{\prime }+34 x+38 y&={\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.208 |
|
| \begin{align*}
x^{\prime }&=x f \left (t \right )+y g \left (t \right ) \\
y^{\prime }&=-x g \left (t \right )+y f \left (t \right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.072 |
|
| \begin{align*}
x^{\prime }+\left (a x+b y\right ) f \left (t \right )&=g \left (t \right ) \\
y^{\prime }+\left (c x+d y\right ) f \left (t \right )&=h \left (t \right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.078 |
|
| \begin{align*}
x^{\prime }&=x \cos \left (t \right ) \\
y^{\prime }&=x \,{\mathrm e}^{-\sin \left (t \right )} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.069 |
|
| \begin{align*}
t x^{\prime }+y&=0 \\
y^{\prime } t +x&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.063 |
|
| \begin{align*}
t x^{\prime }+2 x&=t \\
y^{\prime } t -\left (t +2\right ) x-t y&=-t \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.073 |
|
| \begin{align*}
t x^{\prime }+2 x-2 y&=t \\
y^{\prime } t +x+5 y&=t^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.076 |
|
| \begin{align*}
t^{2} \left (1-\sin \left (t \right )\right ) x^{\prime }&=t \left (1-2 \sin \left (t \right )\right ) x+t^{2} y \\
t^{2} \left (1-\sin \left (t \right )\right ) y^{\prime }&=\left (t \cos \left (t \right )-\sin \left (t \right )\right ) x+t \left (1-t \cos \left (t \right )\right ) y \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.099 |
|
| \begin{align*}
x^{\prime }+y^{\prime }+y&=f \left (t \right ) \\
x^{\prime \prime }+y^{\prime \prime }+y^{\prime }+x+y&=g \left (t \right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.133 |
|
| \begin{align*}
2 x^{\prime }+y^{\prime }-3 x&=0 \\
x^{\prime \prime }+y^{\prime }-2 y&={\mathrm e}^{2 t} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.122 |
|
| \begin{align*}
x^{\prime }+x-y^{\prime }&=2 t \\
x^{\prime \prime }+y^{\prime }-9 x+3 y&=\sin \left (2 t \right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.122 |
|
| \begin{align*}
x^{\prime }-x+2 y&=0 \\
x^{\prime \prime }-2 y^{\prime }&=2 t -\cos \left (2 t \right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.116 |
|
| \begin{align*}
t x^{\prime }-y^{\prime } t -2 y&=0 \\
t x^{\prime \prime }+2 x^{\prime }+t x&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.110 |
|
| \begin{align*}
x^{\prime \prime }+a y&=0 \\
y^{\prime \prime }-a^{2} y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.106 |
|
| \begin{align*}
x^{\prime \prime }&=a x+b y \\
y^{\prime \prime }&=c x+d y \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.108 |
|
| \begin{align*}
x^{\prime \prime }&=a_{1} x+b_{1} y+c_{1} \\
y^{\prime \prime }&=a_{2} x+b_{2} y+c_{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.107 |
|
| \begin{align*}
x^{\prime \prime }+x+y&=-5 \\
y^{\prime \prime }-4 x-3 y&=-3 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.104 |
|
| \begin{align*}
x^{\prime \prime }&=\left (3 \cos \left (a t +b \right )^{2}-1\right ) c^{2} x+\frac {3 c^{2} y \sin \left (2 a t b \right )}{2} \\
y^{\prime \prime }&=\left (3 \sin \left (a t +b \right )^{2}-1\right ) c^{2} y+\frac {3 c^{2} x \sin \left (2 a t b \right )}{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.122 |
|
| \begin{align*}
x^{\prime \prime }+6 x+7 y&=0 \\
y^{\prime \prime }+3 x+2 y&=2 t \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.110 |
|
| \begin{align*}
x^{\prime \prime }-a y^{\prime }+b x&=0 \\
y^{\prime \prime }+a x^{\prime }+b y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.125 |
|
| \begin{align*}
a_{1} x^{\prime \prime }+b_{1} x^{\prime }+c_{1} x-A y^{\prime }&=B \,{\mathrm e}^{i \omega t} \\
a_{2} y^{\prime \prime }+b_{2} y^{\prime }+c_{2} y+A x^{\prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.138 |
|
| \begin{align*}
x^{\prime \prime }+a \left (x^{\prime }-y^{\prime }\right )+b_{1} x&=c_{1} {\mathrm e}^{i \omega t} \\
y^{\prime \prime }+a \left (y^{\prime }-x^{\prime }\right )+b_{2} y&=c_{2} {\mathrm e}^{i \omega t} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.137 |
|
| \begin{align*}
\operatorname {a11} x^{\prime \prime }+\operatorname {b11} x^{\prime }+\operatorname {c11} x+\operatorname {a12} y^{\prime \prime }+\operatorname {b12} y^{\prime }+\operatorname {c12} y&=0 \\
\operatorname {a21} x^{\prime \prime }+\operatorname {b21} x^{\prime }+\operatorname {c21} x+\operatorname {a22} y^{\prime \prime }+\operatorname {b22} y^{\prime }+\operatorname {c22} y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.149 |
|
| \begin{align*}
x^{\prime \prime }-2 x^{\prime }-y^{\prime }+y&=0 \\
y^{\prime \prime \prime }-y^{\prime \prime }+2 x^{\prime }-x&=t \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.138 |
|
| \begin{align*}
x^{\prime \prime }+y^{\prime \prime }+y^{\prime }&=\sinh \left (2 t \right ) \\
2 x^{\prime \prime }+y^{\prime \prime }&=2 t \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.158 |
|
| \begin{align*}
x^{\prime \prime }-x^{\prime }+y^{\prime }&=0 \\
x^{\prime \prime }+y^{\prime \prime }-x&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.132 |
|
| \begin{align*}
x^{\prime }&=2 x \\
y^{\prime }&=3 x-2 y \\
z^{\prime }&=2 y+3 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.047 |
|
| \begin{align*}
x^{\prime }&=4 x \\
y^{\prime }&=x-2 y \\
z^{\prime }&=x-4 y+z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.094 |
|
| \begin{align*}
x^{\prime }&=y-z \\
y^{\prime }&=x+y \\
z^{\prime }&=x+z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.937 |
|
| \begin{align*}
x^{\prime }-y+z&=0 \\
-x+y^{\prime }-y&=t \\
z^{\prime }-x-z&=t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.220 |
|
| \begin{align*}
a x^{\prime }&=b c \left (y-z\right ) \\
b y^{\prime }&=c a \left (z-x\right ) \\
c z^{\prime }&=a b \left (x-y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.643 |
|
| \begin{align*}
x^{\prime }&=c y-b z \\
y^{\prime }&=a z-c x \\
z^{\prime }&=b x-a y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.173 |
|
| \begin{align*}
x^{\prime }&=x+y-z \\
y^{\prime }&=y+z-x \\
z^{\prime }&=x-y+z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.483 |
|
| \begin{align*}
x^{\prime }&=-3 x+48 y-28 z \\
y^{\prime }&=-4 x+40 y-22 z \\
z^{\prime }&=-6 x+57 y-31 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.322 |
|
| \begin{align*}
x^{\prime }&=6 x-72 y+44 z \\
y^{\prime }&=4 x-4 y+26 z \\
z^{\prime }&=6 x-63 y+38 z \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
26.783 |
|
| \begin{align*}
x^{\prime }&=a x+g y+\beta z \\
y^{\prime }&=g x+b y+\alpha z \\
z^{\prime }&=\beta x+\alpha y+c z \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
160.641 |
|
| \begin{align*}
t x^{\prime }&=2 x-t \\
t^{3} y^{\prime }&=-x+t^{2} y+t \\
t^{4} z^{\prime }&=-x-t^{2} y+t^{3} z+t \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.096 |
|
| \begin{align*}
a t x^{\prime }&=b c \left (y-z\right ) \\
b t y^{\prime }&=c a \left (z-x\right ) \\
c t z^{\prime }&=a b \left (x-y\right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.093 |
|
| \begin{align*}
x_{1}^{\prime }&=a x_{2}+b x_{3} \cos \left (c t \right )+b x_{4} \sin \left (c t \right ) \\
x_{2}^{\prime }&=-a x_{1}+b x_{3} \sin \left (c t \right )-b x_{4} \cos \left (c t \right ) \\
x_{3}^{\prime }&=-b x_{1} \cos \left (c t \right )-b x_{2} \sin \left (c t \right )+a x_{4} \\
x_{4}^{\prime }&=-b x_{1} \sin \left (c t \right )+b x_{2} \cos \left (c t \right )-a x_{3} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.135 |
|
| \begin{align*}
x^{\prime }&=-x \left (x+y\right ) \\
y^{\prime }&=y \left (x+y\right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.094 |
|
| \begin{align*}
x^{\prime }&=\left (a y+b \right ) x \\
y^{\prime }&=\left (c x+d \right ) y \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.095 |
|
| \begin{align*}
x^{\prime }&=x \left (a \left (p x+q y\right )+\alpha \right ) \\
y^{\prime }&=y \left (\beta +b \left (p x+q y\right )\right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.099 |
|
| \begin{align*}
x^{\prime }&=h \left (a -x\right ) \left (c -x-y\right ) \\
y^{\prime }&=k \left (b -y\right ) \left (c -x-y\right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.098 |
|
| \begin{align*}
x^{\prime }&=y^{2}-\cos \left (x\right ) \\
y^{\prime }&=-y \sin \left (x\right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.097 |
|
| \begin{align*}
x^{\prime }&=-x \,y^{2}+x+y \\
y^{\prime }&=y \,x^{2}-x-y \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.095 |
|
| \begin{align*}
x^{\prime }&=x+y-x \left (x^{2}+y^{2}\right ) \\
y^{\prime }&=-x+y-y \left (x^{2}+y^{2}\right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.097 |
|
| \begin{align*}
x^{\prime }&=-y+x \left (x^{2}+y^{2}-1\right ) \\
y^{\prime }&=x+y \left (x^{2}+y^{2}-1\right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.098 |
|
| \begin{align*}
\left (t^{2}+1\right ) x^{\prime }&=-t x+y \\
\left (t^{2}+1\right ) y^{\prime }&=-x-t y \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.075 |
|
| \begin{align*}
\left (x^{2}+y^{2}-t^{2}\right ) x^{\prime }&=-2 t x \\
\left (x^{2}+y^{2}-t^{2}\right ) y^{\prime }&=-2 t y \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.102 |
|
| \begin{align*}
{x^{\prime }}^{2}+t x^{\prime }+a y^{\prime }-x&=0 \\
x^{\prime } y^{\prime }+y^{\prime } t -y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.142 |
|
| \begin{align*}
x&=t x^{\prime }+f \left (x^{\prime }, y^{\prime }\right ) \\
y&=y^{\prime } t +g \left (x^{\prime }, y^{\prime }\right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.157 |
|
| \begin{align*}
x^{\prime \prime }&=a \,{\mathrm e}^{2 x}-{\mathrm e}^{-x}+{\mathrm e}^{-2 x} \cos \left (y\right )^{2} \\
y^{\prime \prime }&={\mathrm e}^{-2 x} \sin \left (y\right ) \cos \left (y\right )-\frac {\sin \left (y\right )}{\cos \left (y\right )^{3}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.124 |
|
| \begin{align*}
x^{\prime \prime }&=\frac {k x}{\left (x^{2}+y^{2}\right )^{{3}/{2}}} \\
y^{\prime \prime }&=\frac {k y}{\left (x^{2}+y^{2}\right )^{{3}/{2}}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.112 |
|
| \begin{align*}
x^{\prime }&=y-z \\
y^{\prime }&=x^{2}+y \\
z^{\prime }&=x^{2}+z \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.108 |
|
| \begin{align*}
a x^{\prime }&=\left (b -c \right ) y z \\
b y^{\prime }&=\left (c -a \right ) z x \\
c z^{\prime }&=\left (a -b \right ) x y \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.121 |
|
| \begin{align*}
x^{\prime }&=x \left (y-z\right ) \\
y^{\prime }&=y \left (z-x\right ) \\
z^{\prime }&=z \left (x-y\right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.114 |
|
| \begin{align*}
x^{\prime }+y^{\prime }&=x y \\
y^{\prime }+z^{\prime }&=y z \\
x^{\prime }+z^{\prime }&=x z \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
0.145 |
|
| \begin{align*}
x^{\prime }&=\frac {x^{2}}{2}-\frac {y}{24} \\
y^{\prime }&=2 x y-3 z \\
z^{\prime }&=3 x z-\frac {y^{2}}{6} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.115 |
|
| \begin{align*}
x^{\prime }&=x \left (y^{2}-z^{2}\right ) \\
y^{\prime }&=y \left (z^{2}-x^{2}\right ) \\
z^{\prime }&=z \left (x^{2}-y^{2}\right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.115 |
|
| \begin{align*}
x^{\prime }&=x \left (y^{2}-z^{2}\right ) \\
y^{\prime }&=-y \left (z^{2}+x^{2}\right ) \\
z^{\prime }&=z \left (x^{2}+y^{2}\right ) \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
0.142 |
|
| \begin{align*}
x^{\prime }&=-x \,y^{2}+x+y \\
y^{\prime }&=y \,x^{2}-x-y \\
z^{\prime }&=y^{2}-x^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.112 |
|
| \begin{align*}
\left (x-y\right ) \left (x-z\right ) x^{\prime }&=f \left (t \right ) \\
\left (-x+y\right ) \left (y-z\right ) y^{\prime }&=f \left (t \right ) \\
\left (z-x\right ) \left (z-y\right ) z^{\prime }&=f \left (t \right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.116 |
|
| \begin{align*}
3 x^{\prime }+3 x+2 y&={\mathrm e}^{t} \\
4 x-3 y^{\prime }+3 y&=3 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| \begin{align*}
x^{\prime }&=-3 y \\
y^{\prime }&=2 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.439 |
|
| \begin{align*}
x^{\prime }&=-2 y \\
y^{\prime }&=-4 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.451 |
|
| \begin{align*}
x^{\prime }&=-3 x \\
y^{\prime }&=2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.328 |
|
| \begin{align*}
x^{\prime }&=4 y \\
y^{\prime }&=2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.362 |
|
| \begin{align*}
x^{\prime }&=x \\
y^{\prime }&=x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.345 |
|
| \begin{align*}
x^{\prime }&=x-y \\
y^{\prime }&=x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.398 |
|
| \begin{align*}
x^{\prime }&=x+2 y \\
y^{\prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.412 |
|
| \begin{align*}
x^{\prime }&=-x-2 y \\
y^{\prime }&=2 x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.412 |
|
| \begin{align*}
x^{\prime }&=-2 x-3 y \\
y^{\prime }&=-x+4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.583 |
|
| \begin{align*}
x^{\prime }&=-3 y \\
y^{\prime }&=-2 x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.431 |
|
| \begin{align*}
x^{\prime }&=-2 x \\
y^{\prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.338 |
|
| \begin{align*}
x^{\prime }&=-2 x-y \\
y^{\prime }&=-4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.360 |
|
| \begin{align*}
x^{\prime }&=x-2 y \\
y^{\prime }&=-2 x+4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.405 |
|
| \begin{align*}
x^{\prime }&=-6 y \\
y^{\prime }&=6 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.330 |
|
| \begin{align*}
x^{\prime }&=2 x+3 y \\
y^{\prime }&=-x-14 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.539 |
|
| \begin{align*}
x^{\prime }&=3 y-3 x \\
y^{\prime }&=x+2 y-1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.100 |
|
| \begin{align*}
x^{\prime }&=-x+y \\
y^{\prime }&=-3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.366 |
|
| \begin{align*}
x^{\prime }&=x \\
y^{\prime }&=3 x-4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.395 |
|
| \begin{align*}
x^{\prime }&=-x+y \\
y^{\prime }&=x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.576 |
|
| \begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=3 y-3 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.737 |
|
| \begin{align*}
x^{\prime }&=x-2 y \\
y^{\prime }&=3 x-4 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 3 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.434 |
|
| \begin{align*}
x^{\prime }&=5 x-y \\
y^{\prime }&=3 x+y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.422 |
|
| \begin{align*}
x^{\prime }&=-3 x+y \\
y^{\prime }&=-3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.274 |
|
| \begin{align*}
x^{\prime }&=x-y \\
y^{\prime }&=x+3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.329 |
|
| \begin{align*}
x^{\prime }&=x+2 y \\
y^{\prime }&=3 x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.405 |
|
| \begin{align*}
x^{\prime }&=-3 x+4 y \\
y^{\prime }&=-3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.308 |
|
| \begin{align*}
x^{\prime }&=2 x+2 y \\
y^{\prime }&=6 x+3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.443 |
|
| \begin{align*}
x^{\prime }&=-5 x+3 y \\
y^{\prime }&=2 x-10 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.439 |
|
| \begin{align*}
x^{\prime }&=2 x \\
y^{\prime }&=2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.260 |
|
| \begin{align*}
x^{\prime }&=3 x-2 y \\
y^{\prime }&=4 x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.539 |
|
| \begin{align*}
x^{\prime }&=5 x-4 y \\
y^{\prime }&=x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.359 |
|
| \begin{align*}
x^{\prime }&=9 y \\
y^{\prime }&=-x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.395 |
|
| \begin{align*}
x^{\prime }&=2 x+y \\
y^{\prime }&=-x \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.368 |
|
| \begin{align*}
x^{\prime }&=x-2 y \\
y^{\prime }&=-2 x+4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.343 |
|
| \begin{align*}
x^{\prime }&=3 x-y+1 \\
y^{\prime }&=x+y+2 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.586 |
|
| \begin{align*}
x^{\prime }&=-5 x+3 y+{\mathrm e}^{-t} \\
y^{\prime }&=2 x-10 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.651 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-x+\cos \left (w t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.815 |
|
| \begin{align*}
x^{\prime }&=3 x+2 y+3 \\
y^{\prime }&=7 x+5 y+2 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.215 |
|
| \begin{align*}
x^{\prime }&=x-3 y \\
y^{\prime }&=3 x+7 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.343 |
|
| \begin{align*}
x^{\prime }+y^{\prime }-2 x-4 y&={\mathrm e}^{t} \\
x^{\prime }+y^{\prime }-y&={\mathrm e}^{4 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.372 |
|
| \begin{align*}
x^{\prime }+y^{\prime }-x&=-2 t \\
x^{\prime }+y^{\prime }-3 x-y&=t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.366 |
|
| \begin{align*}
x^{\prime }+y^{\prime }-x-3 y&={\mathrm e}^{t} \\
x^{\prime }+y^{\prime }+x&={\mathrm e}^{3 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.205 |
|
| \begin{align*}
x^{\prime }+y^{\prime }-x-2 y&=2 \,{\mathrm e}^{t} \\
x^{\prime }+y^{\prime }-3 x-4 y&={\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.141 |
|
| \begin{align*}
2 x^{\prime }+y^{\prime }-x-y&={\mathrm e}^{-t} \\
x^{\prime }+2 x+y^{\prime }+y&={\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.876 |
|
| \begin{align*}
2 x^{\prime }+y^{\prime }-3 x-y&=t \\
x^{\prime }+y^{\prime }-4 x-y&={\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.679 |
|
| \begin{align*}
x^{\prime }+y^{\prime }-x-6 y&={\mathrm e}^{3 t} \\
x^{\prime }+2 y^{\prime }-2 x-6 y&=t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.957 |
|
| \begin{align*}
x^{\prime }+y^{\prime }-x-3 y&=3 t \\
x^{\prime }+2 y^{\prime }-2 x-3 y&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.904 |
|
| \begin{align*}
x^{\prime }+y^{\prime }+2 y&=\sin \left (t \right ) \\
x^{\prime }+y^{\prime }-x-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.227 |
|
| \begin{align*}
x^{\prime }-y^{\prime }-2 x+4 y&=t \\
x^{\prime }+y^{\prime }-x-y&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.793 |
|
| \begin{align*}
2 x^{\prime }+y^{\prime }+x+5 y&=4 t \\
x^{\prime }+y^{\prime }+2 x+2 y&=2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.685 |
|
| \begin{align*}
x^{\prime }+y^{\prime }-x+5 y&=t^{2} \\
x^{\prime }+2 y^{\prime }-2 x+4 y&=2 t +1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.945 |
|
| \begin{align*}
2 x^{\prime }+y^{\prime }+x+y&=t^{2}+4 t \\
x^{\prime }+y^{\prime }+2 x+2 y&=2 t^{2}-2 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.684 |
|
| \begin{align*}
3 x^{\prime }+2 y^{\prime }-x+y&=t -1 \\
x^{\prime }+y^{\prime }-x&=t +2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.822 |
|
| \begin{align*}
2 x^{\prime }+4 y^{\prime }+x-y&=3 \,{\mathrm e}^{t} \\
x^{\prime }+y^{\prime }+2 x+2 y&={\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.720 |
|
| \begin{align*}
2 x^{\prime }+y^{\prime }-x-y&=-2 t \\
x^{\prime }+y^{\prime }+x-y&=t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.670 |
|
| \begin{align*}
2 x^{\prime }+y^{\prime }-x-y&=1 \\
x^{\prime }+y^{\prime }+2 x-y&=t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.644 |
|
| \begin{align*}
x^{\prime }&=3 x+4 y \\
y^{\prime }&=2 x+y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.450 |
|
| \begin{align*}
x^{\prime }&=5 x+3 y \\
y^{\prime }&=4 x+y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.443 |
|
| \begin{align*}
x^{\prime }&=5 x+2 y+5 t \\
y^{\prime }&=3 x+4 y+17 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.706 |
|
| \begin{align*}
x^{\prime }&=5 x-2 y \\
y^{\prime }&=4 x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.430 |
|
| \begin{align*}
x^{\prime }&=5 x-y \\
y^{\prime }&=3 x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.445 |
|
| \begin{align*}
x^{\prime }&=-2 x+7 y \\
y^{\prime }&=3 x+2 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 9 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.477 |
|
| \begin{align*}
x^{\prime }&=-2 x+y \\
y^{\prime }&=7 x+4 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 6 \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.431 |
|
| \begin{align*}
x^{\prime }&=x+y-z \\
y^{\prime }&=2 x+3 y-4 z \\
z^{\prime }&=4 x+y-4 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.749 |
|
| \begin{align*}
x^{\prime }&=x-y-z \\
y^{\prime }&=x+3 y+z \\
z^{\prime }&=-3 x-6 y+6 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.829 |
|
| \begin{align*}
x^{\prime }&=x+3 y \\
y^{\prime }&=3 x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.430 |
|
| \begin{align*}
x^{\prime }&=3 x+2 y \\
y^{\prime }&=x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.425 |
|
| \begin{align*}
x^{\prime }&=3 x+4 y \\
y^{\prime }&=3 x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.434 |
|
| \begin{align*}
x^{\prime }&=2 x+5 y \\
y^{\prime }&=x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.461 |
|
| \begin{align*}
x^{\prime }&=2 x-4 y \\
y^{\prime }&=2 x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.468 |
|
| \begin{align*}
x^{\prime }&=x-2 y \\
y^{\prime }&=4 x+5 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.603 |
|
| \begin{align*}
x^{\prime }&=x-y \\
y^{\prime }&=x+5 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.596 |
|
| \begin{align*}
x^{\prime }&=x+7 y \\
y^{\prime }&=3 x+5 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.448 |
|
| \begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=3 x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.432 |
|
| \begin{align*}
x^{\prime }&=a x+b y \\
y^{\prime }&=c x+d y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.960 |
|
| \begin{align*}
x^{\prime }&=4 x-4 y-x \left (x^{2}+y^{2}\right ) \\
y^{\prime }&=4 x+4 y-y \left (x^{2}+y^{2}\right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.108 |
|
| \begin{align*}
x^{\prime }&=y+\frac {x \left (1-x^{2}-y^{2}\right )}{\sqrt {x^{2}+y^{2}}} \\
y^{\prime }&=-x+\frac {y \left (1-x^{2}-y^{2}\right )}{\sqrt {x^{2}+y^{2}}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.112 |
|
| \begin{align*}
x^{\prime }&=x-x^{2} \\
y^{\prime }&=2 y-y^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.061 |
|
| \begin{align*}
x^{\prime }&=4 x-y \\
y^{\prime }&=2 x+y+t^{2} \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.735 |
|
| \begin{align*}
x^{\prime }&=x-4 y+\cos \left (2 t \right ) \\
y^{\prime }&=x+y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.950 |
|
| \begin{align*}
x^{\prime }&=2 x+2 y \\
y^{\prime }&=6 x+3 y+{\mathrm e}^{t} \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.759 |
|
| \begin{align*}
x^{\prime }&=5 x-4 y+{\mathrm e}^{3 t} \\
y^{\prime }&=x+y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.622 |
|
