| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \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*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.473 |
|
| \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*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.437 |
|
| \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*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.420 |
|
| \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*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.422 |
|
| \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*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.421 |
|
| \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*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.441 |
|
| \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*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.415 |
|
| \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*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.557 |
|
| \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*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.034 |
|
| \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*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.065 |
|
| \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*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.142 |
|
| \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*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.665 |
|
| \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*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.408 |
|
| \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*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.493 |
|
| \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*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.534 |
|
| \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*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.537 |
|
| \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*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.580 |
|
| \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*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.526 |
|
| \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*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.556 |
|
| \begin{align*}
x^{\prime }&=-3 x+10 y \\
y^{\prime }&=-x+3 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.480 |
|
| \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*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.353 |
|
| \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*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.554 |
|
| \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*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.388 |
|
| \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*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.375 |
|
| \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*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.332 |
|
| \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*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.359 |
|
| \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*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.363 |
|
| \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*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.360 |
|
| \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*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.381 |
|
| \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*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.437 |
|
| \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*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.426 |
|
| \begin{align*}
x^{\prime }&=2 y \\
y^{\prime }&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.270 |
|
| \begin{align*}
x^{\prime }&=-2 y \\
y^{\prime }&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.269 |
|
| \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*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.412 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }-7 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.285 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-12 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.309 |
|
| \begin{align*}
x^{\prime }&=\frac {y}{10} \\
y^{\prime }&=\frac {z}{5} \\
z^{\prime }&=\frac {2 x}{5} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
2.207 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-x \\
z^{\prime }&=2 z \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.700 |
|
| \begin{align*}
x^{\prime }&=-2 x+3 y \\
y^{\prime }&=3 x-2 y \\
z^{\prime }&=-z \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.620 |
|
| \begin{align*}
x^{\prime }&=x+3 z \\
y^{\prime }&=-y \\
z^{\prime }&=-3 x+z \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.715 |
|
| \begin{align*}
x^{\prime }&=x \\
y^{\prime }&=2 y-z \\
z^{\prime }&=-y+2 z \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.515 |
|
| \begin{align*}
x^{\prime }&=-2 x+y \\
y^{\prime }&=-2 y \\
z^{\prime }&=-z \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.483 |
|
| \begin{align*}
x^{\prime }&=-2 x+y \\
y^{\prime }&=-2 y \\
z^{\prime }&=z \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.494 |
|
| \begin{align*}
x^{\prime }&=-x+2 y \\
y^{\prime }&=2 x-4 y \\
z^{\prime }&=-z \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.623 |
|
| \begin{align*}
x^{\prime }&=-x+2 y \\
y^{\prime }&=2 x-4 y \\
z^{\prime }&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| \begin{align*}
x^{\prime }&=-2 x+y \\
y^{\prime }&=-2 y+z \\
z^{\prime }&=-2 z \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.468 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=z \\
z^{\prime }&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.395 |
|
| \begin{align*}
x^{\prime }&=2 x-y \\
y^{\prime }&=-2 y+3 z \\
z^{\prime }&=-x+3 y-z \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.161 |
|
| \begin{align*}
x^{\prime }&=-4 x+3 y \\
y^{\prime }&=-y+z \\
z^{\prime }&=5 x-5 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.045 |
|
| \begin{align*}
x^{\prime }&=-10 x+10 y \\
y^{\prime }&=28 x-y \\
z^{\prime }&=-\frac {8 z}{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.954 |
|
| \begin{align*}
x^{\prime }&=-y+z \\
y^{\prime }&=-x+z \\
z^{\prime }&=z \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.524 |
|
| \(\left [\begin {array}{cc} 1 & 0 \\ 0 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.250 |
|
| \(\left [\begin {array}{cc} 0 & 1 \\ 2 & 0 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.305 |
|
| \begin{align*}
x^{\prime }&=3 x \\
y^{\prime }&=-2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.306 |
|
| \(\left [\begin {array}{cc} 1 & 0 \\ 2 & 3 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.260 |
|
| \begin{align*}
x^{\prime }&=0 \\
y^{\prime }&=x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.336 |
|
| \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*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.870 |
|
| \begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=-2 x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.437 |
|
| \begin{align*}
x^{\prime }&=-3 x+y \\
y^{\prime }&=-x+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.576 |
|
| \begin{align*}
x^{\prime }&=-3 x+y \\
y^{\prime }&=-x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.572 |
|
| \begin{align*}
x^{\prime }&=-x+y \\
y^{\prime }&=-2 x+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.419 |
|
| \begin{align*}
x^{\prime }&=2 x \\
y^{\prime }&=x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.359 |
|
| \begin{align*}
x^{\prime }&=3 x+y \\
y^{\prime }&=-x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.552 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-4 x-4 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.366 |
|
| \begin{align*}
x^{\prime }&=-3 x-3 y \\
y^{\prime }&=2 x+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.017 |
|
| \begin{align*}
y^{\prime \prime }+5 y^{\prime }+6 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.452 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+5 y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.482 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.496 |
|
| \begin{align*}
y^{\prime \prime }+2 y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= -\sqrt {2} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.030 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-6 y&={\mathrm e}^{4 t} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.424 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+8 y&=2 \,{\mathrm e}^{-3 t} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.444 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=5 \,{\mathrm e}^{3 t} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.441 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+13 y&={\mathrm e}^{-t} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.477 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+13 y&=-3 \,{\mathrm e}^{-2 t} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.441 |
|
| \begin{align*}
y^{\prime \prime }+7 y^{\prime }+10 y&={\mathrm e}^{-2 t} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.530 |
|
| \begin{align*}
y^{\prime \prime }-5 y^{\prime }+4 y&={\mathrm e}^{4 t} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.526 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }-6 y&=4 \,{\mathrm e}^{-3 t} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.484 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+8 y&={\mathrm e}^{-t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.546 |
|
| \begin{align*}
y^{\prime \prime }+7 y^{\prime }+12 y&=3 \,{\mathrm e}^{-t} \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.579 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+13 y&=-3 \,{\mathrm e}^{-2 t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.589 |
|
| \begin{align*}
y^{\prime \prime }+7 y^{\prime }+10 y&={\mathrm e}^{-2 t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.654 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+3 y&={\mathrm e}^{-\frac {t}{2}} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.568 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+3 y&={\mathrm e}^{-2 t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.547 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+3 y&={\mathrm e}^{-4 t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.548 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+20 y&={\mathrm e}^{-\frac {t}{2}} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.665 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+20 y&={\mathrm e}^{-2 t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.575 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+20 y&={\mathrm e}^{-4 t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.597 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&={\mathrm e}^{-t} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.517 |
|
| \begin{align*}
y^{\prime \prime }-5 y^{\prime }+4 y&=5 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.543 |
|
| \begin{align*}
y^{\prime \prime }+5 y^{\prime }+6 y&=2 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.527 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+10 y&=10 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.615 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+6 y&=-8 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.654 |
|
| \begin{align*}
y^{\prime \prime }+9 y&={\mathrm e}^{-t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.594 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=2 \,{\mathrm e}^{-2 t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.611 |
|
| \begin{align*}
y^{\prime \prime }+2 y&=-3 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.576 |
|
| \begin{align*}
y^{\prime \prime }+4 y&={\mathrm e}^{t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.584 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=6 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.596 |
|
| \begin{align*}
y^{\prime \prime }+2 y&=-{\mathrm e}^{t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.602 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=-3 t^{2}+2 t +3 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.592 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }&=3 t +2 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.285 |
|