| # |
ODE |
Solved |
Maple |
Mma |
Sympy |
time(sec) |
| \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*} |
✓ |
✓ |
✓ |
✓ |
0.364 |
|
| \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*} |
✓ |
✓ |
✓ |
✓ |
0.255 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}-2 x_{2}+t \\
x_{2}^{\prime }&=2 x_{1}-2 x_{2}+3 \,{\mathrm e}^{t} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 2 \\
x_{2} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.252 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}+x_{2}+2 \,{\mathrm e}^{t} \\
x_{2}^{\prime }&=4 x_{1}+x_{2}-{\mathrm e}^{t} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.250 |
|
| \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*} |
✓ |
✓ |
✓ |
✓ |
0.244 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}-5 x_{2}+\sin \left (t \right ) \\
x_{2}^{\prime }&=x_{1}-2 x_{2}+\tan \left (t \right ) \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= -1 \\
x_{2} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
230.430 |
|
| \begin{align*}
x_{1}^{\prime }&=4 x_{1}+5 x_{2}+4 \,{\mathrm e}^{t} \cos \left (t \right ) \\
x_{2}^{\prime }&=-2 x_{1}-2 x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.369 |
|
| \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*} |
✓ |
✓ |
✓ |
✓ |
1.564 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}-2 x_{2} \\
x_{2}^{\prime }&=4 x_{1}-2 x_{2}+\delta \left (t -\pi \right ) \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.477 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}-2 x_{2}+1-\operatorname {Heaviside}\left (t -\pi \right ) \\
x_{2}^{\prime }&=2 x_{1}-2 x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.445 |
|
| \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*} |
✓ |
✓ |
✓ |
✓ |
0.405 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}+x_{3}+{\mathrm e}^{2 t} \\
x_{2}^{\prime }&=2 x_{2} \\
x_{3}^{\prime }&=3 x_{3}+{\mathrm e}^{2 t} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 1 \\
x_{3} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.352 |
|
| \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*} |
✓ |
✓ |
✓ |
✗ |
0.451 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1} \\
x_{2}^{\prime }&=2 x_{1}+x_{2}-2 x_{3} \\
x_{3}^{\prime }&=3 x_{1}+2 x_{2}+x_{3}+{\mathrm e}^{t} \cos \left (2 t \right ) \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= 1 \\
x_{3} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.386 |
|
| \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*} |
✓ |
✓ |
✓ |
✓ |
0.461 |
|
| \begin{align*}
x^{\prime }-x-2 y&=16 \,{\mathrm e}^{t} t \\
2 x-y^{\prime }-2 y&=0 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 4 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.356 |
|
| \begin{align*}
x^{\prime }-2 x+y&=5 \,{\mathrm e}^{t} \cos \left (t \right ) \\
x+y^{\prime }-2 y&=10 \,{\mathrm e}^{t} \sin \left (t \right ) \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.369 |
|
| \begin{align*}
x^{\prime }-4 x+3 y&=\sin \left (t \right ) \\
2 x+y^{\prime }-y&=2 \cos \left (t \right ) \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= x_{0} \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.356 |
|
| \begin{align*}
x^{\prime }-2 x-y&=2 \,{\mathrm e}^{t} \\
x-y^{\prime }+2 y&=3 \,{\mathrm e}^{4 t} \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= x_{0} \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.323 |
|
| \begin{align*}
x^{\prime \prime }+x^{\prime }+y^{\prime }-2 y&=40 \,{\mathrm e}^{3 t} \\
x^{\prime }+x-y^{\prime }&=36 \,{\mathrm e}^{t} \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 3 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.033 |
|
| \begin{align*}
x^{\prime }-2 x-y&=2 \,{\mathrm e}^{t} \\
y^{\prime }-2 y-4 z&=4 \,{\mathrm e}^{2 t} \\
x-z^{\prime }-z&=0 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 9 \\
y \left (0\right ) &= 3 \\
z \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.438 |
|
| \begin{align*}