| \begin{align*}
x^{\prime }&=2 x+5 y \\
y^{\prime }&=-2 x+\cos \left (3 t \right ) \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.381 |
|
| \begin{align*}
x^{\prime }&=x+y+{\mathrm e}^{-t} \\
y^{\prime }&=4 x-2 y+{\mathrm e}^{2 t} \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.783 |
|
| \begin{align*}
x^{\prime }&=8 x+14 y \\
y^{\prime }&=7 x+y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.423 |
|
| \begin{align*}
x^{\prime }&=8 x+14 y \\
y^{\prime }&=7 x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.417 |
|
| \begin{align*}
x^{\prime }&=2 x \\
y^{\prime }&=-5 x-3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.385 |
|
| \begin{align*}
x^{\prime }&=11 x-2 y \\
y^{\prime }&=3 x+4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.462 |
|
| \begin{align*}
x^{\prime }&=x+20 y \\
y^{\prime }&=40 x-19 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.454 |
|
| \begin{align*}
x^{\prime }&=-2 x+2 y \\
y^{\prime }&=x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.416 |
|
| \begin{align*}
x^{\prime }&=-y \\
y^{\prime }&=x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.095 |
|
| \begin{align*}
x^{\prime }&=-2 x+3 y \\
y^{\prime }&=-6 x+4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.629 |
|
| \begin{align*}
x^{\prime }&=-11 x-2 y \\
y^{\prime }&=13 x-9 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.641 |
|
| \begin{align*}
x^{\prime }&=7 x-5 y \\
y^{\prime }&=10 x-3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.600 |
|
| \begin{align*}
x^{\prime }&=5 x-4 y \\
y^{\prime }&=x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.381 |
|
| \begin{align*}
x^{\prime }&=-6 x+2 y \\
y^{\prime }&=-2 x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.380 |
|
| \begin{align*}
x^{\prime }&=-3 x-y \\
y^{\prime }&=x-5 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.369 |
|
| \begin{align*}
x^{\prime }&=13 x \\
y^{\prime }&=13 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.289 |
|
| \begin{align*}
x^{\prime }&=7 x-4 y \\
y^{\prime }&=x+3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.418 |
|
| \begin{align*}
x^{\prime }&=-x+y \\
y^{\prime }&=-x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.338 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-x \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.485 |
|
| \begin{align*}
x^{\prime }+5 x+y&={\mathrm e}^{t} \\
y^{\prime }-x-3 y&={\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.315 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=z \\
z^{\prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.195 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=\frac {y^{2}}{x} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.140 |
|
| \begin{align*}
x^{\prime }&=x-2 y \\
y^{\prime }&=3 x-4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.473 |
|
| \begin{align*}
x^{\prime }&=\frac {5 x}{4}+\frac {3 y}{4} \\
y^{\prime }&=\frac {x}{2}-\frac {3 y}{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.682 |
|
| \begin{align*}
x^{\prime }-x+2 y&=0 \\
y^{\prime }+y-x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.522 |
|
| \begin{align*}
x^{\prime }+5 x-2 y&=0 \\
2 x+y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.646 |
|
| \begin{align*}
x^{\prime }-3 x+2 y&=0 \\
y^{\prime }-x+3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.594 |
|
| \begin{align*}
x^{\prime }+x-z&=0 \\
x+y^{\prime }-y&=0 \\
z^{\prime }+x+2 y-3 z&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.670 |
|
| \begin{align*}
x^{\prime }&=-\frac {x}{2}+2 y-3 z \\
y^{\prime }&=y-\frac {z}{2} \\
z^{\prime }&=-2 x+z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.342 |
|
| \begin{align*}
x^{\prime }+y^{\prime }&=y \\
x^{\prime }-y^{\prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.546 |
|
| \begin{align*}
x^{\prime }+2 y^{\prime }&=t \\
x^{\prime }-y^{\prime }&=x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.697 |
|
| \begin{align*}
x^{\prime }-y^{\prime }&=x+y-t \\
2 x^{\prime }+3 y^{\prime }&=2 x+6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.714 |
|
| \begin{align*}
2 x^{\prime }-y^{\prime }&=t \\
3 x^{\prime }+2 y^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.667 |
|
| \begin{align*}
5 x^{\prime }-3 y^{\prime }&=x+y \\
3 x^{\prime }-y^{\prime }&=t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.707 |
|
| \begin{align*}
x^{\prime }-4 y^{\prime }&=0 \\
2 x^{\prime }-3 y^{\prime }&=y+t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.646 |
|
| \begin{align*}
3 x^{\prime }+2 y^{\prime }&=\sin \left (t \right ) \\
x^{\prime }-2 y^{\prime }&=x+y+t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.875 |
|
| \begin{align*}
x^{\prime }&=-4 x+9 y+12 \,{\mathrm e}^{-t} \\
y^{\prime }&=-5 x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.083 |
|
| \begin{align*}
x^{\prime }&=-7 x+6 y+6 \,{\mathrm e}^{-t} \\
y^{\prime }&=-12 x+5 y+37 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.237 |
|
| \begin{align*}
x^{\prime }&=-7 x+10 y+18 \,{\mathrm e}^{t} \\
y^{\prime }&=-10 x+9 y+37 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.724 |
|
| \begin{align*}
x^{\prime }&=-14 x+39 y+78 \sinh \left (t \right ) \\
y^{\prime }&=-6 x+16 y+6 \cosh \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.741 |
|
| \begin{align*}
x^{\prime }&=2 x+4 y-2 z-2 \sinh \left (t \right ) \\
y^{\prime }&=4 x+2 y-2 z+10 \cosh \left (t \right ) \\
z^{\prime }&=-x+3 y+z+5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.606 |
|
| \begin{align*}
x^{\prime }&=2 x+6 y-2 z+50 \,{\mathrm e}^{t} \\
y^{\prime }&=6 x+2 y-2 z+21 \,{\mathrm e}^{-t} \\
z^{\prime }&=-x+6 y+z+9 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.378 |
|
| \begin{align*}
x^{\prime }&=-2 x-2 y+4 z \\
y^{\prime }&=-2 x+y+2 z \\
z^{\prime }&=-4 x-2 y+6 z+{\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.069 |
|
| \begin{align*}
x^{\prime }&=3 x-2 y+3 z \\
y^{\prime }&=x-y+2 z+2 \,{\mathrm e}^{-t} \\
z^{\prime }&=-2 x+2 y-2 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.243 |
|
| \begin{align*}
x^{\prime }&=7 x+y-1-6 \,{\mathrm e}^{t} \\
y^{\prime }&=-4 x+3 y+4 \,{\mathrm e}^{t}-3 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| \begin{align*}
x^{\prime }&=3 x-2 y+24 \sin \left (t \right ) \\
y^{\prime }&=9 x-3 y+12 \cos \left (t \right ) \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.051 |
|
| \begin{align*}
x^{\prime }&=7 x-4 y+10 \,{\mathrm e}^{t} \\
y^{\prime }&=3 x+14 y+6 \,{\mathrm e}^{2 t} \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
20.925 |
|
| \begin{align*}
x^{\prime }&=-7 x+4 y+6 \,{\mathrm e}^{3 t} \\
y^{\prime }&=-5 x+2 y+6 \,{\mathrm e}^{2 t} \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| \begin{align*}
x^{\prime }&=-3 x-3 y+z \\
y^{\prime }&=2 y+2 z+29 \,{\mathrm e}^{-t} \\
z^{\prime }&=5 x+y+z+39 \,{\mathrm e}^{t} \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 2 \\
z \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✗ |
✓ |
✗ |
33.086 |
|
| \begin{align*}
x^{\prime }&=2 x+y-z+5 \sin \left (t \right ) \\
y^{\prime }&=y+z-10 \cos \left (t \right ) \\
z^{\prime }&=x+z+2 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 2 \\
z \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.474 |
|
| \begin{align*}
x^{\prime }&=-3 x+3 y+z+5 \sin \left (2 t \right ) \\
y^{\prime }&=x-5 y-3 z+5 \cos \left (2 t \right ) \\
z^{\prime }&=-3 x+7 y+3 z+23 \,{\mathrm e}^{t} \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 2 \\
z \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.145 |
|
| \begin{align*}
x^{\prime }&=-3 x+y-3 z+2 \,{\mathrm e}^{t} \\
y^{\prime }&=4 x-y+2 z+4 \,{\mathrm e}^{t} \\
z^{\prime }&=4 x-2 y+3 z+4 \,{\mathrm e}^{t} \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 2 \\
z \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.068 |
|
| \begin{align*}
x^{\prime }&=x+5 y+10 \sinh \left (t \right ) \\
y^{\prime }&=19 x-13 y+24 \sinh \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.928 |
|
| \begin{align*}
x^{\prime }&=9 x-3 y-6 t \\
y^{\prime }&=-x+11 y+10 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.835 |
|
| \begin{align*}
x^{\prime }&=1+y \\
y^{\prime }&=1+x \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= -2 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.664 |
|
| \begin{align*}
x^{\prime }&=x-2 y \\
y^{\prime }&=x-y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.468 |
|
| \begin{align*}
4 x^{\prime }-y^{\prime }+3 x&=\sin \left (t \right ) \\
x^{\prime }+y&=\cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.003 |
|
| \begin{align*}
x^{\prime }&=2 x-3 y \\
y^{\prime }&=5 x+6 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.375 |
|
| \begin{align*}
x^{\prime }&=-4 x-10 y \\
y^{\prime }&=x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.640 |
|
| \begin{align*}
x^{\prime }&=12 x+18 y \\
y^{\prime }&=-8 x-12 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.407 |
|
| \begin{align*}
x^{\prime }&=-x+y \\
y^{\prime }&=-x-3 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (1\right ) &= 0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.411 |
|
| \begin{align*}
x^{\prime }&=x-5 y \\
y^{\prime }&=x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.483 |
|
| \begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.717 |
|
| \begin{align*}
x^{\prime }&=-4 x+2 y \\
y^{\prime }&=3 x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.696 |
|
| \begin{align*}
x^{\prime }&=x+2 y \\
y^{\prime }&=2 x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.674 |
|
| \begin{align*}
x^{\prime }&=4 x-2 y \\
y^{\prime }&=3 x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.510 |
|
| \begin{align*}
x^{\prime }&=2 x+y \\
y^{\prime }&=-x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.295 |
|
| \begin{align*}
x^{\prime }&=3 x-y \\
y^{\prime }&=x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.393 |
|
| \begin{align*}
x^{\prime }&=x-y \\
y^{\prime }&=2 x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.469 |
|
| \begin{align*}
x^{\prime }&=x \\
y^{\prime }&=2 x-3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.460 |
|
| \begin{align*}
x^{\prime }&=x \\
y^{\prime }&=x+3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.445 |
|
| \begin{align*}
x^{\prime }&=-y \\
y^{\prime }&=2 x-4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.675 |
|
| \begin{align*}
x^{\prime }&=x \\
y^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.332 |
|
| \begin{align*}
x^{\prime }&=0 \\
y^{\prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.332 |
|
| \begin{align*}
x^{\prime }&=x-5 y \\
y^{\prime }&=x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.504 |
|
| \begin{align*}
y_{1}^{\prime }&=2 y_{1}-3 y_{2} \\
y_{2}^{\prime }&=y_{1}-2 y_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.563 |
|
| \begin{align*}
y_{1}^{\prime }&=y_{1}-2 y_{2} \\
y_{2}^{\prime }&=y_{1}+3 y_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.723 |
|
| \begin{align*}
y_{1}^{\prime }&=y_{1}+2 y_{2}+x -1 \\
y_{2}^{\prime }&=3 y_{1}+2 y_{2}-5 x -2 \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= -2 \\
y_{2} \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.956 |
|
| \begin{align*}
y_{1}^{\prime }&=\frac {2 y_{1}}{x}-\frac {y_{2}}{x^{2}}-3+\frac {1}{x}-\frac {1}{x^{2}} \\
y_{2}^{\prime }&=2 y_{1}+1-6 x \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (1\right ) &= -2 \\
y_{2} \left (1\right ) &= -5 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.134 |
|
| \begin{align*}
y_{1}^{\prime }&=\frac {5 y_{1}}{x}+\frac {4 y_{2}}{x}-2 x \\
y_{2}^{\prime }&=-\frac {6 y_{1}}{x}-\frac {5 y_{2}}{x}+5 x \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (-1\right ) &= 3 \\
y_{2} \left (-1\right ) &= -3 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.138 |
|
| \begin{align*}
y_{1}^{\prime }&=3 y_{1}-2 y_{2} \\
y_{2}^{\prime }&=y_{2}-y_{1} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.842 |
|
| \begin{align*}
y_{1}^{\prime }&=\sin \left (x \right ) y_{1}+\sqrt {x}\, y_{2}+\ln \left (x \right ) \\
y_{2}^{\prime }&=\tan \left (x \right ) y_{1}-{\mathrm e}^{x} y_{2}+1 \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (1\right ) &= 1 \\
y_{2} \left (1\right ) &= -1 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.073 |
|
| \begin{align*}
y_{1}^{\prime }&=\sin \left (x \right ) y_{1}+\sqrt {x}\, y_{2}+\ln \left (x \right ) \\
y_{2}^{\prime }&=\tan \left (x \right ) y_{1}-{\mathrm e}^{x} y_{2}+1 \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (2\right ) &= 1 \\
y_{2} \left (2\right ) &= -1 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.119 |
|
| \begin{align*}
y_{1}^{\prime }&={\mathrm e}^{-x} y_{1}-\sqrt {x +1}\, y_{2}+x^{2} \\
y_{2}^{\prime }&=\frac {y_{1}}{\left (x -2\right )^{2}} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 0 \\
y_{2} \left (0\right ) &= 1 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.139 |
|
| \begin{align*}
y_{1}^{\prime }&={\mathrm e}^{-x} y_{1}-\sqrt {x +1}\, y_{2}+x^{2} \\
y_{2}^{\prime }&=\frac {y_{1}}{\left (x -2\right )^{2}} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (3\right ) &= 1 \\
y_{2} \left (3\right ) &= 0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.115 |
|
| \begin{align*}
y_{1}^{\prime }&=2 y_{1}-3 y_{2}+5 \,{\mathrm e}^{x} \\
y_{2}^{\prime }&=y_{1}+4 y_{2}-2 \,{\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.407 |
|
| \begin{align*}
y_{1}^{\prime }&=y_{2}-2 y_{1}+\sin \left (2 x \right ) \\
y_{2}^{\prime }&=-3 y_{1}+y_{2}-2 \cos \left (3 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
5.342 |
|
| \begin{align*}
y_{1}^{\prime }&=2 y_{2} \\
y_{2}^{\prime }&=3 y_{1} \\
y_{3}^{\prime }&=2 y_{3}-y_{1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.089 |
|
| \begin{align*}
y_{1}^{\prime }&=2 x y_{1}-x^{2} y_{2}+4 x \\
y_{2}^{\prime }&={\mathrm e}^{x} y_{1}+3 \,{\mathrm e}^{-x} y_{2}-\cos \left (3 x \right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.120 |
|
| \begin{align*}
y_{1}^{\prime }&=2 y_{1}-3 y_{2} \\
y_{2}^{\prime }&=y_{1}-2 y_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.543 |
|
| \begin{align*}
y_{1}^{\prime }&=2 y_{1}-3 y_{2}+4 x -2 \\
y_{2}^{\prime }&=y_{1}-2 y_{2}+3 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.954 |
|
| \begin{align*}
y_{1}^{\prime }&=\frac {5 y_{1}}{x}+\frac {4 y_{2}}{x} \\
y_{2}^{\prime }&=-\frac {6 y_{1}}{x}-\frac {5 y_{2}}{x} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.130 |
|
| \begin{align*}
y_{1}^{\prime }&=\frac {5 y_{1}}{x}+\frac {4 y_{2}}{x}-2 x \\
y_{2}^{\prime }&=-\frac {6 y_{1}}{x}-\frac {5 y_{2}}{x}+5 x \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.112 |
|
| \begin{align*}
y_{1}^{\prime }&=2 y_{1}+y_{2}-2 y_{3} \\
y_{2}^{\prime }&=3 y_{2}-2 y_{3} \\
y_{3}^{\prime }&=3 y_{1}+y_{2}-3 y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.904 |
|
| \begin{align*}
y_{1}^{\prime }&=5 y_{1}-5 y_{2}-5 y_{3} \\
y_{2}^{\prime }&=-y_{1}+4 y_{2}+2 y_{3} \\
y_{3}^{\prime }&=3 y_{1}-5 y_{2}-3 y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.375 |
|
| \begin{align*}
y_{1}^{\prime }&=4 y_{1}+6 y_{2}+6 y_{3} \\
y_{2}^{\prime }&=y_{1}+3 y_{2}+2 y_{3} \\
y_{3}^{\prime }&=-y_{1}-4 y_{2}-3 y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.956 |
|
| \begin{align*}
y_{1}^{\prime }&=y_{1}+2 y_{2}-3 y_{3} \\
y_{2}^{\prime }&=-3 y_{1}+4 y_{2}-2 y_{3} \\
y_{3}^{\prime }&=2 y_{1}+y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.365 |
|
| \begin{align*}
y_{1}^{\prime }&=-2 y_{1}-y_{2}+y_{3} \\
y_{2}^{\prime }&=-y_{1}-2 y_{2}-y_{3} \\
y_{3}^{\prime }&=y_{1}-y_{2}-2 y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.748 |
|
| \begin{align*}
y_{1}^{\prime }&=y_{1}+y_{2}+2 y_{3} \\
y_{2}^{\prime }&=y_{1}+y_{2}+2 y_{3} \\
y_{3}^{\prime }&=2 y_{1}+2 y_{2}+4 y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.813 |
|
| \begin{align*}
y_{1}^{\prime }&=2 y_{1}+y_{2} \\
y_{2}^{\prime }&=-y_{1}+2 y_{2} \\
y_{3}^{\prime }&=3 y_{3}-4 y_{4} \\
y_{4}^{\prime }&=4 y_{3}+3 y_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.518 |
|
| \begin{align*}
y_{1}^{\prime }&=y_{2} \\
y_{2}^{\prime }&=-3 y_{1}+2 y_{3} \\
y_{3}^{\prime }&=y_{4} \\
y_{4}^{\prime }&=2 y_{1}-5 y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.615 |
|
| \begin{align*}
y_{1}^{\prime }&=3 y_{1}+2 y_{2} \\
y_{2}^{\prime }&=3 y_{2}-2 y_{1} \\
y_{3}^{\prime }&=y_{3} \\
y_{4}^{\prime }&=2 y_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.319 |
|
| \begin{align*}
y_{1}^{\prime }&=y_{2}+y_{4} \\
y_{2}^{\prime }&=y_{1}-y_{3} \\
y_{3}^{\prime }&=y_{4} \\
y_{4}^{\prime }&=y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.961 |
|
| \begin{align*}
x^{\prime }&=-2 x+3 y \\
y^{\prime }&=-x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.560 |
|
| \begin{align*}
x^{\prime }&=-x+2 y \\
y^{\prime }&=-2 x+3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.442 |
|
| \begin{align*}
x^{\prime }&=-x-2 y \\
y^{\prime }&=2 x-3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.553 |
|
| \begin{align*}
x^{\prime }&=-x-2 y \\
y^{\prime }&=5 x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.616 |
|
| \begin{align*}
x^{\prime }&=-x+2 y \\
y^{\prime }&=-2 x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.551 |
|
| \begin{align*}
x^{\prime }&=x-2 y \\
y^{\prime }&=2 x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.572 |
|
| \begin{align*}
x^{\prime }&=-5 x-y+2 \\
y^{\prime }&=3 x-y-3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.926 |
|
| \begin{align*}
x^{\prime }&=3 x-2 y-6 \\
y^{\prime }&=4 x-y+2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.236 |
|
| \begin{align*}
x^{\prime }&=x-y \\
y^{\prime }&=x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.388 |
|
| \begin{align*}
x^{\prime }&=2 x-y \\
y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.556 |
|
| \begin{align*}
x^{\prime }&=x \\
y^{\prime }&=2 x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.445 |
|
| \begin{align*}
x^{\prime }&=-x+2 y \\
y^{\prime }&=2 x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.586 |
|
| \begin{align*}
x^{\prime }&=2 x+y \\
y^{\prime }&=x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.787 |
|
| \begin{align*}
x^{\prime }&=3 y \\
y^{\prime }&=3 \pi y-\frac {x}{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.023 |
|
| \begin{align*}
p^{\prime }&=3 p-2 q-7 r \\
q^{\prime }&=-2 p+6 r \\
r^{\prime }&=\frac {73 q}{100}+2 r \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
64.147 |
|
| \begin{align*}
x^{\prime }&=-3 x+2 \pi y \\
y^{\prime }&=4 x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.996 |
|
| \begin{align*}
x^{\prime }&=\beta y \\
y^{\prime }&=\gamma x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.013 |
|
| \begin{align*}
x^{\prime }&=2 y \\
y^{\prime }&=x+y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= -2 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.598 |
|
| \begin{align*}
x^{\prime }&=x-y \\
y^{\prime }&=x+3 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.409 |
|
| \begin{align*}
x^{\prime }&=-2 x-y \\
y^{\prime }&=2 x-5 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.536 |
|
| \begin{align*}
x^{\prime }&=-2 x-3 y \\
y^{\prime }&=3 x-2 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.577 |
|
| \begin{align*}
x^{\prime }&=2 x+3 y \\
y^{\prime }&=x \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.644 |
|
| \begin{align*}
x^{\prime }&=1 \\
y^{\prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.526 |
|
| \begin{align*}
x^{\prime }&=3 x \\
y^{\prime }&=-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.494 |
|
| \begin{align*}
x^{\prime }&=-4 x-2 y \\
y^{\prime }&=-x-3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.615 |
|
| \begin{align*}
x^{\prime }&=-5 x-2 y \\
y^{\prime }&=-x-4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.590 |
|
| \begin{align*}
x^{\prime }&=2 x+y \\
y^{\prime }&=-x+4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.499 |
|
| \begin{align*}
x^{\prime }&=-\frac {x}{2} \\
y^{\prime }&=x-\frac {y}{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.486 |
|
| \begin{align*}
x^{\prime }&=5 x+4 y \\
y^{\prime }&=9 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.624 |
|
| \begin{align*}
x^{\prime }&=3 x+4 y \\
y^{\prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.582 |
|
| \begin{align*}
x^{\prime }&=2 x-y \\
y^{\prime }&=-x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.787 |
|
| \begin{align*}
x^{\prime }&=2 x+y \\
y^{\prime }&=x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.720 |
|
| \begin{align*}
x^{\prime }&=-x-2 y \\
y^{\prime }&=x-4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.571 |
|
| \begin{align*}
x^{\prime }&=-2 x-2 y \\
y^{\prime }&=-2 x+y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.637 |
|
| \begin{align*}
x^{\prime }&=-2 x-2 y \\
y^{\prime }&=-2 x+y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.547 |
|
| \begin{align*}
x^{\prime }&=-2 x-2 y \\
y^{\prime }&=-2 x+y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.529 |
|
| \begin{align*}
x^{\prime }&=3 x \\
y^{\prime }&=x-2 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.473 |
|
| \begin{align*}
x^{\prime }&=3 x \\
y^{\prime }&=x-2 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.451 |
|
| \begin{align*}
x^{\prime }&=3 x \\
y^{\prime }&=x-2 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.478 |
|
| \begin{align*}
x^{\prime }&=-4 x+y \\
y^{\prime }&=2 x-3 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.533 |
|
| \begin{align*}
x^{\prime }&=-4 x+y \\
y^{\prime }&=2 x-3 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.528 |
|
| \begin{align*}
x^{\prime }&=-4 x+y \\
y^{\prime }&=2 x-3 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= -1 \\
y \left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.503 |
|
| \begin{align*}
x^{\prime }&=4 x-2 y \\
y^{\prime }&=x+y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.504 |
|
| \begin{align*}
x^{\prime }&=4 x-2 y \\
y^{\prime }&=x+y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.490 |
|
| \begin{align*}
x^{\prime }&=4 x-2 y \\
y^{\prime }&=x+y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= -1 \\
y \left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.509 |
|
| \begin{align*}
x^{\prime }&=2 y \\
y^{\prime }&=-2 x \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| \begin{align*}
x^{\prime }&=2 x+2 y \\
y^{\prime }&=-4 x+6 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.798 |
|
| \begin{align*}
x^{\prime }&=-3 x-5 y \\
y^{\prime }&=3 x+y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 4 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.726 |
|
| \begin{align*}
x^{\prime }&=2 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*} |
✓ |
✓ |
✓ |
✓ |
1.802 |
|
| \begin{align*}
x^{\prime }&=2 x-6 y \\
y^{\prime }&=2 x+y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.812 |
|
| \begin{align*}
x^{\prime }&=x+4 y \\
y^{\prime }&=-3 x+2 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.841 |
