| # |
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]] |
✓ |
✓ |
✓ |
✓ |
0.171 |
|
| \begin{align*}
x^{\prime \prime \prime \prime }-3 x^{\prime \prime \prime }+2 x^{\prime }-5 x&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.101 |
|
| \begin{align*}
t^{3} x^{\prime \prime \prime }+4 t^{2} x^{\prime \prime }+3 t x^{\prime }+x&=0 \\
\end{align*} |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.177 |
|
| \begin{align*}
x^{\prime }&=x \\
y^{\prime }&=-3 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.347 |
|
| \begin{align*}
x^{\prime }&=a x \\
y^{\prime }&=a y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.282 |
|
| \begin{align*}
x^{\prime }&=a x+y \\
y^{\prime }&=a y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.333 |
|
| \begin{align*}
x^{\prime }&=3 x-y \\
y^{\prime }&=x+3 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.470 |
|
| \begin{align*}
x^{\prime }&=2 x+y \\
y^{\prime }&=-x+2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.459 |
|
| \begin{align*}
x^{\prime }&=x+3 y \\
y^{\prime }&=-3 x+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.482 |
|
| \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 |
✓ |
✓ |
✓ |
✓ |
0.365 |
|
| \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 |
✓ |
✓ |
✓ |
✓ |
0.472 |
|
| \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 |
✓ |
✓ |
✓ |
✓ |
0.436 |
|
| \begin{align*}
x^{\prime }&=3 x+t \\
y^{\prime }&=-y+2 t \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.550 |
|
| \begin{align*}
x^{\prime }&=-x \\
y^{\prime }&=3 x+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.393 |
|
| \begin{align*}
x^{\prime }&=2 x+6 y \\
y^{\prime }&=x+3 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.480 |
|
| \begin{align*}
x^{\prime }&=2 x+6 y+{\mathrm e}^{t} \\
y^{\prime }&=x+3 y-{\mathrm e}^{t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.708 |
|
| \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 |
✓ |
✓ |
✓ |
✓ |
0.436 |
|
| \begin{align*}
x^{\prime }&=x+2 y+2 t \\
y^{\prime }&=3 y+t^{2} \\
\end{align*} | system_of_ODEs | ✓ | ✓ | ✓ | ✓ | 0.783 |
|
| \begin{align*}
x^{\prime }&=3 x-y \\
y^{\prime }&=2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.382 |
|
| \begin{align*}
x^{\prime }&=x \\
y^{\prime }&=4 x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.398 |
|
| \begin{align*}
x^{\prime }&=x \\
y^{\prime }&=3 x+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.335 |
|
| \begin{align*}
x^{\prime }&=x+3 y \\
y^{\prime }&=x-y \\
\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 |
✓ |
✓ |
✓ |
✓ |
0.574 |
|
| \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 |
✓ |
✓ |
✓ |
✓ |
0.435 |
|
| \begin{align*}
x^{\prime }&=x+3 y+2 t \\
y^{\prime }&=x-y+t^{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.001 |
|
| \begin{align*}
x^{\prime }&=x+2 y+{\mathrm e}^{t} \\
y^{\prime }&=x-2 y-{\mathrm e}^{t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
2.277 |
|
| \begin{align*}
x^{\prime }&=x \\
y^{\prime }&=x-y \\
z^{\prime }&=-2 x+2 z \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.687 |
|
| \begin{align*}
x^{\prime }&=x \\
y^{\prime }&=2 y+z \\
z^{\prime }&=x+3 z \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.658 |
|
| \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 |
✓ |
✓ |
✓ |
✓ |
0.711 |
|
| \begin{align*}
x^{\prime }&=x \\
y^{\prime }&=2 y+z \\
z^{\prime }&=x+z \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.563 |
|
| \begin{align*}
x^{\prime \prime \prime }-2 x^{\prime \prime }+3 x^{\prime }+x&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.110 |
|
| \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*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| \begin{align*}
x^{\prime }&=2 x \\
y^{\prime }&=2 y+z \\
z^{\prime }&=-x-z \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.648 |
|
| \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 |