x^{\prime \prime }+2 x-2 y^{\prime }&=0 \\
3 x^{\prime }+y^{\prime \prime }-8 y&=240 \,{\mathrm e}^{t} \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.033 |
|
| \begin{align*}
x^{\prime }-x-2 y&=0 \\
x-y^{\prime }&=15 \cos \left (t \right ) \operatorname {Heaviside}\left (t -\pi \right ) \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= x_{0} \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.380 |
|
| \begin{align*}
x^{\prime }-x+y&=2 \sin \left (t \right ) \left (1-\operatorname {Heaviside}\left (t -\pi \right )\right ) \\
2 x-y^{\prime }-y&=0 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.433 |
|
| \begin{align*}
2 x^{\prime }+x-5 y^{\prime }-4 y&=28 \,{\mathrm e}^{t} \operatorname {Heaviside}\left (-2+t \right ) \\
3 x^{\prime }-2 x-4 y^{\prime }+y&=0 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.454 |
|
| \begin{align*}
x^{\prime }+y^{\prime }+x&=0 \\
x^{\prime }-x+2 y^{\prime }&={\mathrm e}^{-t} \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.118 |
|
| \begin{align*}
y_{1}^{\prime }&=-5 y_{1}+y_{2} \\
y_{2}^{\prime }&=-9 y_{1}+5 y_{2} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.614 |
|
| \begin{align*}
y_{1}^{\prime }&=5 y_{1}-2 y_{2} \\
y_{2}^{\prime }&=6 y_{1}-2 y_{2} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.569 |
|
| \begin{align*}
y_{1}^{\prime }&=4 y_{1}-4 y_{2} \\
y_{2}^{\prime }&=5 y_{1}-4 y_{2} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.580 |
|
| \begin{align*}
y_{1}^{\prime }&=6 y_{2} \\
y_{2}^{\prime }&=-6 y_{1} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 5 \\
y_{2} \left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.576 |
|
| \begin{align*}
y_{1}^{\prime }&=-4 y_{1}-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 ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.556 |
|
| \begin{align*}
y_{1}^{\prime }&=2 y_{1}-64 y_{2} \\
y_{2}^{\prime }&=y_{1}-14 y_{2} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 0 \\
y_{2} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.553 |
|
| \begin{align*}
y_{1}^{\prime }&=-4 y_{1}-y_{2}+2 \,{\mathrm e}^{t} \\
y_{2}^{\prime }&=y_{1}-2 y_{2}+\sin \left (2 t \right ) \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| \begin{align*}
y_{1}^{\prime }&=5 y_{1}-y_{2}+{\mathrm e}^{-t} \\
y_{2}^{\prime }&=y_{1}+3 y_{2}+2 \,{\mathrm e}^{t} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= -3 \\
y_{2} \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.601 |
|
| \begin{align*}
y_{1}^{\prime }&=-y_{1}-5 y_{2}+3 \\
y_{2}^{\prime }&=y_{1}+3 y_{2}+5 \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*} |
✓ |
✓ |
✓ |
✓ |
0.634 |
|
| \begin{align*}
y_{1}^{\prime }&=-2 y_{1}+y_{2} \\
y_{2}^{\prime }&=y_{1}-2 y_{2}+\sin \left (t \right ) \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 0 \\
y_{2} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.596 |
|
| \begin{align*}
y_{1}^{\prime }&=y_{2}-y_{3} \\
y_{2}^{\prime }&=y_{1}+y_{3}-{\mathrm e}^{-t} \\
y_{3}^{\prime }&=y_{1}+y_{2}+{\mathrm e}^{t} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 2 \\
y_{3} \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.810 |
|
| \begin{align*}
x_{1}^{\prime }&=-4 x_{1}-x_{2} \\
x_{2}^{\prime }&=x_{1}-2 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.568 |
|
| \begin{align*}
x_{1}^{\prime }&=5 x_{1}-x_{2} \\
x_{2}^{\prime }&=x_{1}+3 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.520 |
|
| \begin{align*}
x_{1}^{\prime }&=-x_{1}-5 x_{2} \\
x_{2}^{\prime }&=x_{1}+3 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.494 |
|
| \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*} |
✓ |
✓ |
✓ |
✓ |
0.735 |
|
| \begin{align*}
x^{\prime }&=2 x+3 y+2 \sin \left (2 t \right ) \\
y^{\prime }&=-3 x+2 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.079 |
|
| \begin{align*}
x^{\prime }&=-4 x-y+{\mathrm e}^{-t} \\
y^{\prime }&=x-2 y+2 \,{\mathrm e}^{-3 t} \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.002 |