|
| \begin{align*}
x^{\prime }&=2 y \\
y^{\prime }&=-2 x \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.590 |
|
| \begin{align*}
x^{\prime }&=2 x+2 y \\
y^{\prime }&=-4 x+6 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.661 |
|
| \begin{align*}
x^{\prime }&=-3 x-5 y \\
y^{\prime }&=3 x+y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 4 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.726 |
|
| \begin{align*}
x^{\prime }&=2 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*} |
✓ |
✓ |
✓ |
✓ |
0.715 |
|
| \begin{align*}
x^{\prime }&=2 x-6 y \\
y^{\prime }&=2 x+y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.714 |
|
| \begin{align*}
x^{\prime }&=x+4 y \\
y^{\prime }&=-3 x+2 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.735 |
|
| \begin{align*}
x^{\prime }&=-\frac {9 x}{10}-2 y \\
y^{\prime }&=x+\frac {11 y}{10} \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.779 |
|
| \begin{align*}
x^{\prime }&=-3 x+10 y \\
y^{\prime }&=-x+3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.648 |
|
| \begin{align*}
x^{\prime }&=-3 x \\
y^{\prime }&=x-3 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.454 |
|
| \begin{align*}
x^{\prime }&=2 x+y \\
y^{\prime }&=-x-2 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.631 |
|
| \begin{align*}
x^{\prime }&=-2 x-y \\
y^{\prime }&=x-4 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.434 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-x-2 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.434 |
|
| \begin{align*}
x^{\prime }&=-3 x \\
y^{\prime }&=x-3 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.384 |
|
| \begin{align*}
x^{\prime }&=2 x+y \\
y^{\prime }&=-x+4 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.418 |
|
| \begin{align*}
x^{\prime }&=-2 x-y \\
y^{\prime }&=x-4 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.412 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-x-2 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.411 |
|
| \begin{align*}
x^{\prime }&=2 y \\
y^{\prime }&=-y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.454 |
|
| \begin{align*}
x^{\prime }&=2 x+4 y \\
y^{\prime }&=3 x+6 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.896 |
|
| \begin{align*}
x^{\prime }&=4 x+2 y \\
y^{\prime }&=2 x+y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.537 |
|
| \begin{align*}
x^{\prime }&=2 y \\
y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.328 |
|
| \begin{align*}
x^{\prime }&=-2 y \\
y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.421 |
|
| \begin{align*}
x^{\prime }&=-3 x-y \\
y^{\prime }&=4 x+y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= -1 \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.549 |
|
| \begin{align*}
x^{\prime }&=\frac {y}{10} \\
y^{\prime }&=\frac {z}{5} \\
z^{\prime }&=\frac {2 x}{5} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.934 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-x \\
z^{\prime }&=2 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.902 |
|
| \begin{align*}
x^{\prime }&=-2 x+3 y \\
y^{\prime }&=3 x-2 y \\
z^{\prime }&=-z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.849 |
|
| \begin{align*}
x^{\prime }&=x+3 z \\
y^{\prime }&=-y \\
z^{\prime }&=-3 x+z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.935 |
|
| \begin{align*}
x^{\prime }&=x \\
y^{\prime }&=2 y-z \\
z^{\prime }&=-y+2 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.701 |
|
| \begin{align*}
x^{\prime }&=-2 x+y \\
y^{\prime }&=-2 y \\
z^{\prime }&=-z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.673 |
|
| \begin{align*}
x^{\prime }&=-2 x+y \\
y^{\prime }&=-2 y \\
z^{\prime }&=z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.635 |
|
| \begin{align*}
x^{\prime }&=-x+2 y \\
y^{\prime }&=2 x-4 y \\
z^{\prime }&=-z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.857 |
|
| \begin{align*}
x^{\prime }&=-x+2 y \\
y^{\prime }&=2 x-4 y \\
z^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.739 |
|
| \begin{align*}
x^{\prime }&=-2 x+y \\
y^{\prime }&=-2 y+z \\
z^{\prime }&=-2 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.650 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=z \\
z^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.567 |
|
| \begin{align*}
x^{\prime }&=2 x-y \\
y^{\prime }&=-2 y+3 z \\
z^{\prime }&=-x+3 y-z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.444 |
|
| \begin{align*}
x^{\prime }&=-4 x+3 y \\
y^{\prime }&=z-y \\
z^{\prime }&=5 x-5 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.352 |
|
| \begin{align*}
x^{\prime }&=-10 x+10 y \\
y^{\prime }&=28 x-y \\
z^{\prime }&=-\frac {8 z}{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.266 |
|
| \begin{align*}
x^{\prime }&=z-y \\
y^{\prime }&=z-x \\
z^{\prime }&=z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.734 |
|
| \begin{align*}
x^{\prime }&=3 x \\
y^{\prime }&=-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.456 |
|
| \begin{align*}
x^{\prime }&=0 \\
y^{\prime }&=x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.412 |
|
| \begin{align*}
x^{\prime }&=\pi ^{2} x+\frac {187 y}{5} \\
y^{\prime }&=\sqrt {555}\, x+\frac {400617 y}{5000} \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.151 |
|
| \begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=-2 x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.638 |
|
| \begin{align*}
x^{\prime }&=-3 x+y \\
y^{\prime }&=-x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.757 |
|
| \begin{align*}
x^{\prime }&=-3 x+y \\
y^{\prime }&=-x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.775 |
|
| \begin{align*}
x^{\prime }&=-x+y \\
y^{\prime }&=-2 x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.634 |
|
| \begin{align*}
x^{\prime }&=2 x \\
y^{\prime }&=x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.554 |
|
| \begin{align*}
x^{\prime }&=3 x+y \\
y^{\prime }&=-x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.738 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-4 x-4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.579 |
|
| \begin{align*}
x^{\prime }&=-3 x-3 y \\
y^{\prime }&=2 x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.762 |
|
| \begin{align*}
x^{\prime }&=2 y \\
y^{\prime }&=1-2 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.898 |
|
| \begin{align*}
x^{\prime }&=4 x-3 y \\
y^{\prime }&=6 x-7 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.664 |
|
| \begin{align*}
t x^{\prime }+2 x&=15 y \\
y^{\prime } t&=x \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.124 |
|
| \begin{align*}
x^{\prime }&=x+2 y \\
y^{\prime }&=5 x-2 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 7 \\
y \left (0\right ) &= -7 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.540 |
|
| \begin{align*}
x^{\prime }&=5 x+4 y \\
y^{\prime }&=8 x+y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 9 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.535 |
|
| \begin{align*}
x^{\prime }&=4 x+2 y \\
y^{\prime }&=3 x-y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= -21 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.567 |
|
| \begin{align*}
x^{\prime }&=x+2 y \\
y^{\prime }&=5 x-2 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 15 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.496 |
|
| \begin{align*}
x^{\prime }&=2 y \\
y^{\prime }&=2 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.443 |
|
| \begin{align*}
x^{\prime }&=2 y \\
y^{\prime }&=-2 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.582 |
|
| \begin{align*}
x^{\prime }&=-2 y \\
y^{\prime }&=8 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.651 |
|
| \begin{align*}
x^{\prime }&=4 x-13 y \\
y^{\prime }&=x \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.811 |
|
| \begin{align*}
x^{\prime }&=3 x+2 y \\
y^{\prime }&=-2 x+3 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= a_{1} \\
y \left (0\right ) &= a_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.635 |
|
| \begin{align*}
x^{\prime }&=8 x+2 y-17 \\
y^{\prime }&=4 x+y-13 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.853 |
|
| \begin{align*}
x^{\prime }&=8 x+2 y+7 \,{\mathrm e}^{2 t} \\
y^{\prime }&=4 x+y-7 \,{\mathrm e}^{2 t} \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= -1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.770 |
|
| \begin{align*}
x^{\prime }&=4 x+3 y-6 \,{\mathrm e}^{3 t} \\
y^{\prime }&=x+6 y+2 \,{\mathrm e}^{3 t} \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 4 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.839 |
|
| \begin{align*}
x^{\prime }&=-y \\
y^{\prime }&=4 x+24 t \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.796 |
|
| \begin{align*}
x^{\prime }&=4 x-13 y \\
y^{\prime }&=x+19 \cos \left (4 t \right )-13 \sin \left (4 t \right ) \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 13 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.118 |
|
| \begin{align*}
x^{\prime }&=4 x+3 y+5 \operatorname {Heaviside}\left (-2+t \right ) \\
y^{\prime }&=x+6 y+17 \operatorname {Heaviside}\left (-2+t \right ) \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.549 |
|
| \begin{align*}
x^{\prime }&=5 x+4 y \\
y^{\prime }&=8 x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.491 |
|
| \begin{align*}
x^{\prime }&=2 x-5 y \\
y^{\prime }&=3 x-7 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.870 |
|
| \begin{align*}
x^{\prime }&=2 x-5 y+4 \\
y^{\prime }&=3 x-7 y+5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.363 |
|
| \begin{align*}
x^{\prime }&=3 x+y \\
y^{\prime }&=6 x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.631 |
|
| \begin{align*}
x^{\prime }&=x y-6 y \\
y^{\prime }&=x-y-5 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.240 |
|
| \begin{align*}
x^{\prime }&=-x+2 y \\
y^{\prime }&=2 x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.463 |
|
| \begin{align*}
x^{\prime }&=4 y \\
y^{\prime }&=-x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.993 |
|
| \begin{align*}
x^{\prime }&=4 y \\
y^{\prime }&=-4 x \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 4 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.604 |
|
| \begin{align*}
x^{\prime }&=-5 x+4 y \\
y^{\prime }&=2 x+2 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 4 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| \begin{align*}
x^{\prime }&=6 \\
y^{\prime }&=\cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.322 |
|
| \begin{align*}
x^{\prime }&=x \\
y^{\prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.381 |
|
| \begin{align*}
x^{\prime }&=0 \\
y^{\prime }&=-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.250 |
|
| \begin{align*}
x^{\prime }&=x^{2} \\
y^{\prime }&={\mathrm e}^{t} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.043 |
|
| \begin{align*}
x_{1}^{\prime }&=-3 x_{1} \\
x_{2}^{\prime }&=1 \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= -1 \\
x_{2} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.468 |
|
| \begin{align*}
x_{1}^{\prime }&=-x_{1}+1 \\
x_{2}^{\prime }&=x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.454 |
|
| \begin{align*}
x^{\prime }&=-3 x+6 y \\
y^{\prime }&=4 x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.314 |
|
| \begin{align*}
x^{\prime }&=8 x-y \\
y^{\prime }&=x+6 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.273 |
|
| \begin{align*}
x^{\prime }&=-x-2 y \\
y^{\prime }&=x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.342 |
|
| \begin{align*}
x^{\prime }&=4 x+2 y \\
y^{\prime }&=-x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.437 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=1-x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.477 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-x+\sin \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.526 |
|
| \begin{align*}
x_{1}^{\prime }&=-2 t x_{1}^{2} \\
x_{2}^{\prime }&=\frac {x_{2}+t}{t} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.058 |
|
| \begin{align*}
x_{1}^{\prime }&={\mathrm e}^{t -x_{1}} \\
x_{2}^{\prime }&=2 \,{\mathrm e}^{x_{1}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.057 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=\frac {y^{2}}{x} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.056 |
|
| \begin{align*}
x_{1}^{\prime }&=\frac {x_{1}^{2}}{x_{2}} \\
x_{2}^{\prime }&=x_{2}-x_{1} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.056 |
|
| \begin{align*}
x^{\prime }&=\frac {{\mathrm e}^{-x}}{t} \\
y^{\prime }&=\frac {x \,{\mathrm e}^{-y}}{t} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.079 |
|
| \begin{align*}
x^{\prime }&=\frac {y+t}{x+y} \\
y^{\prime }&=\frac {x-t}{x+y} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
0.060 |
|
| \begin{align*}
x^{\prime }&=\frac {t -y}{-x+y} \\
y^{\prime }&=\frac {x-t}{-x+y} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.086 |
|
| \begin{align*}
x^{\prime }&=\frac {y+t}{x+y} \\
y^{\prime }&=\frac {t +x}{x+y} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
0.196 |
|
| \begin{align*}
x^{\prime }&=-9 y \\
y^{\prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.364 |
|
| \begin{align*}
x^{\prime }&=y+t \\
y^{\prime }&=x-t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.474 |
|
| \begin{align*}
x^{\prime }+3 x+4 y&=0 \\
y^{\prime }+2 x+5 y&=0 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.384 |
|
| \begin{align*}
x^{\prime }&=x+5 y \\
y^{\prime }&=-x-3 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= -2 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.475 |
|
| \begin{align*}
4 x^{\prime }-y^{\prime }+3 x&=\sin \left (t \right ) \\
x^{\prime }+y&=\cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.753 |
|
| \begin{align*}
x^{\prime }&=z-y \\
y^{\prime }&=z \\
z^{\prime }&=z-x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.662 |
|
| \begin{align*}
x^{\prime }&=y+z \\
y^{\prime }&=x+z \\
z^{\prime }&=x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.536 |
|
| \begin{align*}
x^{\prime \prime }&=y \\
y^{\prime \prime }&=x \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.079 |
|
| \begin{align*}
x^{\prime \prime }+y^{\prime }+x&=0 \\
x^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.033 |
|
| \begin{align*}
x^{\prime \prime }&=3 x+y \\
y^{\prime }&=-2 x \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.079 |
|
| \begin{align*}
x^{\prime \prime }&=x^{2}+y \\
y^{\prime }&=-2 x x^{\prime }+x \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
0.019 |
|
| \begin{align*}
x^{\prime }&=x^{2}+y^{2} \\
y^{\prime }&=2 x y \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.075 |
|
| \begin{align*}
x^{\prime }&=-\frac {1}{y} \\
y^{\prime }&=\frac {1}{x} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.056 |
|
| \begin{align*}
x^{\prime }&=\frac {x}{y} \\
y^{\prime }&=\frac {y}{x} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.079 |
|
| \begin{align*}
x^{\prime }&=\frac {y}{x-y} \\
y^{\prime }&=\frac {x}{x-y} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.033 |
|
| \begin{align*}
x^{\prime }&=\sin \left (x\right ) \cos \left (y\right ) \\
y^{\prime }&=\cos \left (x\right ) \sin \left (y\right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.056 |
|
| \begin{align*}
{\mathrm e}^{t} x^{\prime }&=\frac {1}{y} \\
{\mathrm e}^{t} y^{\prime }&=\frac {1}{x} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.057 |
|
| \begin{align*}
x^{\prime }&=\cos \left (x\right )^{2} \cos \left (y\right )^{2}+\sin \left (x\right )^{2} \cos \left (y\right )^{2} \\
y^{\prime }&=-\frac {\sin \left (2 x\right ) \sin \left (2 y\right )}{2} \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.065 |
|
| \begin{align*}
x^{\prime }&=8 y-x \\
y^{\prime }&=x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.364 |
|
| \begin{align*}
x^{\prime }&=x-y \\
y^{\prime }&=-x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.318 |
|
| \begin{align*}
x^{\prime }&=2 x+y \\
y^{\prime }&=x-3 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.641 |
|
| \begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=-2 x+4 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.408 |
|
| \begin{align*}
x^{\prime }&=4 x-5 y \\
y^{\prime }&=x \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.437 |
|
| \begin{align*}
x^{\prime }&=y+z-x \\
y^{\prime }&=x-y+z \\
z^{\prime }&=x+y-z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.487 |
|
| \begin{align*}
x^{\prime }&=2 x-y+z \\
y^{\prime }&=x+2 y-z \\
z^{\prime }&=x-y+2 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.536 |
|
| \begin{align*}
x^{\prime }&=2 x-y+z \\
y^{\prime }&=x+z \\
z^{\prime }&=y-2 z-3 x \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
z \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.597 |
|
| \begin{align*}
x^{\prime }+2 x-y&=-{\mathrm e}^{2 t} \\
y^{\prime }+3 x-2 y&=6 \,{\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.642 |
|
| \begin{align*}
x^{\prime }&=x+y-\cos \left (t \right ) \\
y^{\prime }&=-y-2 x+\cos \left (t \right )+\sin \left (t \right ) \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.899 |
|
| \begin{align*}
x^{\prime }&=y+\tan \left (t \right )^{2}-1 \\
y^{\prime }&=\tan \left (t \right )-x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.856 |
|
| \begin{align*}
x^{\prime }&=-4 x-2 y+\frac {2}{{\mathrm e}^{t}-1} \\
y^{\prime }&=6 x+3 y-\frac {3}{{\mathrm e}^{t}-1} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.059 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-x+\frac {1}{\cos \left (t \right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.629 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=1-x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.470 |
|
| \begin{align*}
x^{\prime }&=3-2 y \\
y^{\prime }&=2 x-2 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.585 |
|
| \begin{align*}
x^{\prime }&=-y+\sin \left (t \right ) \\
y^{\prime }&=x+\cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.530 |
|
| \begin{align*}
x^{\prime }&=x+y+{\mathrm e}^{t} \\
y^{\prime }&=x+y-{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.490 |
|
| \begin{align*}
x^{\prime }&=4 x-5 y+4 t -1 \\
y^{\prime }&=x-2 y+t \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.579 |
|
| \begin{align*}
x^{\prime }&=y-x+{\mathrm e}^{t} \\
y^{\prime }&=x-y+{\mathrm e}^{t} \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.550 |
|
| \begin{align*}
x^{\prime }+y&=t^{2} \\
-x+y^{\prime }&=t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.513 |
|
| \begin{align*}
x^{\prime }+y^{\prime }+y&={\mathrm e}^{-t} \\
2 x^{\prime }+y^{\prime }+2 y&=\sin \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.492 |
|
| \begin{align*}
x^{\prime }&=2 x+y-2 z+2-t \\
y^{\prime }&=1-x \\
z^{\prime }&=x+y-z+1-t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.149 |
|
| \begin{align*}
x^{\prime }+x+2 y&=2 \,{\mathrm e}^{-t} \\
y^{\prime }+y+z&=1 \\
z^{\prime }+z&=1 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 1 \\
z \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.737 |
|
| \begin{align*}
x^{\prime }&=5 x+4 y \\
y^{\prime }&=x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.351 |
|
| \begin{align*}
x^{\prime }&=6 x+y \\
y^{\prime }&=4 x+3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.382 |
|
| \begin{align*}
x^{\prime }&=2 x-4 y+1 \\
y^{\prime }&=-x+5 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| \begin{align*}
x^{\prime }&=3 x+y+{\mathrm e}^{t} \\
y^{\prime }&=x+3 y-{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.514 |
|
| \begin{align*}
x^{\prime }&=2 x+4 y+\cos \left (t \right ) \\
y^{\prime }&=-x-2 y+\sin \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.519 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=4+x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.496 |
|
| \begin{align*}
x^{\prime }&=x+2 y+\sin \left (t \right ) \\
y^{\prime }&=-x+y-\cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.219 |
|
| \begin{align*}
x^{\prime }&=-2 t x+y \\
y^{\prime }&=3 x-y \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.057 |
|
| \begin{align*}
x^{\prime }&=x+2 y+4 \\
y^{\prime }&=-2 x+y-3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.658 |
|
| \begin{align*}
x^{\prime }&=3 x-y \\
y^{\prime }&=x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.991 |
|
| \begin{align*}
x^{\prime }&=-x+t y \\
y^{\prime }&=t x-y \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.063 |
|
| \begin{align*}
x^{\prime }&=x+y+4 \\
y^{\prime }&=-2 x+\sin \left (t \right ) y \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
0.059 |
|
| \begin{align*}
x^{\prime }&=3 x-4 y \\
y^{\prime }&=x+3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.438 |
|
| \begin{align*}
x^{\prime }&=2 x-y \\
y^{\prime }&=3 x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.383 |
|
| \begin{align*}
x^{\prime }&=-x+2 y \\
y^{\prime }&=-2 x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.421 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-x+2 \sin \left (t \right ) \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.663 |
|
| \begin{align*}
x^{\prime }&=x-4 y+2 t \\
y^{\prime }&=x-3 y-3 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.572 |
|
| \begin{align*}
x^{\prime }&=-x+y+1 \\
y^{\prime }&=x+y-3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.730 |
|
| \begin{align*}
x^{\prime }&=-x-4 y-4 \\
y^{\prime }&=x-y-6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.666 |
|
| \begin{align*}
x^{\prime }&=-\frac {x}{4}-\frac {3 y}{4}+8 \\
y^{\prime }&=\frac {x}{2}+y-\frac {23}{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.705 |
|
| \begin{align*}
x^{\prime }&=-2 x+y-11 \\
y^{\prime }&=-5 x+4 y-35 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.602 |
|
| \begin{align*}
x^{\prime }&=x+y-3 \\
y^{\prime }&=-x+y+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.613 |
|
| \begin{align*}
x^{\prime }&=-5 x+4 y-35 \\
y^{\prime }&=-2 x+y-11 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.630 |
|
| \begin{align*}
x^{\prime }&=3 x-2 y \\
y^{\prime }&=2 x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.399 |
|
| \begin{align*}
x^{\prime }&=x-2 y \\
y^{\prime }&=3 x-4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.383 |
|
| \begin{align*}
x^{\prime }&=2 x-y \\
y^{\prime }&=3 x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.422 |
|
| \begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=4 x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.388 |
|
| \begin{align*}
x^{\prime }&=4 x-3 y \\
y^{\prime }&=8 x-6 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.394 |
|
| \begin{align*}
x^{\prime }&=-2 x+y \\
y^{\prime }&=x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.352 |
|
| \begin{align*}
x^{\prime }&=\frac {5 x}{4}+\frac {3 y}{4} \\
y^{\prime }&=\frac {3 x}{4}+\frac {5 y}{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.359 |
|
| \begin{align*}
x^{\prime }&=-\frac {3 x}{4}-\frac {7 y}{4} \\
y^{\prime }&=\frac {x}{4}+\frac {5 y}{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.388 |
