| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
x^{\prime \prime \prime \prime }+x^{\prime \prime \prime }&=t \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
x^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.214 |
|
| \begin{align*}
x^{\prime \prime \prime \prime }-3 x^{\prime \prime \prime }+2 x^{\prime }-5 x&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.116 |
|
| \begin{align*}
t^{3} x^{\prime \prime \prime }+4 t^{2} x^{\prime \prime }+3 x^{\prime } t +x&=0 \\
\end{align*} |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.209 |
|
| \begin{align*}
x^{\prime }&=x \\
y^{\prime }&=-3 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.395 |
|
| \begin{align*}
x^{\prime }&=a x \\
y^{\prime }&=a y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.316 |
|
| \begin{align*}
x^{\prime }&=a x+y \\
y^{\prime }&=a y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.383 |
|
| \begin{align*}
x^{\prime }&=3 x-y \\
y^{\prime }&=x+3 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.618 |
|
| \begin{align*}
x^{\prime }&=2 x+y \\
y^{\prime }&=-x+2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.560 |
|
| \begin{align*}
x^{\prime }&=x+3 y \\
y^{\prime }&=-3 x+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.576 |
|
| \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*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.454 |
|
| \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*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.560 |
|
| \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*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.532 |
|
| \begin{align*}
x^{\prime }&=3 x+t \\
y^{\prime }&=-y+2 t \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.639 |
|
| \begin{align*}
x^{\prime }&=-x \\
y^{\prime }&=3 x+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.482 |
|
| \begin{align*}
x^{\prime }&=2 x+6 y \\
y^{\prime }&=x+3 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.533 |
|
| \begin{align*}
x^{\prime }&=2 x+6 y+{\mathrm e}^{t} \\
y^{\prime }&=x+3 y-{\mathrm e}^{t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.833 |
|
| \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*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.516 |
|
| \begin{align*}
x^{\prime }&=x+2 y+2 t \\
y^{\prime }&=3 y+t^{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.763 |
|
| \begin{align*}
x^{\prime }&=3 x-y \\
y^{\prime }&=2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.460 |
|
| \begin{align*}
x^{\prime }&=x \\
y^{\prime }&=4 x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.465 |
|
| \begin{align*}
x^{\prime }&=x \\
y^{\prime }&=3 x+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.376 |
|
| \begin{align*}
x^{\prime }&=x+3 y \\
y^{\prime }&=x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| \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*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.712 |
|
| \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*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.529 |
|
| \begin{align*}
x^{\prime }&=x+3 y+2 t \\
y^{\prime }&=x-y+t^{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.201 |
|
| \begin{align*}
x^{\prime }&=x+2 y+{\mathrm e}^{t} \\
y^{\prime }&=x-2 y-{\mathrm e}^{t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.446 |
|
| \begin{align*}
x^{\prime }&=x \\
y^{\prime }&=x-y \\
z^{\prime }&=-2 x+2 z \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.853 |
|
| \begin{align*}
x^{\prime }&=x \\
y^{\prime }&=2 y+z \\
z^{\prime }&=x+3 z \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.812 |
|
| \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*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.795 |
|
| \begin{align*}
x^{\prime }&=x \\
y^{\prime }&=2 y+z \\
z^{\prime }&=x+z \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.671 |
|
| \begin{align*}
x^{\prime \prime \prime }-2 x^{\prime \prime }+3 x^{\prime }+x&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.115 |
|
| \begin{align*}
x^{\prime }&=x+z \\
y^{\prime }&=-y+z \\
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*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.734 |
|
| \begin{align*}
x^{\prime }&=2 x \\
y^{\prime }&=2 y+z \\
z^{\prime }&=-x-z \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.654 |
|
| \begin{align*}
x^{\prime }&=\left (a -2\right ) x+y \\
y^{\prime }&=-x+\left (a -2\right ) y \\
z^{\prime }&=-a z \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.034 |
|
| \begin{align*}
x^{\prime }+y t&=-1 \\
x^{\prime }+y^{\prime }&=2 \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.048 |
