| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
5 y^{\prime \prime } x +\left (30+3 x \right ) y^{\prime }+3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.673 |
|
| \begin{align*}
y^{\prime \prime } x -\left (x +4\right ) y^{\prime }+3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Laguerre] |
✓ |
✓ |
✓ |
✗ |
0.655 |
|
| \begin{align*}
2 y^{\prime \prime } x -\left (6+2 x \right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Laguerre] |
✓ |
✓ |
✓ |
✓ |
1.706 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (3 x^{2}+2 x \right ) y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.586 |
|
| \begin{align*}
\left (1-x \right ) x y^{\prime \prime }-3 y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.618 |
|
| \begin{align*}
y^{\prime \prime } x +y^{\prime }-y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.391 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +\left (x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.434 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (x^{2}-3 x \right ) y^{\prime }+4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.513 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x^{2} y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.609 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (2 x^{2}-3 x \right ) y^{\prime }+3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.539 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.625 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {9}{4}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.521 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x \left (x +1\right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.471 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +\left (x^{2}+1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.328 |
|
| \begin{align*}
y^{\prime \prime } x +3 y^{\prime }+y x&=0 \\
\end{align*} |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
0.300 |
|
| \begin{align*}
y^{\prime \prime } x -y^{\prime }+36 x^{3} y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.884 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-5 y^{\prime } x +\left (8+x \right ) y&=0 \\
\end{align*} | [[_2nd_order, _with_linear_symmetries]] | ✓ | ✓ | ✓ | ✓ | 0.203 |
|
| \begin{align*}
36 x^{2} y^{\prime \prime }+60 y^{\prime } x +\left (9 x^{3}-5\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.195 |
|
| \begin{align*}
16 x^{2} y^{\prime \prime }+24 y^{\prime } x +\left (144 x^{3}+1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.213 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +\left (x^{2}+1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.309 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }-12 y^{\prime } x +\left (15+16 x \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.195 |
|
| \begin{align*}
16 x^{2} y^{\prime \prime }-\left (-144 x^{3}+5\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.292 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }-3 y^{\prime } x -2 \left (-x^{5}+14\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.221 |
|
| \begin{align*}
y^{\prime \prime }+x^{4} y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✗ |
0.524 |
|
| \begin{align*}
y^{\prime \prime } x +4 x^{3} y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✗ |
0.533 |
|
| \begin{align*}
y^{\prime \prime } x +2 y^{\prime }+y x&=0 \\
\end{align*} |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
0.296 |
|
| \begin{align*}
y^{\prime }&=y^{2}+x^{2} \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
39.950 |
|
| \begin{align*}
y^{\prime }&=y^{2}+x^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
8.754 |
|
| \begin{align*}
y^{\prime }&=y^{2}+x^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_Riccati, _special]] |
✗ |
✓ |
✓ |
✗ |
8.248 |
|
| \begin{align*}
x^{\prime \prime }+4 x&=0 \\
x \left (0\right ) &= 5 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.207 |
|
| \begin{align*}
x^{\prime \prime }+9 x&=0 \\
x \left (0\right ) &= 3 \\
x^{\prime }\left (0\right ) &= 4 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.156 |
|
| \begin{align*}
x^{\prime \prime }-x^{\prime }-2 x&=0 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.151 |
|
| \begin{align*}
x^{\prime \prime }+8 x^{\prime }+15 x&=0 \\
x \left (0\right ) &= 2 \\
x^{\prime }\left (0\right ) &= -3 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.144 |
|
| \begin{align*}
x^{\prime \prime }+x&=\sin \left (2 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.194 |
|
| \begin{align*}
x^{\prime \prime }+4 x&=\cos \left (t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.174 |