|
| \begin{align*}
x^{\prime }&=-\frac {x}{4}-\frac {3 y}{4} \\
y^{\prime }&=\frac {x}{2}+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.392 |
|
| \begin{align*}
x^{\prime }&=5 x-y \\
y^{\prime }&=3 x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.386 |
|
| \begin{align*}
x^{\prime }&=-2 x+y \\
y^{\prime }&=-5 x+4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.421 |
|
| \begin{align*}
x^{\prime }&=3 x+6 y \\
y^{\prime }&=-x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.363 |
|
| \begin{align*}
x^{\prime }&=x-2 y \\
y^{\prime }&=3 x-4 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 3 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.407 |
|
| \begin{align*}
x^{\prime }&=2 x-y \\
y^{\prime }&=3 x-2 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.375 |
|
| \begin{align*}
x^{\prime }&=5 x-y \\
y^{\prime }&=3 x+y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.388 |
|
| \begin{align*}
x^{\prime }&=-2 x+y \\
y^{\prime }&=-5 x+4 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.353 |
|
| \begin{align*}
x^{\prime }&=3 x-2 y \\
y^{\prime }&=4 x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.494 |
|
| \begin{align*}
x^{\prime }&=-x-4 y \\
y^{\prime }&=x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.418 |
|
| \begin{align*}
x^{\prime }&=2 x-5 y \\
y^{\prime }&=x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.412 |
|
| \begin{align*}
x^{\prime }&=2 x-\frac {5 y}{2} \\
y^{\prime }&=\frac {9 x}{5}-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.551 |
|
| \begin{align*}
x^{\prime }&=x-y \\
y^{\prime }&=5 x-3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.530 |
|
| \begin{align*}
x^{\prime }&=x+2 y \\
y^{\prime }&=-5 x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.429 |
|
| \begin{align*}
x^{\prime }&=-x-4 y \\
y^{\prime }&=x-y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 4 \\
y \left (0\right ) &= -3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.419 |
|
| \begin{align*}
x^{\prime }&=2 x-5 y \\
y^{\prime }&=x-2 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 3 \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.392 |
|
| \begin{align*}
x^{\prime }&=x-5 y \\
y^{\prime }&=x-3 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.477 |
|
| \begin{align*}
x^{\prime }&=-3 x+2 y \\
y^{\prime }&=-x-y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.544 |
|
| \begin{align*}
x^{\prime }&=\frac {3 x}{4}-2 y \\
y^{\prime }&=x-\frac {5 y}{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.521 |
|
| \begin{align*}
x^{\prime }&=-\frac {4 x}{5}+2 y \\
y^{\prime }&=-x+\frac {6 y}{5} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.503 |
|
| \begin{align*}
x^{\prime }&=a x+y \\
y^{\prime }&=-x+a y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.409 |
|
| \begin{align*}
x^{\prime }&=-5 y \\
y^{\prime }&=x+a y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.733 |
|
| \begin{align*}
x^{\prime }&=2 x-5 y \\
y^{\prime }&=a x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.548 |
|
| \begin{align*}
x^{\prime }&=\frac {5 x}{4}+\frac {3 y}{4} \\
y^{\prime }&=a x+\frac {5 y}{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.550 |
|
| \begin{align*}
x^{\prime }&=-x+a y \\
y^{\prime }&=-x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.531 |
|
| \begin{align*}
x^{\prime }&=3 x+a y \\
y^{\prime }&=-6 x-4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.601 |
|
| \begin{align*}
x^{\prime }&=a x+10 y \\
y^{\prime }&=-x-4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.753 |
|
| \begin{align*}
x^{\prime }&=4 x+a y \\
y^{\prime }&=8 x-6 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.579 |
|
| \begin{align*}
i^{\prime }&=\frac {i}{2}-\frac {v}{8} \\
v^{\prime }&=2 i-\frac {v}{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.372 |
|
| \begin{align*}
x^{\prime }&=3 x-4 y \\
y^{\prime }&=x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.335 |
|
| \begin{align*}
x^{\prime }&=\frac {5 x}{4}+\frac {3 y}{4} \\
y^{\prime }&=-\frac {3 x}{4}-\frac {y}{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.342 |
|
| \begin{align*}
x^{\prime }&=-\frac {3 x}{2}+y \\
y^{\prime }&=-\frac {x}{4}-\frac {y}{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.345 |
|
| \begin{align*}
x^{\prime }&=-3 x+\frac {5 y}{2} \\
y^{\prime }&=-\frac {5 x}{2}+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.332 |
|
| \begin{align*}
x^{\prime }&=-x-\frac {y}{2} \\
y^{\prime }&=2 x-3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.352 |
|
| \begin{align*}
x^{\prime }&=2 x+\frac {y}{2} \\
y^{\prime }&=-\frac {x}{2}+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.330 |
|
| \begin{align*}
x^{\prime }&=x-4 y \\
y^{\prime }&=4 x-7 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 3 \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.379 |
|
| \begin{align*}
x^{\prime }&=-\frac {5 x}{2}+\frac {3 y}{2} \\
y^{\prime }&=-\frac {3 x}{2}+\frac {y}{2} \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 3 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.332 |
|
| \begin{align*}
x^{\prime }&=2 x+\frac {3 y}{2} \\
y^{\prime }&=-\frac {3 x}{2}-y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 3 \\
y \left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.338 |
|
| \begin{align*}
x^{\prime }&=\frac {5 x}{4}+\frac {3 y}{4} \\
y^{\prime }&=-\frac {3 x}{4}-\frac {y}{4} \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.329 |
|
| \begin{align*}
x^{\prime }&=-3 x+\frac {5 y}{2} \\
y^{\prime }&=-\frac {5 x}{2}+2 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 3 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.315 |
|
| \begin{align*}
x^{\prime }&=2 x+\frac {y}{2} \\
y^{\prime }&=-\frac {x}{2}+y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.319 |
|
| \begin{align*}
x^{\prime }&=-x \\
y^{\prime }&=-2 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 4 \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.296 |
|
| \begin{align*}
x^{\prime }&=-x \\
y^{\prime }&=2 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 4 \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.292 |
|
| \begin{align*}
x^{\prime }&=-x \\
y^{\prime }&=-2 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 4 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.284 |
|
| \begin{align*}
x^{\prime }&=2 y \\
y^{\prime }&=8 x \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.380 |
|
| \begin{align*}
x^{\prime }&=2 y \\
y^{\prime }&=8 x \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.359 |
|
| \begin{align*}
x^{\prime }&=2 y \\
y^{\prime }&=-8 x \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.391 |
|
| \begin{align*}
x^{\prime }&=2 x-y \\
y^{\prime }&=x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.490 |
|
| \begin{align*}
x^{\prime }&=-x+y \\
y^{\prime }&=x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.432 |
|
| \begin{align*}
x^{\prime }&=2 x-4 y \\
y^{\prime }&=2 x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.406 |
|
| \begin{align*}
x^{\prime }&=-x+y+x^{2} \\
y^{\prime }&=y-2 x y \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.087 |
|
| \begin{align*}
x^{\prime }&=2 y \,x^{2}-3 x^{2}-4 y \\
y^{\prime }&=-2 x \,y^{2}+6 x y \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.059 |
|
| \begin{align*}
x^{\prime }&=3 x-x^{2} \\
y^{\prime }&=2 x y-3 y+2 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.092 |
|
| \begin{align*}
x^{\prime }&=x-x y \\
y^{\prime }&=y+2 x y \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.054 |
|
| \begin{align*}
x^{\prime }&=2-y \\
y^{\prime }&=y-x^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.110 |
|
| \begin{align*}
x^{\prime }&=x-x^{2}-x y \\
y^{\prime }&=\frac {y}{2}-\frac {y^{2}}{4}-\frac {3 x y}{4} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.036 |
|
| \begin{align*}
x^{\prime }&=-\left (x-y\right ) \left (1-x-y\right ) \\
y^{\prime }&=x \left (2+y\right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.095 |
|
| \begin{align*}
x^{\prime }&=y \left (2-x-y\right ) \\
y^{\prime }&=-x-y-2 x y \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.057 |
|
| \begin{align*}
x^{\prime }&=\left (2+x\right ) \left (-x+y\right ) \\
y^{\prime }&=y-x^{2}-y^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.092 |
|
| \begin{align*}
x^{\prime }&=-x+2 x y \\
y^{\prime }&=y-x^{2}-y^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.033 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=x-\frac {x^{3}}{5}-\frac {y}{5} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.092 |
|
| \begin{align*}
x^{\prime }&=x \left (1-x-y\right ) \\
y^{\prime }&=y \left (\frac {3}{4}-y-\frac {x}{2}\right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.060 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}+x_{2}+x_{3} \\
x_{2}^{\prime }&=2 x_{1}+x_{2}-x_{3} \\
x_{3}^{\prime }&=-x_{2}+x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.692 |
|
| \begin{align*}
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{align*} |
✓ |
✓ |
✓ |
✓ |
0.733 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{2}+x_{3} \\
x_{2}^{\prime }&=x_{1}+x_{3} \\
x_{3}^{\prime }&=x_{1}+x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.501 |
|
| \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*} |
✓ |
✓ |
✓ |
✓ |
0.626 |
|
| \begin{align*}
x_{1}^{\prime }&=-4 x_{1}+x_{2} \\
x_{2}^{\prime }&=x_{1}-5 x_{2}+x_{3} \\
x_{3}^{\prime }&=x_{2}-4 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.659 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}+4 x_{2}+4 x_{3} \\
x_{2}^{\prime }&=3 x_{2}+2 x_{3} \\
x_{3}^{\prime }&=2 x_{2}+3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.599 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}-4 x_{2}+2 x_{3} \\
x_{2}^{\prime }&=-4 x_{1}+2 x_{2}-2 x_{3} \\
x_{3}^{\prime }&=2 x_{1}-2 x_{2}-x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.632 |
|
| \begin{align*}
x_{1}^{\prime }&=-2 x_{1}+2 x_{2}-x_{3} \\
x_{2}^{\prime }&=-2 x_{1}+3 x_{2}-2 x_{3} \\
x_{3}^{\prime }&=-2 x_{1}+4 x_{2}-3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.602 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}+x_{2}+6 x_{3} \\
x_{2}^{\prime }&=x_{1}+6 x_{2}+x_{3} \\
x_{3}^{\prime }&=6 x_{1}+x_{2}+x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.678 |
|
| \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*} |
✓ |
✓ |
✓ |
✓ |
0.642 |
|
| \begin{align*}
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{align*} |
✓ |
✓ |
✓ |
✓ |
0.819 |
|
| \begin{align*}
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{align*} |
✓ |
✓ |
✓ |
✓ |
0.730 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}+x_{2}+2 x_{3} \\
x_{2}^{\prime }&=2 x_{2}+2 x_{3} \\
x_{3}^{\prime }&=-x_{1}+x_{2}+3 x_{3} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 11 \\
x_{2} \left (0\right ) &= 1 \\
x_{3} \left (0\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.674 |
|
| \begin{align*}
x_{1}^{\prime }&=-x_{3} \\
x_{2}^{\prime }&=2 x_{1} \\
x_{3}^{\prime }&=-x_{1}+2 x_{2}+4 x_{3} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 7 \\
x_{2} \left (0\right ) &= 5 \\
x_{3} \left (0\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.776 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}+3 x_{3} \\
x_{2}^{\prime }&=-2 x_{2} \\
x_{3}^{\prime }&=3 x_{1}-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 ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.858 |
|
| \begin{align*}
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{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*} |
✓ |
✓ |
✓ |
✓ |
0.668 |
|
| \begin{align*}
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{align*} |
✓ |
✓ |
✓ |
✓ |
1.053 |
|
| \begin{align*}
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{align*} |
✓ |
✓ |
✓ |
✓ |
1.086 |
|
| \begin{align*}
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{align*} |
✓ |
✓ |
✓ |
✓ |
0.813 |
|
| \begin{align*}
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{align*} |
✓ |
✓ |
✓ |
✓ |
1.122 |
|
| \begin{align*}
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{align*} |
✓ |
✓ |
✓ |
✓ |
1.859 |
|
| \begin{align*}
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{align*} |
✓ |
✓ |
✓ |
✓ |
1.546 |
|
| \begin{align*}
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{align*} |
✓ |
✓ |
✓ |
✓ |
4.063 |
|
| \begin{align*}
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{align*} |
✓ |
✓ |
✓ |
✓ |
1.069 |
|
| \begin{align*}
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{align*} |
✓ |
✓ |
✓ |
✓ |
0.908 |
|
| \begin{align*}
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{align*} |
✓ |
✓ |
✓ |
✓ |
1.024 |
|
| \begin{align*}
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{align*} |
✓ |
✓ |
✓ |
✓ |
1.126 |
|
| \begin{align*}
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{align*} |
✓ |
✓ |
✓ |
✓ |
1.043 |
|
| \begin{align*}
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{align*} |
✓ |
✓ |
✓ |
✓ |
0.937 |
|
| \begin{align*}
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{align*} |
✓ |
✓ |
✓ |
✓ |
0.832 |
|
| \begin{align*}
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{align*} |
✓ |
✓ |
✓ |
✓ |
0.684 |
|
| \begin{align*}
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{align*} |
✓ |
✓ |
✓ |
✓ |
0.947 |
|
| \begin{align*}
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{align*} |
✓ |
✓ |
✓ |
✓ |
2.510 |
|
| \begin{align*}
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{align*} |
✓ |
✓ |
✓ |
✓ |
2.276 |
|
| \begin{align*}
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{align*} |
✓ |
✓ |
✓ |
✓ |
2.288 |
|
| \begin{align*}
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{align*} |
✓ |
✓ |
✓ |
✓ |
3.504 |
|
| \begin{align*}
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{align*} |
✓ |
✓ |
✓ |
✓ |
1.826 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}-2 x_{2} \\
x_{2}^{\prime }&=2 x_{1}-2 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.421 |
|
| \begin{align*}
x_{1}^{\prime }&=-3 x_{1}+2 x_{2} \\
x_{2}^{\prime }&=\frac {x_{1}}{2}-3 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.414 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}-4 x_{2} \\
x_{2}^{\prime }&=x_{1}-x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.375 |
|
| \begin{align*}
x_{1}^{\prime }&=\frac {x_{1}}{2}-\frac {x_{2}}{4} \\
x_{2}^{\prime }&=x_{1}-\frac {x_{2}}{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.338 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}-\frac {5 x_{2}}{2} \\
x_{2}^{\prime }&=\frac {x_{1}}{2}-x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.451 |
|
| \begin{align*}
x_{1}^{\prime }&=-x_{1}-4 x_{2} \\
x_{2}^{\prime }&=x_{1}-x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.435 |
|
| \begin{align*}
x_{1}^{\prime }&=5 x_{1}-x_{2} \\
x_{2}^{\prime }&=3 x_{1}+x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.412 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}-x_{2} \\
x_{2}^{\prime }&=5 x_{1}-3 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.544 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}-x_{2} \\
x_{2}^{\prime }&=3 x_{1}-2 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.413 |
|
| \begin{align*}
x_{1}^{\prime }&=\frac {x_{1}}{2}+\frac {x_{2}}{2} \\
x_{2}^{\prime }&=2 x_{1}-x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.427 |
|
| \begin{align*}
x_{1}^{\prime }&=-3 x_{1}+4 x_{2} \\
x_{2}^{\prime }&=-x_{1}-2 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.135 |
|
| \begin{align*}
x_{1}^{\prime }&=-3 x_{1}+\frac {5 x_{2}}{2} \\
x_{2}^{\prime }&=-\frac {5 x_{1}}{2}+2 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| \begin{align*}
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{align*} |
✓ |
✓ |
✓ |
✓ |
0.753 |
|
| \begin{align*}
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{align*} |
✓ |
✓ |
✓ |
✓ |
0.687 |
|
| \begin{align*}
x_{1}^{\prime }&=-3 x_{1}-9 x_{2} \\
x_{2}^{\prime }&=x_{1}-3 x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 4 \\
x_{2} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.497 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}-x_{2} \\
x_{2}^{\prime }&=3 x_{1}-2 x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 2 \\
x_{2} \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.428 |
|
| \begin{align*}
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{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= m_{0} \\
x_{2} \left (0\right ) &= 0 \\
x_{3} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.747 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}-x_{2}+{\mathrm e}^{t} \\
x_{2}^{\prime }&=3 x_{1}-2 x_{2}+t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.796 |
|
| \begin{align*}
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{align*} |
✓ |
✓ |
✓ |
✓ |
0.881 |
|
| \begin{align*}
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{align*} |
✓ |
✓ |
✓ |
✓ |
0.865 |
|
| \begin{align*}
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{align*} |
✓ |
✓ |
✓ |
✓ |
0.698 |
|
| \begin{align*}
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{align*} |
✓ |
✓ |
✓ |
✓ |
0.916 |
|
| \begin{align*}
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{align*} |
✓ |
✓ |
✓ |
✓ |
1.047 |
|
| \begin{align*}
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{align*} |
✓ |
✓ |
✓ |
✓ |
1.066 |
|
| \begin{align*}
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{align*} |
✓ |
✓ |
✓ |
✓ |
1.078 |
|
| \begin{align*}
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{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*} |
✓ |
✓ |
✓ |
✗ |
53.288 |
|
| \begin{align*}
x_{1}^{\prime }&=4 x_{1}-9 x_{2} \\
x_{2}^{\prime }&=x_{1}-2 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.367 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}-9 x_{2} \\
x_{2}^{\prime }&=x_{1}-3 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.394 |
|
| \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*} |
✓ |
✓ |
✓ |
✓ |
0.595 |
|
| \begin{align*}
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{align*} |
✓ |
✓ |
✓ |
✓ |
0.685 |
|
| \begin{align*}
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{align*} |
✓ |
✓ |
✓ |
✓ |
0.800 |
|
| \begin{align*}
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{align*} |
✓ |
✓ |
✓ |
✓ |
0.619 |
|
| \begin{align*}
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{align*} |
✓ |
✓ |
✓ |
✓ |
1.799 |
|
| \begin{align*}
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{align*} |
✓ |
✓ |
✓ |
✓ |
0.874 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}-4 x_{2} \\
x_{2}^{\prime }&=4 x_{1}-7 x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 7 \\
x_{2} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.408 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}-4 x_{2} \\
x_{2}^{\prime }&=x_{1}-x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= -5 \\
x_{2} \left (0\right ) &= 7 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.354 |
|
| \begin{align*}
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{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= -2 \\
x_{3} \left (0\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.625 |
|
| \begin{align*}
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{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 5 \\
x_{2} \left (0\right ) &= 5 \\
x_{3} \left (0\right ) &= -4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.661 |
|
| \begin{align*}
x^{\prime }&=-2 y+x y \\
y^{\prime }&=x+4 x y \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.109 |
|
| \begin{align*}
x^{\prime }&=1+5 y \\
y^{\prime }&=1-6 x^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.033 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=z \\
z^{\prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.313 |
|
| \begin{align*}
y^{\prime }&=y+z \\
z^{\prime }&=y+z+x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.605 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}}{z} \\
z^{\prime }&=\frac {y}{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.116 |
|
| \begin{align*}
y^{\prime }&=1-\frac {1}{z} \\
z^{\prime }&=\frac {1}{-x +y} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.037 |
|
| \begin{align*}
y^{\prime }&=-z \\
z^{\prime }&=y \\
\end{align*}
With initial conditions \begin{align*}
y \left (0\right ) &= 1 \\
z \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.489 |
|
| \begin{align*}
y^{\prime }&=\frac {z^{2}}{y} \\
z^{\prime }&=\frac {y^{2}}{z} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.115 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}}{z} \\
z^{\prime }&=\frac {z^{2}}{y} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.036 |
|
| \begin{align*}
x^{\prime }&=y+z-x \\
y^{\prime }&=x-y+z \\
z^{\prime }&=x+y-z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.566 |
|
| \begin{align*}
x^{\prime }+x+y&=t^{2} \\
y^{\prime }+y+z&=2 t \\
z^{\prime }+z&=t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.924 |
|
| \begin{align*}
x^{\prime }+5 x+y&=7 \,{\mathrm e}^{t}-27 \\
-2 x+y^{\prime }+3 y&=-3 \,{\mathrm e}^{t}+12 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.165 |
|
| \begin{align*}
y^{\prime \prime }+z^{\prime }-2 z&={\mathrm e}^{2 x} \\
z^{\prime }+2 y^{\prime }-3 y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.247 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=x+{\mathrm e}^{t}+{\mathrm e}^{-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.605 |
|
| \begin{align*}
y^{\prime }+\frac {2 z}{x^{2}}&=1 \\
z^{\prime }+y&=x \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.074 |
|
| \begin{align*}
t x^{\prime }-x-3 y&=t \\
y^{\prime } t -x+y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.092 |
|
| \begin{align*}
t x^{\prime }+6 x-y-3 z&=0 \\
y^{\prime } t +23 x-6 y-9 z&=0 \\
t z^{\prime }+x+y-2 z&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.106 |
|
| \begin{align*}
x^{\prime }+5 x+y&={\mathrm e}^{t} \\
y^{\prime }-x+3 y&={\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.685 |
|
| \begin{align*}
x^{\prime }&=x+3 y \\
y^{\prime }&=3 x+y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 5 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.506 |
|
| \begin{align*}
x^{\prime }&=x+2 y \\
y^{\prime }&=3 x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.509 |
|
| \begin{align*}
x^{\prime }&=x+2 y+t -1 \\
y^{\prime }&=3 x+2 y-5 t -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.843 |
|
| \begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.360 |
|
| \begin{align*}
x^{\prime }&=x \\
y^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.328 |
|
| \begin{align*}
x^{\prime }&=-3 x+4 y \\
y^{\prime }&=-2 x+3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.517 |
|
| \begin{align*}
x^{\prime }&=4 x-2 y \\
y^{\prime }&=5 x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.721 |
|
| \begin{align*}
x^{\prime }&=5 x+4 y \\