✓ |
✓ |
✓ |
✓ |
1.045 |
|
| \begin{align*}
x^{\prime }+t y&=-1 \\
x^{\prime }+y^{\prime }&=2 \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.039 |
|
| \begin{align*}
x^{\prime }+y&=3 t \\
y^{\prime }-t x^{\prime }&=0 \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.043 |
|
| \begin{align*}
x^{\prime }-t y&=1 \\
y^{\prime }-t x^{\prime }&=3 \\
\end{align*} | system_of_ODEs | ✗ | ✓ | ✓ | ✗ | 0.041 |
|
| \begin{align*}
t^{2} x^{\prime }-y&=1 \\
y^{\prime }-2 x&=0 \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✗ |
0.038 |
|
| \begin{align*}
x^{\prime }-y&=3 \\
y^{\prime }-3 x^{\prime }&=-2 x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.712 |
|
| \begin{align*}
t x^{\prime }+y^{\prime }&=1 \\
y^{\prime }+x+{\mathrm e}^{x^{\prime }}&=1 \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✗ |
0.074 |
|
| \begin{align*}
x x^{\prime }+y&=2 t \\
y^{\prime }+2 x^{2}&=1 \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✗ |
0.050 |
|
| \begin{align*}
x^{\prime }&=1+x \\
y^{\prime }&=x+3 y-1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.726 |
|
| \begin{align*}
x^{\prime }&=x+3 y+a \\
y^{\prime }&=x-y+b \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.806 |
|
| \begin{align*}
x^{\prime }&=a x+y \\
y^{\prime }&=-2 x+b y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.978 |
|
| \begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=-2 c x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.697 |
|
| \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 |
✓ |
✓ |
✓ |
✓ |
0.507 |
|
| \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 |
✓ |
✓ |
✓ |
✓ |
0.643 |
|
| \begin{align*}
L x^{\prime \prime }+g \sin \left (x\right )&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
48.559 |
|
| \begin{align*}
x^{\prime }&=x-x y \\
y^{\prime }&=-y+x y \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✗ |
0.050 |
|
| \begin{align*}
x^{\prime }&=2 x-7 x y-a x \\
y^{\prime }&=-y+4 x y-a y \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✗ |
✗ |
0.057 |
|
| \begin{align*}
x^{\prime }&=2 x-2 x y \\
y^{\prime }&=-y+x y \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✗ |
0.052 |
|
| \begin{align*}
x^{\prime }&=x-4 x y \\
y^{\prime }&=-2 y+x y \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✗ |
0.049 |
|
| \begin{align*}
x^{\prime }&=x \left (3-y\right ) \\
y^{\prime }&=y \left (x-5\right ) \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✗ |
0.054 |
|
| \begin{align*}
x^{\prime \prime }&=x-x^{3} \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
4.690 |
|
| \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]] | ✓ | ✓ | ✗ | ✗ | 7.876 |
|
| \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]] |
✓ |
✓ |
✗ |
✗ |
5.146 |
|
| \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]] |
✓ |
✓ |
✗ |
✗ |
3.771 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
2.670 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
3.625 |
|
| \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]] |
✓ |
✓ |
✗ |
✗ |
7.002 |
|
| \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]] |
✓ |
✓ |
✗ |
✗ |
9.929 |
|
| \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]] |
✓ |
✓ |
✗ |
✗ |
27.558 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
24.089 |
|
| \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]] |
✓ |
✓ |
✗ |
✗ |
34.511 |
|
| \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]] |
✓ |
✓ |
✗ |
✗ |
4.403 |
|
| \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]] |
✓ |
✓ |
✗ |
✗ |
49.572 |
|
| \begin{align*}
t x^{\prime \prime }&=x \\
\end{align*} Series expansion around \(t=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
4.394 |
|
| \begin{align*}
t x^{\prime \prime }&=x^{\prime } \\
\end{align*} Series expansion around \(t=0\). |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.669 |
|
| \begin{align*}