|
| \begin{align*}
x^{\prime \prime }+x&=\cos \left (3 t \right ) \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. | [[_2nd_order, _linear, _nonhomogeneous]] | ✓ | ✓ | ✓ | ✓ | 0.186 |
|
| \begin{align*}
x^{\prime \prime }+9 x&=1 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.147 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.144 |
|
| \begin{align*}
x^{\prime \prime }+3 x^{\prime }+2 x&=t \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.178 |
|
| \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*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.392 |
|
| \begin{align*}
x^{\prime \prime }+6 x^{\prime }+25 x&=0 \\
x \left (0\right ) &= 2 \\
x^{\prime }\left (0\right ) &= 3 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.161 |
|
| \begin{align*}
x^{\prime \prime }-6 x^{\prime }+8 x&=2 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.150 |
|
| \begin{align*}
x^{\prime \prime }-4 x&=3 t \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.147 |
|
| \begin{align*}
x^{\prime \prime }+4 x^{\prime }+8 x&={\mathrm e}^{-t} \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.202 |
|
| \begin{align*}
x^{\prime \prime \prime }+x^{\prime \prime }-6 x^{\prime }&=0 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
x^{\prime \prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.188 |
|
| \begin{align*}
x^{\prime \prime \prime \prime }-x&=0 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 0 \\
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]] |
✓ |
✓ |
✓ |
✓ |
0.223 |
|
| \begin{align*}
x^{\prime \prime \prime \prime }+x&=0 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
x^{\prime \prime }\left (0\right ) &= 0 \\
x^{\prime \prime \prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.326 |
|
| \begin{align*}
x^{\prime \prime \prime \prime }+13 x^{\prime \prime }+36 x&=0 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 2 \\
x^{\prime \prime }\left (0\right ) &= 0 \\
x^{\prime \prime \prime }\left (0\right ) &= -13 \\
\end{align*} Using Laplace transform method. |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.247 |
|
| \begin{align*}
x^{\prime \prime \prime \prime }+8 x^{\prime \prime }+16 x&=0 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
x^{\prime \prime }\left (0\right ) &= 0 \\
x^{\prime \prime \prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.234 |
|
| \begin{align*}
x^{\prime \prime \prime \prime }+2 x^{\prime \prime }+x&={\mathrm e}^{2 t} \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
x^{\prime \prime }\left (0\right ) &= 0 \\
x^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.283 |
|
| \begin{align*}
x^{\prime \prime }+4 x^{\prime }+13 x&=t \,{\mathrm e}^{-t} \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.228 |
|
| \begin{align*}
x^{\prime \prime }+6 x^{\prime }+18 x&=\cos \left (2 t \right ) \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= -1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.221 |
|
| \begin{align*}
x^{\prime \prime }+9 x&=6 \cos \left (3 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.151 |
|
| \begin{align*}
x^{\prime \prime }+\frac {2 x^{\prime }}{5}+\frac {226 x}{25}&=6 \,{\mathrm e}^{-\frac {t}{5}} \cos \left (3 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.191 |
|
| \begin{align*}
t x^{\prime \prime }+\left (t -2\right ) x^{\prime }+x&=0 \\
x \left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. | [[_2nd_order, _exact, _linear, _homogeneous]] | ✓ | ✓ | ✓ | ✗ | 0.153 |
|
| \begin{align*}
t x^{\prime \prime }+\left (3 t -1\right ) x^{\prime }+3 x&=0 \\
x \left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.152 |
|
| \begin{align*}
t x^{\prime \prime }-\left (4 t +1\right ) x^{\prime }+2 \left (2 t +1\right ) x&=0 \\
x \left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.159 |
|
| \begin{align*}
t x^{\prime \prime }+2 \left (-1+t \right ) x^{\prime }-2 x&=0 \\
x \left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.167 |
|
| \begin{align*}
t x^{\prime \prime }-2 x^{\prime }+t x&=0 \\
x \left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[_Lienard] |
✓ |
✓ |
✓ |
✗ |
0.152 |
|
| \begin{align*}
t x^{\prime \prime }+\left (4 t -2\right ) x^{\prime }+\left (13 t -4\right ) x&=0 \\
x \left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.171 |
|
| \begin{align*}
x^{\prime \prime }+4 x&=f \left (t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.724 |
|
| \begin{align*}
x^{\prime \prime }+2 x^{\prime }+x&=f \left (t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.305 |
|
| \begin{align*}
x^{\prime \prime }+4 x^{\prime }+13 x&=f \left (t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.123 |