y^{\prime }&=-x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.466 |
|
| \begin{align*}
x^{\prime }&=4 x-3 y \\
y^{\prime }&=8 x-6 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.517 |
|
| \begin{align*}
x^{\prime }&=2 x \\
y^{\prime }&=3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.386 |
|
| \begin{align*}
x^{\prime }&=-4 x-y \\
y^{\prime }&=x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.415 |
|
| \begin{align*}
x^{\prime }&=7 x+6 y \\
y^{\prime }&=2 x+6 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.572 |
|
| \begin{align*}
x^{\prime }&=x-2 y \\
y^{\prime }&=4 x+5 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.717 |
|
| \begin{align*}
x^{\prime }&=x+y-5 t +2 \\
y^{\prime }&=4 x-2 y-8 t -8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.822 |
|
| \begin{align*}
x^{\prime }&=2 x \\
y^{\prime }&=3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.378 |
|
| \begin{align*}
x^{\prime }&=-x-2 y \\
y^{\prime }&=4 x-5 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.707 |
|
| \begin{align*}
x^{\prime }&=-3 x+4 y \\
y^{\prime }&=-2 x+3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.479 |
|
| \begin{align*}
x^{\prime }&=5 x+2 y \\
y^{\prime }&=-17 x-5 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.595 |
|
| \begin{align*}
x^{\prime }&=-4 x-y \\
y^{\prime }&=x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.424 |
|
| \begin{align*}
x^{\prime }&=4 x-3 y \\
y^{\prime }&=8 x-6 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.527 |
|
| \begin{align*}
x^{\prime }&=4 x-2 y \\
y^{\prime }&=5 x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.654 |
|
| \begin{align*}
x^{\prime }&=x \\
y^{\prime }&=x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.438 |
|
| \begin{align*}
z^{\prime }+7 y-3 z&=0 \\
7 y^{\prime }+63 y-36 z&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.644 |
|
| \begin{align*}
z^{\prime }+2 y^{\prime }+3 y&=0 \\
y^{\prime }+3 y-2 z&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.591 |
|
| \begin{align*}
y^{\prime }+3 y+z&=0 \\
z^{\prime }+3 y+5 z&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.572 |
|
| \begin{align*}
y^{\prime }+3 y+2 z&=0 \\
z^{\prime }+2 y-4 z&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.801 |
|
| \begin{align*}
y^{\prime }-3 y-2 z&=0 \\
z^{\prime }+y-2 z&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.742 |
|
| \begin{align*}
y^{\prime }+z^{\prime }+6 y&=0 \\
z^{\prime }+5 y+z&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.700 |
|
| \begin{align*}
z^{\prime }+y^{\prime }+5 y-3 z&=x +{\mathrm e}^{x} \\
y^{\prime }+2 y-z&={\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.001 |
|
| \begin{align*}
z^{\prime }+y+3 z&={\mathrm e}^{x} \\
y^{\prime }+3 y+4 z&={\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.946 |
|
| \begin{align*}
z^{\prime }-3 y+2 z&={\mathrm e}^{x} \\
y^{\prime }+2 y-z&={\mathrm e}^{3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.250 |
|
| \begin{align*}
z^{\prime }+5 y-2 z&=x \\
y^{\prime }+4 y+z&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.442 |
|
| \begin{align*}
z^{\prime }+7 y-9 z&={\mathrm e}^{x} \\
y^{\prime }-y-3 z&={\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.010 |
|
| \begin{align*}
y^{\prime }-2 y-2 z&={\mathrm e}^{3 x} \\
z^{\prime }+5 y-2 z&={\mathrm e}^{4 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.569 |
|
| \begin{align*}
x^{\prime }+2 x+y^{\prime }+y&=0 \\
5 x+y^{\prime }+3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.568 |
|
| \begin{align*}
x^{\prime }-7 x+y&=0 \\
y^{\prime }-2 x-5 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.707 |
|
| \begin{align*}
x^{\prime }+2 x-3 y&=t \\
y^{\prime }-3 x+2 y&={\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.809 |
|
| \begin{align*}
4 x^{\prime }+9 y^{\prime }+44 x+49 y&=t \\
3 x^{\prime }+7 y^{\prime }+34 x+38 y&={\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.842 |
|
| \begin{align*}
x^{\prime \prime }-3 x-4 y&=0 \\
x+y^{\prime \prime }+y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.050 |
|
| \begin{align*}
x^{\prime }+2 y^{\prime }-2 x+2 y&=3 \,{\mathrm e}^{t} \\
3 x^{\prime }+y^{\prime }+2 x+y&=4 \,{\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.805 |
|
| \begin{align*}
4 x^{\prime }+9 y^{\prime }+2 x+31 y&={\mathrm e}^{t} \\
3 x^{\prime }+7 y^{\prime }+x+24 y&=3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.213 |
|
| \begin{align*}
x^{\prime }+4 x+3 y&=t \\
y^{\prime }+2 x+5 y&={\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.862 |
|
| \begin{align*}
x^{\prime }&=n y-m z \\
y^{\prime }&=L z-m x \\
z^{\prime }&=m x-L y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
41.149 |
|
| \begin{align*}
t x^{\prime }+y&=0 \\
y^{\prime } t +x&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.093 |
|
| \begin{align*}
x^{\prime }-7 x+y&=0 \\
y^{\prime }-2 x-5 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.911 |
|
| \begin{align*}
x^{\prime }+5 x+y&={\mathrm e}^{t} \\
y^{\prime }-x+3 y&={\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.849 |
|
| \begin{align*}
4 x^{\prime }+9 y^{\prime }+11 x+31 y&={\mathrm e}^{t} \\
3 x^{\prime }+7 y^{\prime }+8 x+24 y&={\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.970 |
|
| \begin{align*}
t x^{\prime }&=t -2 x \\
y^{\prime } t&=t x+t y+2 x-t \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.100 |
|
| \begin{align*}
x^{\prime }&=-4 x-y \\
y^{\prime }&=x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.509 |
|
| \begin{align*}
x^{\prime }&=3 x \\
y^{\prime }&=-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.490 |
|
| \begin{align*}
x^{\prime }&=-y \\
y^{\prime }&=-5 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.819 |
|
| \begin{align*}
x^{\prime }&=2 y \\
y^{\prime }&=-3 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.836 |
|
| \begin{align*}
x^{\prime }&=x-y \\
y^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.486 |
|
| \begin{align*}
x^{\prime }&=2 x+3 y \\
y^{\prime }&=-3 x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.778 |
|
| \begin{align*}
x^{\prime }&=3 x-y \\
y^{\prime }&=2 x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.005 |
|
| \begin{align*}
x^{\prime }&=-y \\
y^{\prime }&=-5 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.716 |
|
| \begin{align*}
x^{\prime }&=x-y \\
y^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.473 |
|
| \begin{align*}
x^{\prime }&=2 x+3 y \\
y^{\prime }&=-3 x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.726 |
|
| \begin{align*}
x^{\prime }&=-4 x-y \\
y^{\prime }&=x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.560 |
|
| \begin{align*}
x^{\prime }&=x-y \\
y^{\prime }&=x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.737 |
|
| \begin{align*}
x^{\prime }&=x \\
y^{\prime }&=-2 x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.612 |
|
| \begin{align*}
x^{\prime }&=12 x-15 y \\
y^{\prime }&=4 x-4 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.769 |
|
| \begin{align*}
x^{\prime }&=2 x-y \\
y^{\prime }&=5 x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.733 |
|
| \begin{align*}
x^{\prime }&=4 x-13 y \\
y^{\prime }&=2 x-6 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.944 |
|
| \begin{align*}
x^{\prime }&=4 x+2 y \\
y^{\prime }&=3 x+3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.716 |
|
| \begin{align*}
x^{\prime }&=3 x+5 y \\
y^{\prime }&=-x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.909 |
|
| \begin{align*}
x^{\prime }&=8 x-5 y \\
y^{\prime }&=16 x+8 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.932 |
|
| \begin{align*}
x^{\prime }&=x-2 y \\
y^{\prime }&=2 x-3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.586 |
|
| \begin{align*}
x^{\prime }&=5 x+4 y+2 z \\
y^{\prime }&=4 x+5 y+2 z \\
z^{\prime }&=2 x+2 y+2 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.073 |
|
| \begin{align*}
x^{\prime }&=2 x-y+{\mathrm e}^{t} \\
y^{\prime }&=3 x-2 y+t \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.168 |
|
| \begin{align*}
x^{\prime }&=5 x+3 y+1 \\
y^{\prime }&=-6 x-4 y+{\mathrm e}^{t} \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.964 |
|
| \begin{align*}
x^{\prime }&=2 x-y+\cos \left (t \right ) \\
y^{\prime }&=5 x-2 y+\sin \left (t \right ) \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.335 |
|
| \begin{align*}
x^{\prime }&=x \cos \left (t \right )-\sin \left (t \right ) y \\
y^{\prime }&=x \sin \left (t \right )+y \cos \left (t \right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.059 |
|
| \begin{align*}
x^{\prime }&=\left (3 t -1\right ) x-\left (1-t \right ) y+t \,{\mathrm e}^{t^{2}} \\
y^{\prime }&=-\left (t +2\right ) x+\left (-2+t \right ) y-{\mathrm e}^{t^{2}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.111 |
|
| \begin{align*}
x^{\prime }&=2 x-4 y \\
y^{\prime }&=-x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.678 |
|
| \begin{align*}
x^{\prime }&=3 x+6 y \\
y^{\prime }&=-2 x-3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.388 |
|
| \begin{align*}
x^{\prime }&=8 x+y \\
y^{\prime }&=-4 x+4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.646 |
|
| \begin{align*}
x^{\prime }&=x-y+2 z \\
y^{\prime }&=-x+y+2 z \\
z^{\prime }&=x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.032 |
|
| \begin{align*}
x^{\prime }&=-x+y-z \\
y^{\prime }&=2 x-y+2 z \\
z^{\prime }&=2 x+2 y-z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.141 |
|
| \begin{align*}
w_{1}^{\prime }&=w_{2} \\
w_{2}^{\prime }&=\frac {a w_{1}}{z^{2}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.055 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-x \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.391 |
|
| \begin{align*}
x^{\prime }&=a y \\
y^{\prime }&=-a x \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.402 |
|
| \begin{align*}
x^{\prime }&=x \\
y^{\prime }&=-3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.291 |
|
| \begin{align*}
x^{\prime }&=a x \\
y^{\prime }&=a y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.241 |
|
| \begin{align*}
x^{\prime }&=a x+y \\
y^{\prime }&=a y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.287 |
|
| \begin{align*}
x^{\prime }&=3 x-y \\
y^{\prime }&=x+3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.392 |
|
| \begin{align*}
x^{\prime }&=2 x+y \\
y^{\prime }&=-x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.379 |
|
| \begin{align*}
x^{\prime }&=x+3 y \\
y^{\prime }&=-3 x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.389 |
|
| \begin{align*}
x^{\prime }&=-x \\
y^{\prime }&=y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.345 |
|
| \begin{align*}
x^{\prime }&=2 y \\
y^{\prime }&=-2 x \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= a \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.365 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-x \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.368 |
|
| \begin{align*}
x^{\prime }&=3 x+t \\
y^{\prime }&=-y+2 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.488 |
|
| \begin{align*}
x^{\prime }&=-x \\
y^{\prime }&=3 x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.328 |
|
| \begin{align*}
x^{\prime }&=2 x+6 y \\
y^{\prime }&=x+3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.356 |
|
| \begin{align*}
x^{\prime }&=2 x+6 y+{\mathrm e}^{t} \\
y^{\prime }&=x+3 y-{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.602 |
|
| \begin{align*}
x^{\prime }&=x+2 y \\
y^{\prime }&=3 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.371 |
|
| \begin{align*}
x^{\prime }&=x+2 y+2 t \\
y^{\prime }&=3 y+t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.576 |
|
| \begin{align*}
x^{\prime }&=3 x-y \\
y^{\prime }&=2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.325 |
|
| \begin{align*}
x^{\prime }&=x \\
y^{\prime }&=4 x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.322 |
|
| \begin{align*}
x^{\prime }&=x \\
y^{\prime }&=3 x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.312 |
|
| \begin{align*}
x^{\prime }&=x+3 y \\
y^{\prime }&=x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.362 |
|
| \begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=x-y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.487 |
|
| \begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=-y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= -1 \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.347 |
|
| \begin{align*}
x^{\prime }&=x+3 y+2 t \\
y^{\prime }&=x-y+t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.803 |
|
| \begin{align*}
x^{\prime }&=x+2 y+{\mathrm e}^{t} \\
y^{\prime }&=x-2 y-{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.112 |
|
| \begin{align*}
x^{\prime }&=x \\
y^{\prime }&=x-y \\
z^{\prime }&=-2 x+2 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.578 |
|
| \begin{align*}
x^{\prime }&=x \\
y^{\prime }&=2 y+z \\
z^{\prime }&=x+3 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.560 |
|
| \begin{align*}
x^{\prime }&=x+z \\
y^{\prime }&=-y \\
z^{\prime }&=4 z \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
z \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.563 |
|
| \begin{align*}
x^{\prime }&=x \\
y^{\prime }&=2 y+z \\
z^{\prime }&=x+z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.487 |
|
| \begin{align*}
x^{\prime }&=x+z \\
y^{\prime }&=z-y \\
z^{\prime }&=y-z \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 1 \\
z \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.594 |
|
| \begin{align*}
x^{\prime }&=2 x \\
y^{\prime }&=2 y+z \\
z^{\prime }&=-x-z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.539 |
|
| \begin{align*}
x^{\prime }&=\left (a -2\right ) x+y \\
y^{\prime }&=-x+\left (a -2\right ) y \\
z^{\prime }&=-a z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.826 |
|
| \begin{align*}
x^{\prime }+t y&=-1 \\
x^{\prime }+y^{\prime }&=2 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.052 |
|
| \begin{align*}
x^{\prime }+y&=3 t \\
y^{\prime }-t x^{\prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.049 |
|
| \begin{align*}
x^{\prime }-t y&=1 \\
y^{\prime }-t x^{\prime }&=3 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.034 |
|
| \begin{align*}
t^{2} x^{\prime }-y&=1 \\
y^{\prime }-2 x&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.046 |
|
| \begin{align*}
x^{\prime }-y&=3 \\
y^{\prime }-3 x^{\prime }&=-2 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.588 |
|
| \begin{align*}
t x^{\prime }+y^{\prime }&=1 \\
y^{\prime }+x+{\mathrm e}^{x^{\prime }}&=1 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.110 |
|
| \begin{align*}
x x^{\prime }+y&=2 t \\
y^{\prime }+2 x^{2}&=1 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.033 |
|
| \begin{align*}
x^{\prime }&=1+x \\
y^{\prime }&=x+3 y-1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.542 |
|
| \begin{align*}
x^{\prime }&=x+3 y+a \\
y^{\prime }&=x-y+b \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.672 |
|
| \begin{align*}
x^{\prime }&=a x+y \\
y^{\prime }&=-2 x+b y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.785 |
|
| \begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=-2 c x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.525 |
|
| \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 ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.408 |
|
| \begin{align*}
x^{\prime }&=x-6 y \\
y^{\prime }&=-2 x-y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.533 |
|
| \begin{align*}
x^{\prime }&=x-x y \\
y^{\prime }&=-y+x y \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.056 |
|
| \begin{align*}
x^{\prime }&=2 x-7 x y-a x \\
y^{\prime }&=-y+4 x y-a y \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
0.061 |
|
| \begin{align*}
x^{\prime }&=2 x-2 x y \\
y^{\prime }&=-y+x y \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.053 |
|
| \begin{align*}
x^{\prime }&=x-4 x y \\
y^{\prime }&=-2 y+x y \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.058 |
|
| \begin{align*}
x^{\prime }&=x \left (3-y\right ) \\
y^{\prime }&=y \left (x-5\right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.053 |
|
| \begin{align*}
x^{\prime }&=-2 x+y \\
y^{\prime }&=7 x-4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.561 |
|
| \begin{align*}
x^{\prime }&=-x-y \\
y^{\prime }&=4 x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.434 |
|
| \begin{align*}
x^{\prime }&=x-y \\
y^{\prime }&=3 x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.671 |
|
| \begin{align*}
x^{\prime }&=-2 a x-y \\
y^{\prime }&=\left (a^{2}+9\right ) x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.608 |
|
| \begin{align*}
x^{\prime }&=-x+4 y \\
y^{\prime }&=3 x-5 y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.430 |
|
| \begin{align*}
x_{1}^{\prime }&=-2 x_{1}+x_{2}+x_{3} \\
x_{2}^{\prime }&=-2 x_{2}+x_{3} \\
x_{3}^{\prime }&=x_{2}-2 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.627 |
|
| \begin{align*}
x_{1}^{\prime }&=a x_{1}+5 x_{3} \\
x_{2}^{\prime }&=-x_{2}-2 x_{3} \\
x_{3}^{\prime }&=-3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.700 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}+x_{2}+x_{3} \\
x_{2}^{\prime }&=x_{1}-2 x_{2}-x_{3} \\
x_{3}^{\prime }&=x_{2}-x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.486 |
|
| \begin{align*}
x_{1}^{\prime }&=a x_{1} \\
x_{2}^{\prime }&=a x_{2}+x_{3} \\
x_{3}^{\prime }&=x_{2}+a x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.628 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{2}+x_{4} \\
x_{2}^{\prime }&=-x_{2}+x_{3} \\
x_{3}^{\prime }&=x_{2}+x_{3} \\
x_{4}^{\prime }&=x_{1}-x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.504 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{2} \\
x_{2}^{\prime }&=x_{3} \\
x_{3}^{\prime }&=-a x_{3}-b x_{2}-c x_{1} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
23.883 |
|
| \begin{align*}
x_{1}^{\prime }&=-x_{1} \\
x_{2}^{\prime }&=-2 x_{2} \\
x_{3}^{\prime }&=x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.524 |
|
| \begin{align*}
x^{\prime }&=-x+y+y^{2} \\
y^{\prime }&=-2 y-x^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.062 |
|
| \begin{align*}
x^{\prime }&=-x^{3} \\
y^{\prime }&=-y^{3} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.059 |
|
| \begin{align*}
2 x^{\prime }-3 x-2 y^{\prime }&=t \\
2 x^{\prime }+3 x+2 y^{\prime }+8 y&=2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.696 |
|
| \begin{align*}
y^{\prime }&=2 y-5 z \\
z^{\prime }&=4 y-2 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.432 |
|
| \begin{align*}
y^{\prime }&=-\sqrt {1-y^{2}} \\
x^{\prime }&=x+2 y \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.056 |
|
| \begin{align*}
x^{\prime }&=8 x-y \\
y^{\prime }&=4 x+12 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.319 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-4 x+4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.335 |
|
| \begin{align*}
x^{\prime }&=2 x-5 y \\
y^{\prime }&=2 x-4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.533 |
|
| \begin{align*}
x^{\prime }&=2 x+2 y-z \\
y^{\prime }&=y+z \\
z^{\prime }&=z-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.757 |
|
| \begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=9 x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.390 |
|
| \begin{align*}
x^{\prime }&=x+2 y \\
y^{\prime }&=4 x+3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.379 |
|
| \begin{align*}
x^{\prime }&=7 x-y+6 z \\
y^{\prime }&=-10 x+4 y-12 z \\
z^{\prime }&=-2 x+y-z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.720 |
|
| \begin{align*}
x+y^{\prime }&=\sin \left (t \right )+\cos \left (t \right ) \\
x^{\prime }+y&=\cos \left (t \right )-\sin \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.790 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-2 x+3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.350 |
|
| \begin{align*}
x^{\prime }&=3 x+2 y \\
y^{\prime }&=-5 x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.542 |
|
| \begin{align*}
x^{\prime }&=4 x-y \\
y^{\prime }&=x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.312 |
|
| \begin{align*}
x^{\prime }&=6 x-3 y \\
y^{\prime }&=2 x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.380 |
|
| \begin{align*}
2 x^{\prime }-3 y^{\prime }&=2 \,{\mathrm e}^{2 t} \\
x^{\prime }-2 y^{\prime }&=0 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.430 |
|
| \begin{align*}
y^{\prime }&=y-3 z \\
z^{\prime }&=2 y-4 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.347 |
|
| \begin{align*}
x^{\prime }&=4 x-y \\
y^{\prime }&=-4 x+4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.395 |
|
| \begin{align*}
x^{\prime }&=7 x-y+6 z \\
y^{\prime }&=-10 x+4 y-12 z \\
z^{\prime }&=-2 x+y-z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.659 |
|
| \begin{align*}
x^{\prime }&=3 x+y-z \\
y^{\prime }&=x+3 y-z \\
z^{\prime }&=3 x+3 y-z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.529 |
|
| \begin{align*}
x^{\prime }&=x-y-z \\
y^{\prime }&=y+3 z \\
z^{\prime }&=3 y+z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.566 |
|
| \begin{align*}
x^{\prime }&=y+{\mathrm e}^{t} \\
y^{\prime }&=-2 x+3 y+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.595 |
|
| \begin{align*}
x^{\prime }&=2 x-y-5 t \\
y^{\prime }&=3 x+6 y-4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.711 |
|
| \begin{align*}
x^{\prime }&=2 x+y+3 \,{\mathrm e}^{2 t} \\
y^{\prime }&=-4 x+2 y+{\mathrm e}^{2 t} t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.776 |
|
| \begin{align*}
x^{\prime }&=2 x-7 y \\
y^{\prime }&=3 x-8 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.386 |
|
| \begin{align*}
x^{\prime }&=2 x+4 y \\
y^{\prime }&=-2 x+6 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| \begin{align*}
x^{\prime }&=x+4 y-y^{2} \\
y^{\prime }&=6 x-y+2 x y \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.077 |
|
| \begin{align*}
x^{\prime }&=\sin \left (x\right )-4 y \\
y^{\prime }&=\sin \left (2 x\right )-5 y \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.076 |
|
| \begin{align*}
x^{\prime }&=8 x-y^{2} \\
y^{\prime }&=6 x^{2}-6 y \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.080 |
|
| \begin{align*}
x^{\prime }&=-x^{2}-y \\
y^{\prime }&=x \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.089 |
|
| \begin{align*}
x^{\prime }&=-x^{3}-y \\
y^{\prime }&=x \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.082 |
|
| \begin{align*}
x^{\prime }&=2 x y \\
y^{\prime }&=3 y^{2}-x^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.032 |
|
| \begin{align*}
x^{\prime }&=x^{2} \\
y^{\prime }&=2 y^{2}-x y \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.076 |
|
| \begin{align*}
x^{\prime }&=-x+y^{2} \\
y^{\prime }&=x^{2}-y \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
0.076 |
|
| \begin{align*}
x^{\prime }+x+y^{\prime }+y&=0 \\
x^{\prime }-y^{\prime }-y&=t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.546 |
|
| \begin{align*}
y^{\prime }-3 z&=5 \\
y-z^{\prime }-x&=3-2 t \\