|
| \begin{align*}
x^{\prime }+y&=3 t \\
y^{\prime }-x^{\prime } t&=0 \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.043 |
|
| \begin{align*}
x^{\prime }-y t&=1 \\
y^{\prime }-x^{\prime } t&=3 \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✗ |
0.047 |
|
| \begin{align*}
t^{2} x^{\prime }-y&=1 \\
y^{\prime }-2 x&=0 \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✗ |
0.040 |
|
| \begin{align*}
x^{\prime }-y&=3 \\
y^{\prime }-3 x^{\prime }&=-2 x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.731 |
|
| \begin{align*}
x^{\prime } t +y^{\prime }&=1 \\
y^{\prime }+x+{\mathrm e}^{x^{\prime }}&=1 \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✗ |
0.105 |
|
| \begin{align*}
x x^{\prime }+y&=2 t \\
y^{\prime }+2 x^{2}&=1 \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✗ |
0.049 |
|
| \begin{align*}
x^{\prime }&=1+x \\
y^{\prime }&=x+3 y-1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.673 |
|
| \begin{align*}
x^{\prime }&=x+3 y+a \\
y^{\prime }&=x-y+b \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.848 |
|
| \begin{align*}
x^{\prime }&=a x+y \\
y^{\prime }&=-2 x+b y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.474 |
|
| \begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=-2 c x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.715 |
|
| \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*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.532 |
|
| \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*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.665 |
|
| \begin{align*}
L x^{\prime \prime }+g \sin \left (x\right )&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
40.904 |
|
| \begin{align*}
x^{\prime }&=x-x y \\
y^{\prime }&=-y+x y \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✗ |
0.056 |
|
| \begin{align*}
x^{\prime }&=2 x-7 x y-a x \\
y^{\prime }&=-y+4 x y-a y \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✗ |
✗ |
0.046 |
|
| \begin{align*}
x^{\prime }&=2 x-2 x y \\
y^{\prime }&=-y+x y \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✗ |
0.062 |
|
| \begin{align*}
x^{\prime }&=x-4 x y \\
y^{\prime }&=-2 y+x y \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✗ |
0.046 |
|
| \begin{align*}
x^{\prime }&=x \left (3-y\right ) \\
y^{\prime }&=y \left (x-5\right ) \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✗ |
0.049 |
|
| \begin{align*}
x^{\prime \prime }&=x-x^{3} \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
5.801 |
|
| \begin{align*}
x^{\prime \prime }&=x^{3}-x \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[[_2nd_order, _missing_x], _Duffing, [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✗ |
✗ |
7.604 |
|
| \begin{align*}
x^{\prime \prime }&=x^{3}-x \\
x \left (0\right ) &= 2 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x], _Duffing, [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✗ |
✗ |
1.976 |
|
| \begin{align*}
x^{\prime \prime }&=x^{3}-x \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x], _Duffing, [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✗ |
✗ |
1.002 |
|
| \begin{align*}
x^{\prime \prime }&=x-x^{3} \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
1.379 |
|
| \begin{align*}
x^{\prime \prime }&=x-x^{3} \\
x \left (0\right ) &= 2 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
1.697 |
|
| \begin{align*}
x^{\prime \prime }&=x-x^{3} \\
x \left (0\right ) &= \frac {\sqrt {2}}{2} \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✗ |
✗ |
29.751 |
|
| \begin{align*}
x^{\prime \prime }+x+8 x^{7}&=0 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= a \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✗ |
✗ |
5.731 |
|
| \begin{align*}
x^{\prime \prime }+x+\frac {x^{2}}{3}&=0 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✗ |
✗ |
2.513 |
|
| \begin{align*}
x^{\prime \prime }-x+3 x^{2}&=0 \\
x \left (0\right ) &= {\frac {1}{2}} \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
2.873 |
|
| \begin{align*}
x^{\prime \prime }-x+3 x^{2}&=0 \\
x \left (0\right ) &= {\frac {1}{4}} \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✗ |
✓ |
✗ |
✗ |
478.628 |
|
| \begin{align*}
x^{\prime \prime }-x+3 x^{2}&=0 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✗ |
✗ |
1.236 |
|
| \begin{align*}
x^{\prime \prime }-x+3 x^{2}&=0 \\
x \left (0\right ) &= -{\frac {1}{4}} \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✗ |
✗ |
2.228 |
|
| \begin{align*}
t x^{\prime \prime }&=x \\
\end{align*}
Series expansion around \(t=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
3.629 |
|
| \begin{align*}
