Link to actual problem [5154] \[ \boxed {x^{\prime \prime }+4 x^{\prime }+3 x={\mathrm e}^{-3 t}} \] With initial conditions \begin {align*} \left [x \left (0\right ) = {\frac {1}{2}}, x^{\prime }\left (0\right ) = -2\right ] \end {align*}
type detected by program
{"kovacic", "second_order_linear_constant_coeff"}
type detected by Maple
[[_2nd_order, _with_linear_symmetries]]
Maple symgen result This shows Maple’s found \(\xi ,\eta \) and the corresponding canonical coordinates \(R,S\)\begin{align*} \\ \\ \end{align*}
\begin{align*} \\ \\ \end{align*}