z+x^{\prime }&=-1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.088 |
|
| \begin{align*}
x^{\prime \prime }-x+y&={\mathrm e}^{t} \\
x^{\prime }+x-y^{\prime }-y&=3 \,{\mathrm e}^{t} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.069 |
|
| \begin{align*}
x^{\prime }-2 x+y^{\prime }-2 y&=1 \\
y^{\prime }+z^{\prime }+z&=2 \\
3 x+z^{\prime }+z&=3 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
z \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.939 |
|
| \begin{align*}
x^{\prime }+3 x-y&=0 \\
y^{\prime }+y-3 x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.381 |
|
| \begin{align*}
x^{\prime }-x-2 y&=0 \\
y^{\prime }-2 y-3 x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.395 |
|
| \begin{align*}
y^{\prime }+y-x^{\prime \prime }+x&={\mathrm e}^{t} \\
y^{\prime }-x^{\prime }+x&={\mathrm e}^{-t} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.112 |
|
| \begin{align*}
x^{\prime }+y^{\prime }-y&=0 \\
y^{\prime }+2 y+z^{\prime }+2 z&=2 \\
x+z^{\prime }-z&=0 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
z \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.961 |
|
| \begin{align*}
x^{\prime \prime }&=1 \\
x^{\prime }+x+y^{\prime \prime }-9 y+z^{\prime }+z&=0 \\
5 x+z^{\prime \prime }-4 z&=2 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
z \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
z^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.044 |
|
| \begin{align*}
y^{\prime }-3 z&=5 \\
y-z^{\prime }-x&=3-2 t \\
z+x^{\prime }&=-1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.019 |
|
| \begin{align*}
y^{\prime }+y-x^{\prime }+x&=t \\
x^{\prime }+y^{\prime }+x-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.622 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=8 x-2 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (1\right ) &= 2 \\
y \left (1\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.506 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=8 x-2 y+{\mathrm e}^{t} \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.654 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-x+3 \\
\end{align*}
With initial conditions \begin{align*}
x \left (\pi \right ) &= 1 \\
y \left (\pi \right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.562 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-9 x+6 y+t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.624 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-2 y-5 z+3 \\
z^{\prime }&=y+2 z \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
z \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
0.945 |
|
| \begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=9 x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.415 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{2} \\
x_{2}^{\prime }&=6 x_{1} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (1\right ) &= 1 \\
x_{2} \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.611 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{2} \\
x_{2}^{\prime }&=6 x_{1}+4 \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.698 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{2} \\
x_{2}^{\prime }&=6 x_{1}+4 \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (1\right ) &= 0 \\
x_{2} \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.640 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{2} \\
x_{2}^{\prime }&=6 x_{1}+4 \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.657 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{2} \\
x_{2}^{\prime }&=6 x_{1}+9 \,{\mathrm e}^{-t} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.763 |
|
| \begin{align*}
x^{\prime }&=x+2 y \\
y^{\prime }&=4 x+3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.365 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{2} \\
x_{2}^{\prime }&=x_{3} \\
x_{3}^{\prime }&=6 t \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= 0 \\
x_{3} \left (0\right ) &= 12 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.674 |
|
| \begin{align*}
y^{\prime }&=x \\
x^{\prime }&=-y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.475 |
|
| \begin{align*}
u^{\prime }&=2 v-1 \\
v^{\prime }&=1+2 u \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.616 |
|
| \begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.552 |
|
| \begin{align*}
y^{\prime \prime }&=x \\
y^{\prime \prime }&=y \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.144 |
|
| \begin{align*}
y^{\prime \prime }&=x-2 \\
y^{\prime \prime }&=2+y \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.042 |
|
| \begin{align*}
y^{\prime }+6 y&=x^{\prime } \\
3 x-x^{\prime }&=2 y^{\prime } \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.526 |
|
| \begin{align*}
x^{\prime }+x+2 y&=1 \\
2 x+y^{\prime }-2 y&=t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.751 |
|
| \begin{align*}
x^{\prime }+y^{\prime }+2 x-y&=-\sin \left (t \right ) \\
x^{\prime }-3 x+y^{\prime }+2 y&=4 \cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.319 |
|
| \begin{align*}
x^{\prime \prime }+2 y^{\prime }+8 x&=32 t \\
y^{\prime \prime }+3 x^{\prime }-2 y&=60 \,{\mathrm e}^{-t} \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 6 \\
x^{\prime }\left (0\right ) &= 0 \\
y \left (0\right ) &= -24 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.065 |
|
| \begin{align*}
x^{\prime }-2 y^{\prime }&={\mathrm e}^{t} \\
x^{\prime }+y^{\prime }&=\sqrt {t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.431 |
|
| \begin{align*}
x^{\prime }+3 y^{\prime }&=x y \\
3 x^{\prime }-y^{\prime }&=\sin \left (t \right ) \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
0.115 |
|
| \begin{align*}
r^{\prime \prime }\left (t \right )&=r \left (t \right )+y \\
y^{\prime \prime }&=5 r \left (t \right )-3 y+t^{2} \\
\end{align*} |
✗ |
✗ |
✓ |
✓ |
0.133 |
|
| \begin{align*}
x y^{\prime }+y x^{\prime }&=t^{2} \\
2 x^{\prime \prime }-y^{\prime }&=5 t \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.070 |
|
| \begin{align*}
x^{\prime \prime }+y^{\prime }+x&=y+\sin \left (t \right ) \\
y^{\prime \prime }+x^{\prime }-y&=2 t^{2}-x \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
x^{\prime }\left (0\right ) &= -1 \\
y \left (0\right ) &= -{\frac {9}{2}} \\
y^{\prime }\left (0\right ) &= -{\frac {7}{2}} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.064 |
|
| \begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=x-y \\
z^{\prime }&=2 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= 0 \\
z \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.888 |
|
| \begin{align*}
x^{\prime }&=y z \\
y^{\prime }&=x z \\
z^{\prime }&=x y \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.138 |
|
| \begin{align*}
x^{\prime }&=x y \\
y^{\prime }&=1+y^{2} \\
z^{\prime }&=z \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.066 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+t z^{\prime }+z&=t \\
y^{\prime } t +z&=\ln \left (t \right ) \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
0.124 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=z \\
z^{\prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.618 |
|
| \begin{align*}
x^{\prime }&=y+z \\
y^{\prime }&=x+z \\
z^{\prime }&=x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.625 |
|
| \begin{align*}
x^{\prime }+6 x+3 y^{\prime }+2 y&=0 \\
x^{\prime }+5 x+2 y^{\prime }+3 y&=0 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.474 |
|
| \begin{align*}
x^{\prime }-x+2 y^{\prime }+7 y&=0 \\
2 x^{\prime }+y^{\prime }+x+5 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.362 |
|
| \begin{align*}
x^{\prime }+5 x+3 y^{\prime }-11 y&=0 \\
x^{\prime }+3 x+y^{\prime }-7 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.511 |
|
| \begin{align*}
x^{\prime }-2 x+4 y&=0 \\
3 x+2 y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.506 |
|
| \begin{align*}
x^{\prime }+3 x+2 y&=0 \\
3 x+y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.700 |
|
| \begin{align*}
x^{\prime }+4 x+3 y^{\prime }+4 y&=0 \\
x^{\prime }+2 x+2 y^{\prime }+2 y&=0 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= -1 \\
y \left (0\right ) &= 6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.378 |
|
| \begin{align*}
x^{\prime }+x+2 y^{\prime }+3 y&=0 \\
x^{\prime }-2 x+5 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.655 |
|
| \begin{align*}
x^{\prime }-x-y&=0 \\
5 x+y^{\prime }-3 y&=0 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.655 |
|
| \begin{align*}
2 x-y^{\prime }-5 y&=0 \\
x^{\prime }+x+2 y&=0 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= -10 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.428 |
|
| \begin{align*}
2 x^{\prime }-6 x+3 y^{\prime }-2 y&=0 \\
7 x^{\prime }+4 x+7 y^{\prime }+20 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.516 |
|
| \begin{align*}
x^{\prime }+x+2 y&=8 \\
2 x+y^{\prime }-2 y&=2 \,{\mathrm e}^{-t}-8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.770 |
|
| \begin{align*}
x^{\prime }+2 y&=4 \,{\mathrm e}^{2 t} \\
x+y^{\prime }-y&=2 \,{\mathrm e}^{2 t} \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 7 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.733 |
|
| \begin{align*}
x^{\prime }-x+2 y^{\prime }+7 y&=3 t -15 \\
2 x^{\prime }+y^{\prime }+x+5 y&=9 t -7 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= -3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.613 |
|
| \begin{align*}
x^{\prime }+3 x-y^{\prime }-y&=0 \\
2 x^{\prime }-9 x+y^{\prime }+4 y&=15 \,{\mathrm e}^{-3 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.776 |
|
| \begin{align*}
3 x-y^{\prime }-2 y&=8 t \\
x^{\prime }-2 x+y&=16 \,{\mathrm e}^{-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.912 |
|
| \begin{align*}
2 x^{\prime }-x-y^{\prime }+y&=4 t \,{\mathrm e}^{-t}-3 \,{\mathrm e}^{-t} \\
x^{\prime }+4 x-2 y^{\prime }-4 y&=2 t \,{\mathrm e}^{-t}-6 \,{\mathrm e}^{-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.728 |
|
| \begin{align*}
2 x^{\prime }-x+7 y^{\prime }+3 y&=90 \sin \left (2 t \right ) \\
x^{\prime }-5 x+8 y^{\prime }-3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.210 |
|
| \begin{align*}
x^{\prime \prime }&=y+4 \,{\mathrm e}^{-2 t} \\
y^{\prime \prime }&=x-{\mathrm e}^{-2 t} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.126 |
|
| \begin{align*}
x^{\prime }-5 x+y^{\prime }+2 z&=24 \,{\mathrm e}^{-t} \\
x^{\prime }-x-y&=0 \\
5 y^{\prime }-11 y+2 z^{\prime }-2 z&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.286 |
|
| \begin{align*}
x^{\prime }+3 x-2 y&={\mathrm e}^{-t} \\
y^{\prime }-x+4 y&=\sin \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.968 |
|
| \begin{align*}
x^{\prime }-x+2 y-z&=t^{2} \\
y^{\prime }+3 x-y+4 z&={\mathrm e}^{t} \\
z^{\prime }-2 x+y-z&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
56.348 |
|
| \begin{align*}
z+x^{\prime }&=x \\
y^{\prime }-2 x&=y+3 t \\
z^{\prime }+4 y&=z-\cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.828 |
|
| \begin{align*}
x^{\prime }+5 x-4 y&=0 \\
y^{\prime }-x+2 y&=0 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 3 \\
y \left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.480 |
|
| \begin{align*}
x^{\prime }+x-5 y&=0 \\
y^{\prime }+4 x+5 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.609 |
|
| \begin{align*}
x^{\prime }-2 x+3 y&=0 \\
-2 x+y^{\prime }+3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.458 |
|
| \begin{align*}
x^{\prime }+3 x-6 y&=0 \\
y^{\prime }&=x-3 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.574 |
|
| \begin{align*}
x^{\prime }&=x+8 y \\
y^{\prime }&=-2 x-7 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.390 |
|
| \begin{align*}
x^{\prime }&=-12 x-7 y \\
y^{\prime }&=19 x+11 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.469 |
|
| \begin{align*}
x^{\prime }-y&=t \\
x+y^{\prime }&=t^{2} \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.726 |
|
| \begin{align*}
x^{\prime }+3 x+4 y&=8 \,{\mathrm e}^{t} \\
-x+y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.676 |
|
| \begin{align*}
x^{\prime }-2 x+y&={\mathrm e}^{-t} \\
y^{\prime }-3 x+2 y&=t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.863 |
|
| \begin{align*}
x^{\prime }+2 x-y&=100 \sin \left (t \right ) \\
y^{\prime }-4 x-y&=36 t \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= -8 \\
y \left (0\right ) &= -21 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.932 |
|
| \begin{align*}
x^{\prime }-3 x-6 y&=9-9 t \\
y^{\prime }+3 x+3 y&=9 t \,{\mathrm e}^{-3 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.943 |
|
| \begin{align*}
x^{\prime }&=2 x-3 y+t \,{\mathrm e}^{-t} \\
y^{\prime }&=2 x-3 y+{\mathrm e}^{-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.695 |
|
| \begin{align*}
x^{\prime }+4 x+2 y-z&=12 \,{\mathrm e}^{t} \\
y^{\prime }-2 x-5 y+3 z&=0 \\
z^{\prime }+4 x+z&=30 \,{\mathrm e}^{-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.424 |
|
| \begin{align*}
x^{\prime \prime }+y^{\prime }+6 x&=0 \\
y^{\prime \prime }-x^{\prime }+6 y&=0 \\
\end{align*}
With initial conditions \begin{align*}
x^{\prime }\left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.230 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}+x_{2} \\
x_{2}^{\prime }&=-3 x_{1}+6 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.674 |
|
| \begin{align*}
x_{1}^{\prime }&=-3 x_{1}+4 x_{2} \\
x_{2}^{\prime }&=-2 x_{1}+3 x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= -1 \\
x_{2} \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.710 |
|
| \begin{align*}
x_{1}^{\prime }&=2 \sin \left (t \right ) x_{1}+\ln \left (t \right ) x_{2} \\
x_{2}^{\prime }&=\frac {x_{1}}{-2+t}+\frac {{\mathrm e}^{t} x_{2}}{1+t} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (3\right ) &= 0 \\
x_{2} \left (3\right ) &= 0 \\
\end{align*} |
✗ |
✓ |
✗ |
✓ |
0.073 |
|
| \begin{align*}
x^{\prime }&=5 x-6 y+1 \\
y^{\prime }&=6 x-7 y+1 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.800 |
|
| \begin{align*}
x^{\prime }&=5 x-6 y \\
y^{\prime }&=6 x-7 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.443 |
|
| \begin{align*}
x^{\prime }&=-2 x+y \\
y^{\prime }&=x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.560 |
|
| \begin{align*}
x^{\prime }&=3 x-2 y \\
y^{\prime }&=2 x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.642 |
|
| \begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.697 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-x \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.607 |
|
| \begin{align*}
x^{\prime }&=-x+y \\
y^{\prime }&=-x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.662 |
|
| \begin{align*}
x^{\prime }&=y-z \\
y^{\prime }&=z-x \\
z^{\prime }&=x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.202 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}+\left (1-t \right ) x_{2} \\
x_{2}^{\prime }&=\frac {x_{1}}{t}-x_{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.125 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{2}-x_{3}+x_{4} \\
x_{2}^{\prime }&=-x_{2}+x_{4} \\
x_{3}^{\prime }&=x_{3}-x_{4} \\
x_{4}^{\prime }&=2 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.334 |
|
| \begin{align*}
x_{1}^{\prime }&=5 x_{1}+2 x_{2}+2 x_{3} \\
x_{2}^{\prime }&=2 x_{1}+2 x_{2}-4 x_{3} \\
x_{3}^{\prime }&=2 x_{1}-4 x_{2}+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 ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.943 |
|
| \begin{align*}
x_{1}^{\prime }&=-10 x_{1}+x_{2}+7 x_{3} \\
x_{2}^{\prime }&=-9 x_{1}+4 x_{2}+5 x_{3} \\
x_{3}^{\prime }&=-17 x_{1}+x_{2}+12 x_{3} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 5 \\
x_{2} \left (0\right ) &= 2 \\
x_{3} \left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.170 |
|
| \begin{align*}
x_{1}^{\prime }&=4 x_{1}-x_{2} \\
x_{2}^{\prime }&=2 x_{1}+x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.636 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}-2 x_{2} \\
x_{2}^{\prime }&=x_{1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.591 |
|
| \begin{align*}
x_{1}^{\prime }&=4 x_{1}-x_{2}+3 \,{\mathrm e}^{2 t} \\
x_{2}^{\prime }&=2 x_{1}+x_{2}+2 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.005 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}-2 x_{2}+1 \\
x_{2}^{\prime }&=x_{1}+t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.921 |
|
| \begin{align*}
x^{\prime }&=5 x-6 y+1 \\
y^{\prime }&=6 x-7 y+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.726 |
|
| \begin{align*}
t x^{\prime }&=3 x-2 y \\
y^{\prime } t&=x+y-t^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.119 |
|
| \begin{align*}
x^{\prime }&=3 x-2 y+2 t^{2} \\
y^{\prime }&=5 x+y-1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.549 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}+2 x_{2} \\
x_{2}^{\prime }&=4 x_{1}+x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.743 |
|
| \begin{align*}
N_{1}^{\prime }&=4 N_{1}-6 N_{2} \\
N_{2}^{\prime }&=8 N_{1}-10 N_{2} \\
\end{align*}
With initial conditions \begin{align*}
N_{1} \left (0\right ) &= 100000 \\
N_{2} \left (0\right ) &= 1000 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.725 |
|
| \begin{align*}
x_{1}^{\prime }&=4 x_{1}-x_{2} \\
x_{2}^{\prime }&=2 x_{1}+x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.551 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}-2 x_{2} \\
x_{2}^{\prime }&=x_{1} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= -1 \\
x_{2} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.540 |
|
| \begin{align*}
x_{1}^{\prime }&=4 x_{1}-x_{2}+3 \,{\mathrm e}^{2 t} \\
x_{2}^{\prime }&=2 x_{1}+x_{2}+2 t \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= -{\frac {5}{18}} \\
x_{2} \left (0\right ) &= {\frac {47}{9}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.834 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}-2 x_{2}+1 \\
x_{2}^{\prime }&=x_{1}+t \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= -{\frac {1}{2}} \\
x_{2} \left (0\right ) &= -{\frac {1}{4}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.833 |
|
| \begin{align*}
x^{\prime }&=5 x-6 y+1 \\
y^{\prime }&=6 x-7 y+1 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.674 |
|
| \begin{align*}
t x^{\prime }&=3 x-2 y \\
y^{\prime } t&=x+y-t^{2} \\
\end{align*}
With initial conditions \begin{align*}
x \left (1\right ) &= 1 \\
y \left (1\right ) &= {\frac {1}{2}} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.069 |
|
| \begin{align*}
x^{\prime }&=3 x-2 y+2 t^{2} \\
y^{\prime }&=5 x+y-1 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= {\frac {534}{2197}} \\
y \left (0\right ) &= {\frac {567}{2197}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.102 |
|
| \begin{align*}
x^{\prime }&=x+2 y \\
y^{\prime }&=4 x-y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.618 |
|
| \begin{align*}
x^{\prime }&=-x \\
y^{\prime }&=-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.329 |
|
| \begin{align*}
x^{\prime }&=-2 x+y \\
y^{\prime }&=x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.564 |
|
| \begin{align*}
x^{\prime }&=3 x-2 y \\
y^{\prime }&=2 x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.645 |
|
| \begin{align*}
x^{\prime }&=-x \\
y^{\prime }&=-x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.468 |
|
| \begin{align*}
x^{\prime }&=-x+y \\
y^{\prime }&=-x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.626 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.589 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.484 |
|
| \begin{align*}
x^{\prime }&=2 x-y \\
y^{\prime }&=9 x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.697 |
|
| \begin{align*}
x^{\prime }&=2 x+y \\
y^{\prime }&=-3 x+6 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.621 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=z \\
z^{\prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.375 |
|
| \begin{align*}
c_{1}^{\prime }&=-\frac {k c_{1}}{V_{1}}+\frac {k c_{2}}{V_{1}} \\
c_{2}^{\prime }&=\frac {k c_{1}}{V_{2}}-\frac {k c_{2}}{V_{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.883 |
|
| \begin{align*}
x^{\prime }&=a \left (b -x\right )-c f y \\
y^{\prime }&=d \left (x-y\right )-c f y-a y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= b \\
y \left (0\right ) &= \frac {d b}{a +d} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.524 |
|
| \begin{align*}
x^{\prime }&=4 x+2 y \\
y^{\prime }&=-3 x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.632 |
|
| \begin{align*}
x^{\prime }&=4 x-2 y \\
y^{\prime }&=x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.576 |
|
| \begin{align*}
x^{\prime }&=3 x-2 y \\
y^{\prime }&=2 x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.533 |
|
| \begin{align*}
x^{\prime }&=-4 x+y \\
y^{\prime }&=-x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.493 |
|
| \begin{align*}
x^{\prime }&=3 x-2 y \\
y^{\prime }&=17 x-7 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.806 |
|
| \begin{align*}
x^{\prime }&=3 x-5 y \\
y^{\prime }&=4 x-5 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.820 |
|
| \begin{align*}
x^{\prime }&=4 x-2 y \\
y^{\prime }&=x+y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.578 |
|
| \begin{align*}
x^{\prime }&=3 x-2 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*} |
✓ |
✓ |
✓ |
✓ |
0.450 |
|
| \begin{align*}
x^{\prime }&=3 x-2 y \\
y^{\prime }&=12 x-7 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.544 |
|
| \begin{align*}
x^{\prime }&=3 x-5 y \\
y^{\prime }&=4 x-5 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (\pi \right ) &= 1 \\
y \left (\pi \right ) &= {\frac {4}{5}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.646 |
|
| \begin{align*}
x^{\prime }&=2 x \\
y^{\prime }&=-3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.396 |
|
| \begin{align*}
x^{\prime }&=4 y \\
y^{\prime }&=-x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.556 |
|
| \begin{align*}
x^{\prime }&=-y \\
y^{\prime }&=-3 x+4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| \begin{align*}
x^{\prime }&=-y \\
y^{\prime }&=x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.483 |
|
| \begin{align*}
x^{\prime }&=4 x+3 y \\
y^{\prime }&=-x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.538 |
|
| \begin{align*}
x^{\prime }&=-2 x+y \\
y^{\prime }&=-x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.458 |
|
| \begin{align*}
x^{\prime }&=3 x+2 y+2 z \\
y^{\prime }&=x+4 y+z \\
z^{\prime }&=-2 x-4 y-z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.913 |
|
| \begin{align*}
x^{\prime }&=3 x-y \\
y^{\prime }&=-x+2 y-z \\
z^{\prime }&=-y+3 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.875 |
|
| \begin{align*}
x^{\prime }&=2 x+y \\
y^{\prime }&=z-x \\
z^{\prime }&=x+3 y+z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.875 |
|
| \begin{align*}
x^{\prime }&=7 x+4 y-4 z \\
y^{\prime }&=4 x-8 y-z \\
z^{\prime }&=-4 x-y-8 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.823 |
|
| \begin{align*}
x^{\prime }&=x+2 y+z-w \\
y^{\prime }&=-y+2 z+2 w \\
z^{\prime }&=2 y+2 z+2 w \\
w^{\prime }&=-3 y-6 z-6 w \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.319 |