t x^{\prime \prime }&=t x+1 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} Series expansion around \(t=0\). | [[_2nd_order, _linear, _nonhomogeneous]] | ✗ | ✗ | ✗ | ✗ | 0.754 |
|
| \begin{align*}
x^{\prime \prime }+t x^{\prime }+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]] |
✓ |
✓ |
✓ |
✓ |
0.436 |
|
| \begin{align*}
4 t^{2} x^{\prime \prime }+4 t x^{\prime }-x&=0 \\
\end{align*} Series expansion around \(t=0\). |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.794 |
|
| \begin{align*}
t^{2} x^{\prime \prime }+3 t x^{\prime }&=0 \\
\end{align*} Series expansion around \(t=0\). |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.668 |
|
| \begin{align*}
t^{2} x^{\prime \prime }-3 t x^{\prime }+\left (-t +4\right ) x&=0 \\
\end{align*} Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.758 |
|
| \begin{align*}
t^{2} x^{\prime \prime }+t x^{\prime }+t^{2} x&=0 \\
\end{align*} Series expansion around \(t=0\). |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
0.617 |
|
| \begin{align*}
t^{2} x^{\prime \prime }+t x^{\prime }+t^{2} x&=0 \\
x^{\prime }\left (0\right ) &= a \\
\end{align*} |
[_Lienard] |
✗ |
✗ |
✗ |
✓ |
2.070 |
|
| \begin{align*}
t^{2} x^{\prime \prime }+t x^{\prime }+\left (t^{2}-1\right ) x&=0 \\
x^{\prime }\left (0\right ) &= a \\
\end{align*} |
[_Bessel] |
✗ |
✓ |
✓ |
✗ |
31.033 |
|
| \begin{align*}
t^{2} x^{\prime \prime }+t x^{\prime }+\left (-m^{2}+t^{2}\right ) x&=0 \\
x \left (0\right ) &= 0 \\
\end{align*} |
[_Bessel] |
✗ |
✗ |
✓ |
✓ |
2.873 |
|
| \begin{align*}
s y^{\prime \prime }+\lambda y&=0 \\
y \left (0\right ) &= 0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✗ |
0.401 |
|
| \begin{align*}
t^{2} x^{\prime \prime }+t x^{\prime }+t^{2} x&=\lambda x \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✓ |
✓ |
2.608 |
|
| \begin{align*}
x^{\prime }+x&={\mathrm e}^{t} \\
x \left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.288 |
|
| \begin{align*}
x^{\prime }+x&=t \\
x \left (0\right ) &= -1 \\
\end{align*} Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.226 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.187 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.273 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.329 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
17.793 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
6.896 |
|
| \begin{align*}
x^{\prime }-x&=k \delta \left (t \right ) \\
x \left (0\right ) &= a \\
\end{align*} Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.196 |
|
| \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]] | ✓ | ✓ | ✓ | ✓ | 1.314 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
1.104 |
|
| \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 |
✓ |
✓ |
✓ |
✗ |
0.380 |
|
| \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 |
✓ |
✓ |
✓ |
✗ |
0.353 |
|
| \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 |
✓ |
✓ |
✓ |
✗ |
0.303 |
|
| \begin{align*}
x^{\prime }&=-2 x+y \\
y^{\prime }&=7 x-4 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✗ |
0.692 |
|
| \begin{align*}
x^{\prime }&=-x-y \\
y^{\prime }&=4 x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✗ |
0.517 |
|
| \begin{align*}
x^{\prime }&=x-y \\
y^{\prime }&=3 x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✗ |
1.274 |
|
| \begin{align*}
x^{\prime }&=-2 a x-y \\
y^{\prime }&=\left (a^{2}+9\right ) x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✗ |
0.725 |
|
| \begin{align*}
x^{\prime }&=-x+4 y \\
y^{\prime }&=3 x-5 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✗ |
0.505 |
|
| \begin{align*}
x^{\prime \prime }+2 x^{\prime }-x&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.303 |
|
| \begin{align*}
x^{\prime \prime }+2 x^{\prime }+x&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.340 |
|
| \begin{align*}
x^{\prime \prime }+2 h x^{\prime }+k^{2} x&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.864 |
|