|
| \begin{align*}
x^{\prime }&=x-y+2 \cos \left (t \right ) \\
y^{\prime }&=x+y+3 \sin \left (t \right ) \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 3 \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.023 |
|
| \begin{align*}
x^{\prime }&=2 x+y \\
y^{\prime }&=-x-4 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.356 |
|
| \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*} |
✓ |
✓ |
✓ |
✗ |
1.270 |
|
| \begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=-y+\delta \left (t \right ) \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.187 |
|
| \begin{align*}
x^{\prime }-6 x+3 y&=8 \,{\mathrm e}^{t} \\
y^{\prime }-2 x-y&=4 \,{\mathrm e}^{t} \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.413 |
|
| \begin{align*}
y^{\prime }+z&=t \\
z^{\prime }+4 y&=0 \\
\end{align*}
With initial conditions \begin{align*}
z \left (0\right ) &= -1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.464 |
|
| \begin{align*}
w^{\prime }+y&=\sin \left (t \right ) \\
y^{\prime }-z&={\mathrm e}^{t} \\
w+y+z^{\prime }&=1 \\
\end{align*}
With initial conditions \begin{align*}
w \left (0\right ) &= 0 \\
z \left (0\right ) &= 1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.904 |
|
| \begin{align*}
y^{\prime }+z&=t \\
z^{\prime }+4 y&=0 \\
\end{align*}
With initial conditions \begin{align*}
y \left (0\right ) &= 1 \\
z \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.527 |
|
| \begin{align*}
w^{\prime }+y&=\sin \left (t \right ) \\
y^{\prime }-z&={\mathrm e}^{t} \\
w+y+z^{\prime }&=1 \\
\end{align*}
With initial conditions \begin{align*}
y \left (0\right ) &= 1 \\
z \left (0\right ) &= 1 \\
w \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.126 |
|
| \begin{align*}
y^{\prime \prime }+z+y&=0 \\
y^{\prime }+z^{\prime }&=0 \\
\end{align*}
With initial conditions \begin{align*}
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
z \left (0\right ) &= 1 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.092 |
|
| \begin{align*}
z^{\prime \prime }+y^{\prime }&=\cos \left (t \right ) \\
y^{\prime \prime }-z&=\sin \left (t \right ) \\
\end{align*}
With initial conditions \begin{align*}
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
z \left (0\right ) &= -1 \\
z^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.099 |
|
| \begin{align*}
w^{\prime \prime }-y+2 z&=3 \,{\mathrm e}^{-t} \\
-2 w^{\prime }+2 y^{\prime }+z&=0 \\
2 w^{\prime }-2 y+z^{\prime }+2 z^{\prime \prime }&=0 \\
\end{align*}
With initial conditions \begin{align*}
y \left (0\right ) &= 2 \\
z \left (0\right ) &= 2 \\
z^{\prime }\left (0\right ) &= -2 \\
w \left (0\right ) &= 1 \\
w^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.088 |
|
| \begin{align*}
y^{\prime }+z&=t \\
z^{\prime }-y&=0 \\
\end{align*}
With initial conditions \begin{align*}
y \left (0\right ) &= 1 \\
z \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.526 |
|
| \begin{align*}
y^{\prime }-z&=0 \\
y-z^{\prime }&=0 \\
\end{align*}
With initial conditions \begin{align*}
y \left (0\right ) &= 1 \\
z \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.507 |
|
| \begin{align*}
w^{\prime }-w-2 y&=1 \\
y^{\prime }-4 w-3 y&=-1 \\
\end{align*}
With initial conditions \begin{align*}
y \left (0\right ) &= 2 \\
w \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.582 |
|
| \begin{align*}
w^{\prime }-y&=0 \\
w+y^{\prime }+z&=1 \\
w-y+z^{\prime }&=2 \sin \left (t \right ) \\
\end{align*}
With initial conditions \begin{align*}
y \left (0\right ) &= 1 \\
w \left (0\right ) &= 1 \\
z \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.148 |
|
| \begin{align*}
u^{\prime \prime }-2 v&=2 \\
u+v^{\prime }&=5 \,{\mathrm e}^{2 t}+1 \\
\end{align*}
With initial conditions \begin{align*}
u \left (0\right ) &= 2 \\
u^{\prime }\left (0\right ) &= 2 \\
v \left (0\right ) &= 1 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.089 |
|
| \begin{align*}
w^{\prime \prime }-2 z&=0 \\
w^{\prime }+y^{\prime }-z&=2 t \\