|
| \begin{align*}
x^{\prime }&=3 x+y \\
y^{\prime }&=x+3 y \\
z^{\prime }&=2 z+w+h \\
w^{\prime }&=z+2 w+h \\
h^{\prime }&=z+w+2 h \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.307 |
|
| \begin{align*}
x^{\prime }&=-10 x+y+7 z \\
y^{\prime }&=-9 x+4 y+5 z \\
z^{\prime }&=-17 x+y+12 z \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.937 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=z \\
z^{\prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.078 |
|
| \begin{align*}
x^{\prime }&=3 x+2 y+2 z \\
y^{\prime }&=x+4 y+z \\
z^{\prime }&=-2 x-4 y-z \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
z \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.819 |
|
| \begin{align*}
x^{\prime }&=3 x-y \\
y^{\prime }&=-x+2 y-z \\
z^{\prime }&=-y+3 z \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
z \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.769 |
|
| \begin{align*}
x^{\prime }&=2 x+y \\
y^{\prime }&=z-x \\
z^{\prime }&=x+3 y+z \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 1 \\
z \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.731 |
|
| \begin{align*}
x^{\prime }&=7 x+4 y-4 z \\
y^{\prime }&=4 x-8 y-z \\
z^{\prime }&=-4 x-y-8 z \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 3 \\
y \left (0\right ) &= 5 \\
z \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.770 |
|
| \begin{align*}
x^{\prime }&=-10 x+y+7 z \\
y^{\prime }&=-9 x+4 y+5 z \\
z^{\prime }&=-17 x+y+12 z \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 6 \\
y \left (0\right ) &= 1 \\
z \left (0\right ) &= 10 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.853 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=z \\
z^{\prime }&=x \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 1 \\
z \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.911 |
|
| \begin{align*}
x^{\prime }&=-2 x+y \\
y^{\prime }&=x-2 y \\
z^{\prime }&=x+y-5 z \\
u^{\prime }&=5 z \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
z \left (0\right ) &= 0 \\
u \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.187 |
|
| \begin{align*}
x^{\prime }&=x \\
y^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.362 |
|
| \begin{align*}
x^{\prime }&=-x \\
y^{\prime }&=2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.428 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.461 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.521 |
|
| \begin{align*}
x^{\prime }&=x \\
y^{\prime }&=2 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.428 |
|
| \begin{align*}
x^{\prime }&=x \\
y^{\prime }&=-2 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.351 |
|
| \begin{align*}
x^{\prime }&=x \\
y^{\prime }&=x+y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.334 |
|
| \begin{align*}
x^{\prime }&=-x \\
y^{\prime }&=-x-y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.336 |
|
| \begin{align*}
x^{\prime }&=-x+y \\
y^{\prime }&=-x-y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= -1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.509 |
|
| \begin{align*}
x^{\prime }&=-y \\
y^{\prime }&=x \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.542 |
|
| \begin{align*}
x^{\prime }&=y^{2}-x^{2} \\
y^{\prime }&=2 x y \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.210 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-\sin \left (x\right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.063 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-4 \sin \left (x\right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.192 |
|
| \begin{align*}
x^{\prime }&=x-x y \\
y^{\prime }&=-y+x y \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.066 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{2} \\
x_{2}^{\prime }&=-x_{1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.532 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{2} \\
x_{2}^{\prime }&=\sin \left (x_{1}\right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.233 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{2} \\
x_{2}^{\prime }&=x_{1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.411 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{2} \\
x_{2}^{\prime }&=x_{1}-x_{1}^{3} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.196 |
|
| \begin{align*}
x^{\prime }&=a x+b y \\
y^{\prime }&=c x+d y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.335 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.525 |
|
| \begin{align*}
x^{\prime }&=-y \\
y^{\prime }&=-x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.493 |
|
| \begin{align*}
x^{\prime }&=-x+y \\
y^{\prime }&=2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.484 |
|
| \begin{align*}
x^{\prime }&=-x+y \\
y^{\prime }&=-x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.563 |
|
| \begin{align*}
x^{\prime }&=x-y \\
y^{\prime }&=x+3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.444 |
|
| \begin{align*}
x^{\prime }&=x-y \\
y^{\prime }&=5 x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.645 |
|
| \begin{align*}
x^{\prime }&=-3 x+4 y \\
y^{\prime }&=-2 x+3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.529 |
|
| \begin{align*}
x^{\prime }&=5 x-6 y \\
y^{\prime }&=6 x-7 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.454 |
|
| \begin{align*}
x^{\prime }&=-3 x+5 y \\
y^{\prime }&=-x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.741 |
|
| \begin{align*}
x^{\prime }&=3 x-2 y \\
y^{\prime }&=4 x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.763 |
|
| \begin{align*}
x^{\prime }&=4 x-6 y \\
y^{\prime }&=8 x-10 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| \begin{align*}
x^{\prime }&=5 x-6 y+1 \\
y^{\prime }&=6 x-7 y+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.675 |
|
| \begin{align*}
x^{\prime }&=5 x-6 y+x y \\
y^{\prime }&=6 x-7 y-x y \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.194 |
|
| \begin{align*}
x^{\prime }&=3 x-2 y+\left (x^{2}+y^{2}\right )^{2} \\
y^{\prime }&=4 x-y+\left (x^{2}-y^{2}\right )^{5} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.082 |
|
| \begin{align*}
x^{\prime }&=y+x^{2}-x y \\
y^{\prime }&=-2 x+3 y+y^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.226 |
|
| \begin{align*}
x^{\prime }&=x-x y \\
y^{\prime }&=-y+x y \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.056 |
|
| \begin{align*}
x^{\prime }&=-x-x^{2}+y^{2} \\
y^{\prime }&=-y+2 x y \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
0.194 |
|
| \begin{align*}
x^{\prime }&=x \\
y^{\prime }&=3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.336 |
|
| \begin{align*}
x^{\prime }&=-x \\
y^{\prime }&=-3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.437 |
|
| \begin{align*}
x^{\prime }&=x \\
y^{\prime }&=-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.392 |
|
| \begin{align*}
x^{\prime }&=-x \\
y^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.431 |
|
| \begin{align*}
x^{\prime }&=2 x \\
y^{\prime }&=2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.348 |
|
| \begin{align*}
x^{\prime }&=-x \\
y^{\prime }&=-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.345 |
|
| \begin{align*}
x^{\prime }&=-x \\
y^{\prime }&=x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.384 |
|
| \begin{align*}
x^{\prime }&=x \\
y^{\prime }&=-x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.388 |
|
| \begin{align*}
x^{\prime }&=-2 x+y \\
y^{\prime }&=-x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.585 |
|
| \begin{align*}
x^{\prime }&=-y \\
y^{\prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.526 |
|
| \begin{align*}
x^{\prime }&=-x+y \\
y^{\prime }&=-x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.569 |
|
| \begin{align*}
x^{\prime }&=-x+y \\
y^{\prime }&=-x-3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.450 |
|
| \begin{align*}
x^{\prime }&=4 x+6 y \\
y^{\prime }&=-7 x-9 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.571 |
|
| \begin{align*}
x^{\prime }&=2 x-y \\
y^{\prime }&=-x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.520 |
|
| \begin{align*}
x^{\prime }&=-2 x+y-x^{2}+2 y^{2} \\
y^{\prime }&=3 x+2 y+x^{2} y^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.191 |
|
| \begin{align*}
x^{\prime }&=-x+x^{2} \\
y^{\prime }&=-3 y+x y \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.059 |
|
| \begin{align*}
x^{\prime }&=-x+x y \\
y^{\prime }&=y+\left (x^{2}+y^{2}\right )^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.194 |
|
| \begin{align*}
x^{\prime }&=2 x+y^{2} \\
y^{\prime }&=3 y-x^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.059 |
|
| \begin{align*}
x^{\prime }&=x-x y \\
y^{\prime }&=-y+x y \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.191 |
|
| \begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=x-3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.684 |
|
| \begin{align*}
x^{\prime }&=3 x-2 y \\
y^{\prime }&=2 x+3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.588 |
|
| \begin{align*}
x^{\prime }&=-2 x-3 y \\
y^{\prime }&=-3 x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.707 |
|
| \begin{align*}
x^{\prime }&=-3 x+2 y \\
y^{\prime }&=-2 x-3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.612 |
|
| \begin{align*}
x^{\prime }&=x \\
y^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.345 |
|
| \begin{align*}
x^{\prime }&=-x \\
y^{\prime }&=-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.345 |
|
| \begin{align*}
x^{\prime }&=-x \\
y^{\prime }&=-x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.389 |
|
| \begin{align*}
x^{\prime }&=-3 x+2 y \\
y^{\prime }&=-2 x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.627 |
|
| \begin{align*}
y^{\prime }&=-2 \\
z^{\prime }&=x \,{\mathrm e}^{2 x +y} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.241 |
|
| \begin{align*}
y^{\prime }+y&={\mathrm e}^{x} \\
z^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.579 |
|
| \begin{align*}
y^{\prime }&=z \\
z^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.520 |
|
| \begin{align*}
y y^{\prime }&=-x \\
y z^{\prime }&=2 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.233 |
|
| \begin{align*}
y^{\prime }+2 z&=y \\
z^{\prime }+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.747 |
|
| \begin{align*}
y^{\prime }&=x +2 z \\
z^{\prime }&=3 x +y-z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.865 |
|
| \begin{align*}
y^{\prime }&=x^{2}+6 y+4 z \\
z^{\prime }&=y+3 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.895 |
|
| \begin{align*}
y^{\prime }&=y+z+x \\
z^{\prime }&=1-y-z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.628 |
|
| \begin{align*}
y^{\prime }&=f \left (x \right )+a y+b z \\
z^{\prime }&=g \left (x \right )+c y+d z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.309 |
|
| \begin{align*}
y^{\prime } x&=y \\
z^{\prime }&=3 y-x \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.048 |
|
| \begin{align*}
y^{\prime }&=z \\
z^{\prime }&=w \\
w^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.084 |
|
| \begin{align*}
x^{\prime }-x-y^{\prime }&=0 \\
y^{\prime }+3 x-2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.729 |
|
| \begin{align*}
x-y+z^{\prime }&=0 \\
x^{\prime }-y&=1 \\
y^{\prime }-y+z&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.450 |
|
| \begin{align*}
v^{\prime }-2 v+2 w^{\prime }&=2-4 \,{\mathrm e}^{2 x} \\
2 v^{\prime }-3 v+3 w^{\prime }-w&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.642 |
|
| \begin{align*}
y^{\prime }-2 y-v^{\prime }-v&=6 \,{\mathrm e}^{3 x} \\
2 y^{\prime }-3 y+v^{\prime }-3 v&=6 \,{\mathrm e}^{3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.551 |
|
| \begin{align*}
y^{\prime }+y-v^{\prime }-v&=0 \\
y^{\prime }+v^{\prime }-v&={\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| \begin{align*}
2 v^{\prime }+2 v+w^{\prime }-w&=3 x \\
v^{\prime }+v+w^{\prime }+w&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.504 |
|
| \begin{align*}
3 v^{\prime }+2 v+w^{\prime }-6 w&=5 \,{\mathrm e}^{x} \\
4 v^{\prime }+2 v+w^{\prime }-8 w&=5 \,{\mathrm e}^{x}+2 x -3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.763 |
|
| \begin{align*}
2 y^{\prime }+2 y+w^{\prime }-w&=x +1 \\
y^{\prime }+3 y+w^{\prime }+w&=4 x +14 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.046 |
|
| \begin{align*}
y_{1}^{\prime }-6 y_{1}&=-4 y_{2} \\
y_{2}^{\prime }&=2 y_{1} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 2 \\
y_{2} \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.483 |
|
| \begin{align*}
y_{1}^{\prime }-3 y_{1}&=-4 y_{2} \\
y_{2}^{\prime }+y_{2}&=y_{1} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.365 |
|
| \begin{align*}
y_{1}^{\prime }&=2 y_{2} \\
y_{2}^{\prime }&=-2 y_{1} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.402 |
|
| \begin{align*}
y_{1}^{\prime }-2 y_{1}&=2 y_{2} \\
y_{2}^{\prime \prime }+2 y_{2}^{\prime }+y_{2}&=-2 y_{1} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 3 \\
y_{2} \left (0\right ) &= 0 \\
y_{2}^{\prime }\left (0\right ) &= 3 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.047 |
|
| \begin{align*}
y_{1}^{\prime }+4 y_{1}&=10 y_{2} \\
y_{2}^{\prime \prime }-6 y_{2}^{\prime }+23 y_{2}&=9 y_{1} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 0 \\
y_{2} \left (0\right ) &= 2 \\
y_{2}^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.026 |
|
| \begin{align*}
y_{1}^{\prime }-2 y_{1}&=-2 y_{2} \\
y_{2}^{\prime \prime }+y_{2}^{\prime }+6 y_{2}&=4 y_{1} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 5 \\
y_{2}^{\prime }\left (0\right ) &= 4 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.063 |
|
| \begin{align*}
y_{1}^{\prime \prime }+2 y_{1}^{\prime }+6 y_{1}&=5 y_{2} \\
y_{2}^{\prime \prime }-2 y_{2}^{\prime }+6 y_{2}&=9 y_{1} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 0 \\
y_{1}^{\prime }\left (0\right ) &= 0 \\
y_{2} \left (0\right ) &= 6 \\
y_{2}^{\prime }\left (0\right ) &= 6 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.029 |
|
| \begin{align*}
y_{1}^{\prime \prime }+2 y_{1}&=-3 y_{2} \\
y_{2}^{\prime \prime }+2 y_{2}^{\prime }-9 y_{2}&=6 y_{1} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= -1 \\
y_{1}^{\prime }\left (0\right ) &= -4 \\
y_{2} \left (0\right ) &= 1 \\
y_{2}^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.085 |
|
| \begin{align*}
y_{1}^{\prime }&=y_{2} \\
y_{2}^{\prime }&=y_{1} y_{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.114 |
|
| \begin{align*}
y_{1}^{\prime }&=y_{1}+y_{2}+t^{2} \\
y_{2}^{\prime }&=-y_{1}+y_{2}+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.699 |
|
| \begin{align*}
y_{1}^{\prime }&=\sin \left (t \right ) y_{1} \\
y_{2}^{\prime }&=y_{1}+\cos \left (t \right ) y_{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.075 |
|
| \begin{align*}
y_{1}^{\prime }&=t \sin \left (y_{1}\right )-y_{2} \\
y_{2}^{\prime }&=y_{1}+t \cos \left (y_{2}\right ) \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
0.119 |
|
| \begin{align*}
y_{1}^{\prime }&=y_{1} \\
y_{2}^{\prime }&=2 y_{1}+y_{4} \\
y_{3}^{\prime }&=y_{4} \\
y_{4}^{\prime }&=y_{2}+2 y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.152 |
|
| \begin{align*}
y_{1}^{\prime }&=\frac {y_{1}}{2}-y_{2}+5 \\
y_{2}^{\prime }&=-y_{1}+\frac {y_{2}}{2}-5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.625 |
|
| \begin{align*}
y_{1}^{\prime }&=5 y_{1}-2 y_{2} \\
y_{2}^{\prime }&=4 y_{1}-y_{2} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 0 \\
y_{2} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.447 |
|
| \begin{align*}
y_{1}^{\prime }&=3 y_{1}-y_{2} \\
y_{2}^{\prime }&=4 y_{1}-y_{2} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.366 |
|
| \begin{align*}
y_{1}^{\prime }&=2 y_{1}-y_{2} \\
y_{2}^{\prime }&=3 y_{1}-2 y_{2} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.405 |
|
| \begin{align*}
y_{1}^{\prime }&=y_{2}+t \\
y_{2}^{\prime }&=-y_{1}-t \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.595 |
|
| \begin{align*}
y_{1}^{\prime }&=-y_{1} \\
y_{2}^{\prime }&=3 y_{2} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.380 |
|
| \begin{align*}
y_{1}^{\prime }&=y_{2} \\
y_{2}^{\prime }&=-2 y_{1} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.483 |
|
| \begin{align*}
y_{1}^{\prime }&=2 y_{1}+y_{2} \\
y_{2}^{\prime }&=2 y_{2} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= -1 \\
y_{2} \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.359 |
|
| \begin{align*}
y_{1}^{\prime }&=-y_{1}+2 y_{2} \\
y_{2}^{\prime }&=-2 y_{1}-y_{2} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.415 |
|
| \begin{align*}
y_{1}^{\prime }&=2 y_{1}-y_{2} \\
y_{2}^{\prime }&=3 y_{1}-2 y_{2} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.418 |
|
| \begin{align*}
y_{1}^{\prime }&=2 y_{1}-5 y_{2} \\
y_{2}^{\prime }&=y_{1}-2 y_{2} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.440 |
|
| \begin{align*}
y_{1}^{\prime }&=3 y_{1}-4 y_{2} \\
y_{2}^{\prime }&=y_{1}-y_{2} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.381 |
|
| \begin{align*}
y_{1}^{\prime }&=-y_{1}+3 y_{3} \\
y_{2}^{\prime }&=2 y_{2} \\
y_{3}^{\prime }&=y_{3} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 1 \\
y_{3} \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.563 |
|
| \begin{align*}
y_{1}^{\prime }&=4 y_{2} \\
y_{2}^{\prime }&=-y_{1} \\
y_{3}^{\prime }&=y_{1}+4 y_{2}-y_{3} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 2 \\
y_{2} \left (0\right ) &= 1 \\
y_{3} \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.749 |
|
| \begin{align*}
y_{1}^{\prime }&=2 y_{1}-y_{2}+{\mathrm e}^{t} \\
y_{2}^{\prime }&=3 y_{1}-2 y_{2}+{\mathrm e}^{t} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.661 |
|
| \begin{align*}
y_{1}^{\prime }&=-y_{1}+2 y_{2}+5 \\
y_{2}^{\prime }&=-2 y_{1}-y_{2} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.647 |
|
| \begin{align*}
y_{1}^{\prime }&=2 y_{1}-5 y_{2}+2 \cos \left (t \right ) \\
y_{2}^{\prime }&=y_{1}-2 y_{2}+\cos \left (t \right ) \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.869 |
|
| \begin{align*}
y_{1}^{\prime }&=-y_{1}-4 y_{2}+4 \\
y_{2}^{\prime }&=y_{1}-y_{2}+1 \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 2 \\
y_{2} \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.688 |
|
| \begin{align*}
y_{1}^{\prime }&=2 y_{1}+y_{2}+{\mathrm e}^{t} \\
y_{2}^{\prime }&=y_{1}+2 y_{2}-{\mathrm e}^{t} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.600 |
|
| \begin{align*}
y_{1}^{\prime }&=5 y_{1}+2 y_{2}+t \\
y_{2}^{\prime }&=-8 y_{1}-3 y_{2}-2 t \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 0 \\
y_{2} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.594 |
|
| \begin{align*}
y_{1}^{\prime }&=-2 y_{1}+2 y_{2}+y_{3}+{\mathrm e}^{-2 t} \\
y_{2}^{\prime }&=-y_{2} \\
y_{3}^{\prime }&=2 y_{1}-2 y_{2}-y_{3}-{\mathrm e}^{-2 t} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 2 \\
y_{2} \left (0\right ) &= 1 \\
y_{3} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.862 |
|
| \begin{align*}
y_{1}^{\prime }&=y_{2}+y_{3}+{\mathrm e}^{2 t} \\
y_{2}^{\prime }&=y_{1}+y_{2}-y_{3}+{\mathrm e}^{2 t} \\
y_{3}^{\prime }&=-2 y_{1}+y_{2}+3 y_{3}-{\mathrm e}^{2 t} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 0 \\
y_{2} \left (0\right ) &= 0 \\
y_{3} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.889 |
|
| \begin{align*}
y_{1}^{\prime }&=-2 y_{1}+y_{2} \\
y_{2}^{\prime }&=-4 y_{1}+3 y_{2} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.470 |
|
| \begin{align*}
y_{1}^{\prime }&=5 y_{1}-3 y_{2} \\
y_{2}^{\prime }&=2 y_{1} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 2 \\
y_{2} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.413 |
|
| \begin{align*}
y_{1}^{\prime }&=y_{2} t \\
y_{2}^{\prime }&=-y_{1} t \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 0 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.041 |
|
| \begin{align*}
y_{1}^{\prime }&=y_{1} t +y_{2} t \\
y_{2}^{\prime }&=-y_{1} t -y_{2} t \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 4 \\
y_{2} \left (0\right ) &= 0 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.101 |
|
| \begin{align*}
y_{1}^{\prime }&=\frac {y_{1}}{t}+y_{2} \\
y_{2}^{\prime }&=-y_{1}+\frac {y_{2}}{t} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (\pi \right ) &= 1 \\
y_{2} \left (\pi \right ) &= -1 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.102 |
|
| \begin{align*}
y_{1}^{\prime }&=\left (2 t +1\right ) y_{1}+2 y_{2} t \\
y_{2}^{\prime }&=-2 y_{1} t +\left (1-2 t \right ) y_{2} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 0 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.085 |
|
| \begin{align*}
y_{1}^{\prime }&=y_{1}+y_{2} \\
y_{2}^{\prime }&=\frac {y_{1}}{t}+\frac {y_{2}}{t} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (1\right ) &= -3 \\
y_{2} \left (1\right ) &= 4 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.101 |
|
| \begin{align*}
y_{1}^{\prime }&=\frac {y_{1}}{t}+1 \\
y_{2}^{\prime }&=\frac {y_{2}}{t}+t \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (1\right ) &= 1 \\
y_{2} \left (1\right ) &= 2 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.078 |
|
| \begin{align*}
y_{1}^{\prime }&=-\frac {y_{2}}{t}+1 \\
y_{2}^{\prime }&=\frac {y_{1}}{t}+\frac {2 y_{2}}{t}-1 \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (1\right ) &= 2 \\
y_{2} \left (1\right ) &= 0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.079 |
|
| \begin{align*}
y_{1}^{\prime }&=\frac {4 t y_{1}}{t^{2}+1}+\frac {6 y_{2} t}{t^{2}+1}-3 t \\
y_{2}^{\prime }&=-\frac {2 t y_{1}}{t^{2}+1}-\frac {4 y_{2} t}{t^{2}+1}+t \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (1\right ) &= 1 \\
y_{2} \left (1\right ) &= -1 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.107 |
|
| \begin{align*}
y_{1}^{\prime }&=3 \sec \left (t \right ) y_{1}+5 \sec \left (t \right ) y_{2} \\
y_{2}^{\prime }&=-\sec \left (t \right ) y_{1}-3 \sec \left (t \right ) y_{2} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 2 \\
y_{2} \left (0\right ) &= 1 \\
\end{align*} |
✗ |
✓ |
✗ |
✓ |
0.091 |
|
| \begin{align*}
y_{1}^{\prime }&=y_{1} t +y_{2} t +4 t \\
y_{2}^{\prime }&=-y_{1} t -y_{2} t +4 t \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 4 \\
y_{2} \left (0\right ) &= 0 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.086 |
|
| \begin{align*}
x^{\prime }&=x+3 y \\
y^{\prime }&=5 x+3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.483 |
|
| \begin{align*}
x^{\prime \prime }&=4 y+{\mathrm e}^{t} \\
y^{\prime \prime }&=4 x-{\mathrm e}^{t} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.135 |
|
| \begin{align*}
x^{\prime }-x+2 y&=0 \\
y^{\prime }+3 x-2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.501 |
|
| \begin{align*}
x^{\prime }+y^{\prime }-x&=0 \\
x^{\prime }+2 y^{\prime }&=4 \,{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.678 |
|
| \begin{align*}
y^{\prime }&=-y+2 z \\
z^{\prime }&=4 y+z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.505 |
|
| \begin{align*}
y^{\prime }&=4 y-z \\