t x^{\prime \prime }&=x^{\prime } \\
\end{align*}
Series expansion around \(t=0\). |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.777 |
|
| \begin{align*}
t x^{\prime \prime }&=x t +1 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Series expansion around \(t=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
✗ |
0.864 |
|
| \begin{align*}
x^{\prime \prime }+x^{\prime } t +x&=0 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Series expansion around \(t=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.477 |
|
| \begin{align*}
4 t^{2} x^{\prime \prime }+4 x^{\prime } t -x&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.944 |
|
| \begin{align*}
t^{2} x^{\prime \prime }+3 x^{\prime } t&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.760 |
|
| \begin{align*}
t^{2} x^{\prime \prime }-3 x^{\prime } t +\left (4-t \right ) x&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.867 |
|
| \begin{align*}
t^{2} x^{\prime \prime }+x^{\prime } t +x t^{2}&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
0.714 |
|
| \begin{align*}
t^{2} x^{\prime \prime }+x^{\prime } t +x t^{2}&=0 \\
x^{\prime }\left (0\right ) &= a \\
\end{align*} |
[_Lienard] |
✗ |
✗ |
✗ |
✓ |
38.700 |
|
| \begin{align*}
t^{2} x^{\prime \prime }+x^{\prime } t +\left (t^{2}-1\right ) x&=0 \\
x^{\prime }\left (0\right ) &= a \\
\end{align*} |
[_Bessel] |
✗ |
✓ |
✓ |
✗ |
43.345 |
|
| \begin{align*}
t^{2} x^{\prime \prime }+x^{\prime } t +\left (-m^{2}+t^{2}\right ) x&=0 \\
x \left (0\right ) &= 0 \\
\end{align*} |
[_Bessel] |
✗ |
✗ |
✓ |
✓ |
46.713 |
|
| \begin{align*}
s y^{\prime \prime }+\lambda y&=0 \\
y \left (0\right ) &= 0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✗ |
0.485 |
|
| \begin{align*}
t^{2} x^{\prime \prime }+x^{\prime } t +x t^{2}&=\lambda x \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✓ |
✓ |
28.497 |
|
| \begin{align*}
x^{\prime }+x&={\mathrm e}^{t} \\
x \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.424 |
|
| \begin{align*}
x^{\prime }+x&=t \\
x \left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.327 |
|
| \begin{align*}
x^{\prime \prime }-2 x^{\prime }+x&=0 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.206 |
|
| \begin{align*}
x^{\prime \prime }-4 x^{\prime }+3 x&=1 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.278 |
|
| \begin{align*}
x^{\prime \prime \prime \prime }+x^{\prime \prime }&=0 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
x^{\prime \prime }\left (0\right ) &= 0 \\
x^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.362 |
|
| \begin{align*}
x^{\prime }-x&=\operatorname {Heaviside}\left (t -a \right ) \\
x \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
36.665 |
|
| \begin{align*}
x^{\prime }+x&=\operatorname {Heaviside}\left (t -a \right ) \\
x \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
7.824 |
|
| \begin{align*}
x^{\prime }-x&=k \delta \left (t \right ) \\
x \left (0\right ) &= a \\
\end{align*}
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.212 |
|
| \begin{align*}
x^{\prime \prime }+x&=g \left (t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.359 |
|
| \begin{align*}
x^{\prime \prime }&=\delta \left (-t +a \right ) \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.984 |
|
| \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*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✗ |
0.431 |
|
| \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*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✗ |
0.405 |
|
| \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*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✗ |
0.355 |
|
| \begin{align*}
x^{\prime }&=-2 x+y \\
y^{\prime }&=7 x-4 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✗ |
0.695 |
|
| \begin{align*}
x^{\prime }&=-x-y \\
y^{\prime }&=4 x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✗ |
0.534 |
|
| \begin{align*}
x^{\prime }&=x-y \\
y^{\prime }&=3 x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✗ |
1.266 |
|
| \begin{align*}
x^{\prime }&=-2 a x-y \\
y^{\prime }&=\left (a^{2}+9\right ) x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✗ |
0.740 |
|
| \begin{align*}
x^{\prime }&=-x+4 y \\
y^{\prime }&=3 x-5 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✗ |
0.517 |
|
| \begin{align*}
x^{\prime \prime }+2 x^{\prime }-x&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.377 |
|
| \begin{align*}
x^{\prime \prime }+2 x^{\prime }+x&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.428 |
|
| \begin{align*}
x^{\prime \prime }+2 h x^{\prime }+k^{2} x&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.081 |
|