w^{\prime }-2 y+z^{\prime \prime }&=0 \\
\end{align*}
With initial conditions \begin{align*}
w \left (0\right ) &= 0 \\
w^{\prime }\left (0\right ) &= 0 \\
z \left (0\right ) &= 1 \\
z^{\prime }\left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.138 |
|
| \begin{align*}
w^{\prime \prime }+y+z&=-1 \\
w+y^{\prime \prime }-z&=0 \\
-w-y^{\prime }+z^{\prime \prime }&=0 \\
\end{align*}
With initial conditions \begin{align*}
w \left (0\right ) &= 0 \\
w^{\prime }\left (0\right ) &= 1 \\
z \left (0\right ) &= -1 \\
z^{\prime }\left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
0.125 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-x \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.678 |
|
| \begin{align*}
x^{\prime }+x-5 y&=0 \\
y^{\prime }+4 x+5 y&=0 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= -1 \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.340 |
|
| \begin{align*}
x^{\prime }+3 y^{\prime }+y&={\mathrm e}^{t} \\
-x+y^{\prime }&=y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.409 |
|
| \begin{align*}
x^{\prime }-3 x-6 y&=27 t^{2} \\
x^{\prime }+y^{\prime }-3 y&=5 \,{\mathrm e}^{t} \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 5 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.352 |
|
| \begin{align*}
x^{\prime \prime }&=-2 y \\
y^{\prime }&=y-x^{\prime } \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 10 \\
y \left (0\right ) &= 5 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.125 |
|
| \begin{align*}
y^{\prime \prime }&=x-2 \\
x^{\prime \prime }&=2+y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -3 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.110 |
|
| \begin{align*}
x^{\prime }+y^{\prime }&=\cos \left (t \right ) \\
x+y^{\prime \prime }&=2 \\
\end{align*}
With initial conditions \begin{align*}
x \left (\pi \right ) &= 2 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.122 |
|
| \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*} |
✓ |
✓ |
✓ |
✓ |
3.379 |
|
| \begin{align*}
x^{\prime }&=x+y+z \\
y^{\prime }&=2 x+5 y+3 z \\
z^{\prime }&=3 x+9 y+5 z \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= -2 \\
y \left (0\right ) &= -1 \\
z \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.254 |
|
| \begin{align*}
x^{\prime \prime }&=y+4 \,{\mathrm e}^{-2 t} \\
y^{\prime \prime }&=x-{\mathrm e}^{-2 t} \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.119 |
|
| \begin{align*}
x^{\prime }+y&=4 \\
x-y^{\prime }&=3 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.761 |
|
| \begin{align*}
x^{\prime \prime }+y^{\prime \prime }&=t \\
x^{\prime \prime }-y^{\prime \prime }&=3 t \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.149 |
|
| \begin{align*}
4 x^{\prime }-2 y&=\cos \left (2 t \right ) \\
x-2 y^{\prime }&=0 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.261 |
|
| \begin{align*}
x^{\prime }+2 x+y^{\prime }+y&={\mathrm e}^{-3 t} \\
5 x+y^{\prime }+3 y&=5 \,{\mathrm e}^{-t} \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= -1 \\
y \left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.338 |
|
| \begin{align*}
4 x^{\prime }+2 y^{\prime }+3 x&=E \sin \left (t \right ) \\
4 x+2 x^{\prime }+3 y&=0 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.294 |
|
| \begin{align*}
y_{1}^{\prime }&=-y_{2} \\
y_{2}^{\prime }-2 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*} |
✓ |
✓ |
✓ |
✓ |
4.187 |
|
| \begin{align*}
y_{1}^{\prime }-y_{1}&=-2 y_{2} \\
y_{2}^{\prime }-y_{2}&=2 y_{1} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 2 \\
y_{2} \left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
4.589 |
|
| \begin{align*}
y_{1}^{\prime }-2 y_{1}&=-y_{2} \\
y_{2}^{\prime \prime }-y_{2}^{\prime }+y_{2}&=y_{1} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 0 \\
y_{2} \left (0\right ) &= -1 \\
y_{2}^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.152 |
|
| \begin{align*}
y_{1}^{\prime }+2 y_{1}&=5 y_{2} \\