z^{\prime }&=2 y+z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.494 |
|
| \begin{align*}
x^{\prime }+y^{\prime }+2 x-y&=-\sin \left (t \right ) \\
x^{\prime }-3 x+y^{\prime }+2 y&=4 \cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.319 |
|
| \begin{align*}
y^{\prime \prime }-y+5 y^{\prime }&=t \\
2 y^{\prime }-x^{\prime \prime }+4 x&=2 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.140 |
|
| \begin{align*}
x^{\prime }&=3 x \\
y^{\prime }&=2 x+3 y \\
z^{\prime }&=3 y-2 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.756 |
|
| \begin{align*}
y_{1}^{\prime }&=3 y_{1}+6 y_{2} \\
y_{2}^{\prime }&=2 y_{1}-6 y_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.789 |
|
| \begin{align*}
y_{1}^{\prime }&=2 y_{1} \\
y_{2}^{\prime }&=3 y_{1}-2 y_{2} \\
y_{3}^{\prime }&=2 y_{2}+3 y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.852 |
|
| \begin{align*}
y_{1}^{\prime }&=y_{2} \\
y_{2}^{\prime }&=-y_{1}+2 y_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.434 |
|
| \begin{align*}
y^{\prime }&=y+z-w \\
z^{\prime }&=y-z+w \\
w^{\prime }&=-y+z+w \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.819 |
|
| \begin{align*}
y^{\prime }&=y-2 z \\
z^{\prime }&=4 y+5 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.733 |
|
| \begin{align*}
y^{\prime }&=3 y-z \\
z^{\prime }&=y+3 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.520 |
|
| \begin{align*}
y^{\prime }&=-2 z \\
z^{\prime }&=y+2 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.655 |
|
| \begin{align*}
y^{\prime }&=-3 y+z-w \\
z^{\prime }&=5 y-z-7 w \\
w^{\prime }&=-y+z-3 w \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.852 |
|
| \begin{align*}
y^{\prime }&=3 y-4 z \\
z^{\prime }&=y-z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.452 |
|
| \begin{align*}
y_{1}^{\prime }&=y_{1}+y_{2} \\
y_{2}^{\prime }&=y_{1}-y_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.629 |
|
| \begin{align*}
y_{1}^{\prime }&=4 y_{1}-y_{2} \\
y_{2}^{\prime }&=y_{1}+2 y_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.438 |
|
| \begin{align*}
x^{\prime }&=-x+2 y \\
y^{\prime }&=2 x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.483 |
|
| \begin{align*}
x^{\prime }&=3 x-2 y \\
y^{\prime }&=2 x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.411 |
|
| \begin{align*}
x^{\prime \prime }&=y \\
y^{\prime \prime }&=x \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.131 |
|
| \begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=x+y+t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.686 |
|
| \begin{align*}
x^{\prime }&=\frac {1}{y} \\
y^{\prime }&=\frac {1}{x} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.127 |
|
| \begin{align*}
x^{\prime }&=x-2 y \\
y^{\prime }&=3 x-4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.512 |
|
| \begin{align*}
x^{\prime }&=x+2 y \\
y^{\prime }&=2 x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.464 |
|
| \begin{align*}
x^{\prime }&=-x+2 y \\
y^{\prime }&=-2 x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.543 |
|
| \begin{align*}
x^{\prime }&=x+2 y \\
y^{\prime }&=-5 x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.580 |
|
| \begin{align*}
x^{\prime }&=-2 x+y+x \,y^{2} \\
y^{\prime }&=-7 x-2 y-7 y \,x^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.129 |
|
| \begin{align*}
x^{\prime }&=-y+x^{2} y^{3} \\
y^{\prime }&=x-x^{3} y^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.052 |
|
| \begin{align*}
x^{\prime }&=y+x^{3} \\
y^{\prime }&=x-y^{3} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.125 |
|
| \begin{align*}
x^{\prime }&=-2 x+\sin \left (y\right ) \\
y^{\prime }&=5 \,{\mathrm e}^{x}-5-y \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.046 |
|
| \begin{align*}
x^{\prime }&=2 x-y \cos \left (y\right ) \\
y^{\prime }&=3 x-2 y-x \,y^{2} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
0.121 |
|
| \begin{align*}
x^{\prime }&=3-2 y \\
y^{\prime }&=2 x-2 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.961 |
|
| \begin{align*}
x^{\prime }&=x-2 y \\
y^{\prime }&=x+3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.813 |
|
| \begin{align*}
x^{\prime }+3 x+y&=0 \\
y^{\prime }+y-x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.507 |
|
| \begin{align*}
x^{\prime }&=3 x-\frac {y}{2}-3 t^{2}-\frac {t}{2}+\frac {3}{2} \\
y^{\prime }&=2 y-2 t -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.829 |
|
| \begin{align*}
x^{\prime }&=-7 x+y \\
y^{\prime }&=-2 x-5 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.820 |
|
| \begin{align*}
x^{\prime }&=2 x-9 y \\
y^{\prime }&=x+8 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.533 |
|
| \begin{align*}
x^{\prime }&=y+z \\
y^{\prime }&=x+z \\
z^{\prime }&=x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.822 |
|
| \begin{align*}
x^{\prime }&=y+z \\
y^{\prime }&=3 x+z \\
z^{\prime }&=3 x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.990 |
|
| \begin{align*}
x^{\prime }&=8 y \\
y^{\prime }&=-2 z \\
z^{\prime }&=2 x+8 y-2 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.197 |
|
| \begin{align*}
x^{\prime }&=2 x+y-2 z+2-t \\
y^{\prime }&=1-x \\
z^{\prime }&=x+y-z+1-t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.773 |
|
| \begin{align*}
x^{\prime }&=-x+y+z+{\mathrm e}^{t} \\
y^{\prime }&=x-y+z+{\mathrm e}^{3 t} \\
z^{\prime }&=x+y+z+4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.630 |
|
| \begin{align*}
x^{\prime }&=x \cos \left (t \right ) \\
2 y^{\prime }&=\left ({\mathrm e}^{t}+{\mathrm e}^{-t}\right ) y \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.089 |
|
| \begin{align*}
x^{\prime }&={\mathrm e}^{t}-y-5 x \\
y^{\prime }&={\mathrm e}^{2 t}+x-3 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= {\frac {119}{900}} \\
y \left (0\right ) &= {\frac {211}{900}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.859 |
|
| \begin{align*}
x^{\prime }&=3 x+8 y \\
y^{\prime }&=-x-3 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 6 \\
y \left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.592 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-x \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.544 |
|
| \begin{align*}
x^{\prime }&=-4 x-4 y \\
x^{\prime }+4 y^{\prime }&=-4 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.536 |
|
| \begin{align*}
x^{\prime }&=4 x-5 y \\
y^{\prime }&=x \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.690 |
|
| \begin{align*}
x^{\prime }&=x+y+t \\
y^{\prime }&=x-2 y+2 t \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= -{\frac {7}{9}} \\
y \left (0\right ) &= -{\frac {5}{9}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.612 |
|
| \begin{align*}
x^{\prime }&=x+5 y \\
y^{\prime }&=-x-3 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= -2 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.761 |
|
| \begin{align*}
x^{\prime }+2 y^{\prime }&=17 x+8 y \\
13 x^{\prime }&=53 x+2 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.683 |
|
| \begin{align*}
x^{\prime }&=y \\
x^{\prime }-y^{\prime }&=x+y \\
\end{align*}
With initial conditions \begin{align*}
x \left (\pi \right ) &= -1 \\
y \left (\pi \right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.586 |
|
| \begin{align*}
x^{\prime }+y^{\prime }&={\mathrm e}^{-t}-y \\
2 x^{\prime }+y^{\prime }&=\sin \left (t \right )-2 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= -2 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.793 |
|
| \begin{align*}
2 x^{\prime }&=6 x-y-6 t^{2}-t +3 \\
y^{\prime }&=2 y-2 t -1 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.741 |
|
| \begin{align*}
x^{\prime }&=\frac {1}{y} \\
y^{\prime }&=\frac {1}{x} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.059 |
|
| \begin{align*}
t x^{\prime }&=t -2 x \\
y^{\prime } t&=t x+t y+2 x-t \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.089 |
|
| \begin{align*}
x^{\prime }&=x-13 y \\
y^{\prime }&=\frac {x}{4}-2 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.766 |
|
| \begin{align*}
x^{\prime }&=-x-3 y \\
y^{\prime }&=x-y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.768 |
|
| \begin{align*}
x^{\prime }&=3 x+y \\
y^{\prime }&=-2 x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.762 |
|
| \begin{align*}
x^{\prime }&=-x+2 y \\
y^{\prime }&=x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.733 |
|
| \begin{align*}
x^{\prime }&=-x+3 y \\
y^{\prime }&=-x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.647 |
|
| \begin{align*}
x^{\prime }&=-2 x-y \\
y^{\prime }&=3 x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.888 |
|
| \begin{align*}
x^{\prime }&=3 x+7 y \\
y^{\prime }&=2 x+5 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.879 |
|
| \begin{align*}
x^{\prime }&=-2 x+\frac {5 y}{7} \\
y^{\prime }&=7 x-3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.888 |
|
| \begin{align*}
x^{\prime }&=3 x-y \\
y^{\prime }&=x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.491 |
|
| \begin{align*}
x^{\prime }&=-x-y \\
y^{\prime }&=x-3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.517 |
|
| \begin{align*}
x^{\prime }&=3 x \\
y^{\prime }&=3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.358 |
|
| \begin{align*}
x^{\prime }&=-3 x+\alpha y \\
y^{\prime }&=2 x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.923 |
|
| \begin{align*}
x^{\prime }&=x+2 y-\sin \left (y\right )^{2} \\
y^{\prime }&=-x-3 y+x \left ({\mathrm e}^{\frac {x^{2}}{2}}-1\right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.194 |
|
| \begin{align*}
x^{\prime }&=-x+3 y+x^{2} \sin \left (y\right ) \\
y^{\prime }&=-x-4 y+1-\cos \left (y^{2}\right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.072 |
|
| \begin{align*}
x^{\prime }&=-2 x+8 \sin \left (y\right )^{2} \\
y^{\prime }&=x-3 y+4 x^{3} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.196 |
|
| \begin{align*}
x^{\prime }&=3 x-22 \sin \left (y\right )+x^{2}-y^{3} \\
y^{\prime }&=\sin \left (x\right )-5 y+{\mathrm e}^{x^{2}}-1 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.059 |
|
| \begin{align*}
x^{\prime }&=-10 x+4 \,{\mathrm e}^{y}-4 \cos \left (y^{2}\right ) \\
y^{\prime }&=2 \,{\mathrm e}^{x}-2-y+x^{4} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.187 |
|
| \begin{align*}
x^{\prime }&=7 x+2 \sin \left (y\right )-4 y^{4} \\
y^{\prime }&={\mathrm e}^{x}-3 y-1+\frac {5 x^{2}}{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.066 |
|
| \begin{align*}
x^{\prime }&=-\frac {2 x}{3}+\frac {\sin \left (2 y\right )}{2}-x^{3} y \\
y^{\prime }&=-y-2 x+x^{4}-y^{7} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.181 |
|
| \begin{align*}
x^{\prime }&=\frac {5 x \,{\mathrm e}^{x}}{2}-3 y+\sin \left (x^{2}\right ) \\
y^{\prime }&=2 x+y \,{\mathrm e}^{-\frac {y^{2}}{2}}-y^{4} \cos \left (x\right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.136 |
|
| \begin{align*}
x^{\prime }&=\frac {3 \sin \left (x\right )}{4}-7 y \left (1-y\right )^{{1}/{3}}+x^{3} \\
y^{\prime }&=\frac {2 x}{3}-3 y \cos \left (y\right )-11 y^{5} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.178 |
|
| \begin{align*}
x^{\prime }&=\frac {{\mathrm e}^{x}}{4}-\frac {1}{4}-9 y+x^{4} \\
y^{\prime }&=\frac {x}{5}-\sin \left (y\right )+y^{14} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.071 |
|
| \begin{align*}
x^{\prime }&=5 x+y \cos \left (y\right )-\frac {x^{3}}{3} \\
y^{\prime }&=3 x+2 y+\frac {x^{4}}{12}-y^{3} {\mathrm e}^{y} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.175 |
|
| \begin{align*}
x_{1}^{\prime }&=5 x_{1}+3 x_{2} \\
x_{2}^{\prime }&=x_{1}+3 x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.762 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}+8 x_{2} \\
x_{2}^{\prime }&=x_{1}-x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 2 \\
x_{2} \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.962 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}-x_{2} \\
x_{2}^{\prime }&=4 x_{1}+2 x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= -2 \\
x_{2} \left (0\right ) &= 7 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.050 |
|
| \begin{align*}
x_{1}^{\prime }&=5 x_{1}-4 x_{2}+4 x_{3} \\
x_{2}^{\prime }&=12 x_{1}-11 x_{2}+12 x_{3} \\
x_{3}^{\prime }&=4 x_{1}-4 x_{2}+5 x_{3} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= -3 \\
x_{3} \left (0\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.992 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1} \\
x_{2}^{\prime }&=5 x_{1}-4 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.620 |
|
| \begin{align*}
x_{1}^{\prime }&=4 x_{1}+2 x_{2} \\
x_{2}^{\prime }&=3 x_{1}+3 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}+x_{2} \\
x_{2}^{\prime }&=x_{1}+x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.617 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}+x_{2}-2 x_{3} \\
x_{2}^{\prime }&=3 x_{1}-2 x_{2} \\
x_{3}^{\prime }&=3 x_{1}-x_{2}-3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
17.430 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}+2 x_{2}+x_{3} \\
x_{2}^{\prime }&=6 x_{1}-x_{2} \\
x_{3}^{\prime }&=-x_{1}-2 x_{2}-x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
114.886 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}-4 x_{2} \\
x_{2}^{\prime }&=2 x_{1}-3 x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 7 \\
x_{2} \left (0\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.636 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}-2 x_{2} \\
x_{2}^{\prime }&=-6 x_{1} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= -19 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.658 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}-10 x_{2} \\
x_{2}^{\prime }&=-x_{1}-x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= -3 \\
x_{2} \left (0\right ) &= 6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.620 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}-x_{2}+x_{3} \\
x_{2}^{\prime }&=x_{1}+x_{2}-x_{3} \\
x_{3}^{\prime }&=x_{1}-x_{2}+x_{3} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 5 \\
x_{3} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.846 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}+x_{2}-x_{3} \\
x_{2}^{\prime }&=3 x_{1}-2 x_{2} \\
x_{3}^{\prime }&=3 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 ) &= 7 \\
x_{3} \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.068 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}-4 x_{2} \\
x_{2}^{\prime }&=x_{1}+2 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.697 |
|
| \begin{align*}
x_{1}^{\prime }&=5 x_{2} \\
x_{2}^{\prime }&=-x_{1}-2 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.816 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}-5 x_{2} \\
x_{2}^{\prime }&=x_{1}-x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.796 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}-x_{2}+x_{3} \\
x_{2}^{\prime }&=x_{1}-x_{2} \\
x_{3}^{\prime }&=x_{1}-x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.905 |
|
| \begin{align*}
x_{1}^{\prime }&=-2 x_{1}+x_{2} \\
x_{2}^{\prime }&=-5 x_{1} \\
x_{3}^{\prime }&=3 x_{2}-2 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.182 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1} \\
x_{2}^{\prime }&=5 x_{1}+2 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.436 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}+2 x_{2} \\
x_{2}^{\prime }&=3 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.444 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}+5 x_{2} \\
x_{2}^{\prime }&=x_{2} \\
x_{3}^{\prime }&=4 x_{1}+8 x_{2}+x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.668 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}+5 x_{2}+6 x_{3} \\
x_{2}^{\prime }&=8 x_{2}+9 x_{3} \\
x_{3}^{\prime }&=x_{2}-2 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.555 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{2} \\
x_{2}^{\prime }&=x_{3} \\
x_{3}^{\prime }&=x_{4} \\
x_{4}^{\prime }&=-x_{1}-2 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
21.700 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}+5 x_{2}-2 x_{3}+6 x_{4} \\
x_{2}^{\prime }&=3 x_{2}+4 x_{4} \\
x_{3}^{\prime }&=3 x_{2}+4 x_{4} \\
x_{4}^{\prime }&=x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.262 |
|
| \begin{align*}
x_{1}^{\prime }&=5 x_{1}+2 x_{2}-3 \,{\mathrm e}^{t} \\
x_{2}^{\prime }&=-2 x_{1}+x_{2}+{\mathrm e}^{3 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.907 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}-4 x_{2}+1 \\
x_{2}^{\prime }&=x_{1}-2 x_{2}+3 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.743 |
|
| \begin{align*}
x_{1}^{\prime }&=7 x_{1}-x_{2}+2 \,{\mathrm e}^{6 t} \\
x_{2}^{\prime }&=x_{1}+5 x_{2}+6 t \,{\mathrm e}^{6 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.849 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}+{\mathrm e}^{2 t} \cos \left (3 t \right ) \\
x_{2}^{\prime }&=6 x_{2}-4 x_{3}-2 \\
x_{3}^{\prime }&=4 x_{2}-2 x_{3}-2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.217 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1} \\
x_{2}^{\prime }&=4 x_{1}+3 x_{2}-2 \,{\mathrm e}^{t} \\
x_{3}^{\prime }&=3 x_{3} \\
x_{4}^{\prime }&=-x_{1}+2 x_{2}+9 x_{3}+x_{4}+{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.554 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}+2 \\
x_{2}^{\prime }&=5 x_{1}+2 x_{2}+10 t \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.660 |
|
| \begin{align*}
x_{1}^{\prime }&=5 x_{1}-4 x_{2}+2 \,{\mathrm e}^{t} \\
x_{2}^{\prime }&=4 x_{1}-3 x_{2}+2 \,{\mathrm e}^{t} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= -1 \\
x_{2} \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.697 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}-3 x_{2}+x_{3}+10 \,{\mathrm e}^{2 t} \\
x_{2}^{\prime }&=2 x_{2}+4 x_{3}+6 \,{\mathrm e}^{2 t} \\
x_{3}^{\prime }&=x_{3}-{\mathrm e}^{2 t} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 5 \\
x_{2} \left (0\right ) &= 11 \\
x_{3} \left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.425 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}-3 x_{2}+t \,{\mathrm e}^{-2 t} \\
x_{2}^{\prime }&=3 x_{1}-5 x_{2}+t \,{\mathrm e}^{-2 t} \\
x_{3}^{\prime }&=4 x_{1}+7 x_{2}-2 x_{3}+t^{2} {\mathrm e}^{-2 t} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 6 \\
x_{2} \left (0\right ) &= 2 \\
x_{3} \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.198 |
|
| \begin{align*}
x_{1}^{\prime }&=-2 x_{1}+x_{2} \\
x_{2}^{\prime }&=-4 x_{1}+3 x_{2}+10 \cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.002 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}+3 x_{2}+8 \\
x_{2}^{\prime }&=x_{1}+5 x_{2}+4 \,{\mathrm e}^{3 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.036 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}+x_{2}+6 \,{\mathrm e}^{3 t} \\
x_{2}^{\prime }&=x_{1}+x_{2}+4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.852 |
|
| \begin{align*}
x_{1}^{\prime }&=6 x_{1}+5 x_{2}-4 \cos \left (3 t \right ) \\
x_{2}^{\prime }&=x_{1}+2 x_{2}+8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.453 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}-2 x_{2}+3 \,{\mathrm e}^{2 t} \\
x_{2}^{\prime }&=9 x_{1}-3 x_{2}+{\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.142 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}+x_{2}+6 \,{\mathrm e}^{2 t} \\
x_{2}^{\prime }&=x_{1}+x_{2}+2 \,{\mathrm e}^{2 t} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 6 \\
x_{2} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.805 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}-2 x_{2}+2 t \\
x_{2}^{\prime }&=-x_{1}+2 x_{2}+5 \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 13 \\
x_{2} \left (0\right ) &= 12 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.834 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}-5 x_{2}+5 \sin \left (t \right ) \\
x_{2}^{\prime }&=x_{1}-2 x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 10 \\
x_{2} \left (0\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.099 |
|
| \begin{align*}
x_{1}^{\prime }&=5 x_{1}-4 x_{2}+3 x_{3}-3 \,{\mathrm e}^{-3 t} \\
x_{2}^{\prime }&=12 x_{1}-11 x_{2}+12 x_{3}+t \\
x_{3}^{\prime }&=4 x_{1}-4 x_{2}+5 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 ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.098 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}-x_{2}-x_{3} \\
x_{2}^{\prime }&=x_{1}+x_{2}-x_{3}+t \\
x_{3}^{\prime }&=x_{1}-x_{2}+x_{3}+2 \,{\mathrm e}^{t} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 2 \\
x_{3} \left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.117 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{2}-x_{1} \\
x_{2}^{\prime }&=-5 x_{1}+x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.691 |
|
| \begin{align*}
x_{1}^{\prime }&=-2 x_{1}+x_{2} \\
x_{2}^{\prime }&=2 x_{1}-x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.592 |
|
| \begin{align*}
x_{1}^{\prime }&=5 x_{1}-2 x_{2} \\
x_{2}^{\prime }&=4 x_{1}+8 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.996 |
|
| \begin{align*}
x_{1}^{\prime }&=4 x_{1}-x_{2} \\
x_{2}^{\prime }&=2 x_{1}-2 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.849 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}+x_{3} \\
x_{2}^{\prime }&=-2 x_{1}+x_{2}+x_{3} \\
x_{3}^{\prime }&=x_{1}-x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.240 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}-5 x_{2} \\
x_{2}^{\prime }&=5 x_{1}-7 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.526 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}+4 x_{2} \\
x_{2}^{\prime }&=3 x_{1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.617 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}-5 x_{2} \\
x_{2}^{\prime }&=x_{1}-x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.670 |
|
| \begin{align*}
x_{1}^{\prime }&=9 x_{1}-7 x_{2} \\
x_{2}^{\prime }&=6 x_{1}-4 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.628 |
|
| \begin{align*}
x_{1}^{\prime }&=7 x_{1}-17 x_{2} \\
x_{2}^{\prime }&=2 x_{1}+x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.867 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}-7 x_{2} \\
x_{2}^{\prime }&=5 x_{1}-10 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.639 |
|
| \begin{align*}
x_{1}^{\prime }&=4 x_{1}-x_{2} \\
x_{2}^{\prime }&=x_{1}+2 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.510 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}-5 x_{2} \\
x_{2}^{\prime }&=8 x_{1}-3 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.778 |
|
| \begin{align*}
x_{1}^{\prime }&=-2 x_{1}-x_{2} \\
x_{2}^{\prime }&=3 x_{1}-2 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.762 |
|
| \begin{align*}
x_{1}^{\prime }&=-6 x_{1}-7 x_{2} \\
x_{2}^{\prime }&=7 x_{1}-20 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.536 |
|
| \begin{align*}
x^{\prime }&=x-\frac {x y}{2} \\
y^{\prime }&=2 x y-\frac {6 y}{5} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.207 |
|
| \begin{align*}
x^{\prime }&=2 x+y \\
y^{\prime }&=3 x+4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.328 |
|