|
| \begin{align*}
x^{\prime \prime }+4 x&=\delta \left (t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.132 |
|
| \begin{align*}
x^{\prime \prime }+4 x&=\delta \left (t \right )+\delta \left (t -\pi \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.568 |
|
| \begin{align*}
x^{\prime \prime }+4 x^{\prime }+4 x&=1+\delta \left (t -2\right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.533 |
|
| \begin{align*}
x^{\prime \prime }+2 x^{\prime }+x&=t +\delta \left (t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.148 |
|
| \begin{align*}
x^{\prime \prime }+2 x^{\prime }+2 x&=2 \delta \left (t -\pi \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.359 |
|
| \begin{align*}
x^{\prime \prime }+9 x&=\delta \left (t -3 \pi \right )+\cos \left (3 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.408 |
|
| \begin{align*}
x^{\prime \prime }+4 x^{\prime }+5 x&=\delta \left (t -\pi \right )+\delta \left (t -2 \pi \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.166 |
|
| \begin{align*}
x^{\prime \prime }+2 x^{\prime }+x&=\delta \left (t \right )-\delta \left (t -2\right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.529 |
|
| \begin{align*}
x^{\prime \prime }+4 x&=f \left (t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.173 |
|
| \begin{align*}
x^{\prime \prime }+6 x^{\prime }+9 x&=f \left (t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.312 |
|
| \begin{align*}
x^{\prime \prime }+6 x^{\prime }+8 x&=f \left (t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. | [[_2nd_order, _linear, _nonhomogeneous]] | ✓ | ✓ | ✓ | ✓ | 0.421 |
|
| \begin{align*}
x^{\prime \prime }+4 x^{\prime }+8 x&=f \left (t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.914 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.315 |
|
| \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 |
✓ |
✓ |
✓ |
✓ |
0.392 |
|
| \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*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.395 |
|
| \begin{align*}
x^{\prime }&=\frac {y}{2} \\
y^{\prime }&=-8 x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.373 |
|
| \begin{align*}
x^{\prime }&=8 y \\
y^{\prime }&=-2 x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.368 |
|
| \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*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.415 |
|
| \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*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.431 |
|
| \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*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.543 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-9 x+6 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.320 |
|
| \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*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.187 |
|
| \begin{align*}
x^{\prime }&=-x+3 y \\
y^{\prime }&=2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.323 |
|
| \begin{align*}
x^{\prime }&=x-2 y \\
y^{\prime }&=2 x-3 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.308 |
|
| \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*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.420 |
|
| \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*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.414 |
|
| \begin{align*}
x^{\prime }&=-3 x-4 y \\
y^{\prime }&=2 x+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.500 |
|
| \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*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.572 |
|
| \begin{align*}
x^{\prime }&=4 x+y+2 t \\
y^{\prime }&=-2 x+y \\
\end{align*} | system_of_ODEs | ✓ | ✓ | ✓ | ✓ | 0.641 |
|
| \begin{align*}
x^{\prime }&=2 x+y \\
y^{\prime }&=x+2 y-{\mathrm e}^{2 t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.564 |
|
| \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*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.950 |
|
| \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*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.394 |
|
| \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*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.925 |
|
| \begin{align*}
x^{\prime }&=x+2 y+z \\
y^{\prime }&=6 x-y \\
z^{\prime }&=-x-2 y-z \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.711 |
|
| \begin{align*}
x^{\prime }&=x-2 y \\
y^{\prime }&=-4 x+4 y-2 z \\
z^{\prime }&=-4 y+4 z \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
49.599 |
|
| \begin{align*}
x^{\prime }&=y+z+{\mathrm e}^{-t} \\
y^{\prime }&=x+z \\
z^{\prime }&=x+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.889 |
|