y_{2}^{\prime \prime }-2 y_{2}^{\prime }+5 y_{2}&=2 y_{1} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 0 \\
y_{2}^{\prime }\left (0\right ) &= 3 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.166 |
|
| \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 ) &= 10 \\
y_{1}^{\prime }\left (0\right ) &= 0 \\
y_{2} \left (0\right ) &= 10 \\
y_{2}^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.160 |
|
| \begin{align*}
x^{\prime }+y&=3 \,{\mathrm e}^{2 t} \\
x+y^{\prime }&=0 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
5.105 |
|
| \begin{align*}
x^{\prime \prime }+y^{\prime }&=2 \\
x^{\prime \prime }-y^{\prime \prime }&=0 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 2 \\
y \left (0\right ) &= -2 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.224 |
|
| \begin{align*}
x^{\prime }+y&=0 \\
x+y^{\prime }&=0 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
5.957 |
|
| \begin{align*}
x^{\prime }+x-2 y&=0 \\
y^{\prime }+x+4 y&=0 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
5.928 |
|
| \begin{align*}
x^{\prime }&=-y \\
y^{\prime }&=2 x+2 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.001 |
|
| \begin{align*}
x^{\prime }+2 y&=3 t \\
y^{\prime }-2 x&=4 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.006 |
|
| \begin{align*}
x^{\prime }+x&=y+{\mathrm e}^{t} \\
y+y^{\prime }&=x+{\mathrm e}^{t} \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
5.953 |
|
| \begin{align*}
x^{\prime }+y^{\prime }&=y+{\mathrm e}^{t} \\
2 x^{\prime }+y^{\prime }+2 y&=\cos \left (t \right ) \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.060 |
|
| \begin{align*}
x^{\prime }&=y-z \\
y^{\prime }&=x+y \\
z^{\prime }&=x+z \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 2 \\
z \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.652 |
|
| \begin{align*}
x^{\prime }&=4 y+z \\
y^{\prime }&=z \\
z^{\prime }&=4 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 5 \\
y \left (0\right ) &= 0 \\
z \left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.629 |
|
| \begin{align*}
x^{\prime }+2 y^{\prime }+x+y+z&=0 \\
x^{\prime }+y^{\prime }+x+z&=0 \\
z^{\prime }+2 y^{\prime }-y&=0 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 1 \\
z \left (0\right ) &= -4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.745 |
|
| \begin{align*}
x^{\prime }-2 y^{\prime }&=1 \\
x^{\prime }-x+y&=0 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.571 |
|
| \begin{align*}
2 x^{\prime }-3 y+y^{\prime }&=0 \\
x^{\prime }+y^{\prime }&=t \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.405 |
|
| \begin{align*}
x^{\prime }+2 y^{\prime }-y&=1 \\
2 x^{\prime }+y&=0 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.377 |
|
| \begin{align*}
x^{\prime }+y^{\prime }-x&=\cos \left (t \right ) \\
x^{\prime }+2 y^{\prime }&=0 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.417 |
|
| \begin{align*}
3 x^{\prime }-y&=2 t \\
x^{\prime }+y^{\prime }-y&=0 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.385 |
|
| \begin{align*}
x^{\prime }+4 y^{\prime }-y&=0 \\
x^{\prime }+2 y&={\mathrm e}^{-t} \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.385 |
|
| \begin{align*}
x^{\prime }+2 x-y^{\prime }&=0 \\
x^{\prime }+x+y&=t^{2} \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.405 |
|
| \begin{align*}
x^{\prime }+4 x-y&=0 \\
x^{\prime }+y^{\prime }&=t \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.383 |
|
| \begin{align*}
x^{\prime }+y^{\prime }+x-y&=0 \\
x^{\prime }+2 y^{\prime }+x&=1 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.397 |
|
| \begin{align*}
x^{\prime }-x+2 y^{\prime }&=0 \\
4 x^{\prime }+3 y^{\prime }+y&=-6 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.474 |
|
| \begin{align*}
y_{1}^{\prime }-2 y_{2}^{\prime }+3 y_{1}&=0 \\
y_{1}-4 y_{2}^{\prime }+3 y_{3}&=t \\
y_{1}-2 y_{2}^{\prime }+3 y_{3}^{\prime }&=-1 \\
\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*} |
✓ |
✓ |
✓ |
✓ |
9.293 |
|