Link to actual problem [12038] \[ \boxed {x^{\prime \prime }+4 x^{\prime }+4 x={\mathrm e}^{2 t}} \]
type detected by program
{"kovacic", "second_order_linear_constant_coeff", "linear_second_order_ode_solved_by_an_integrating_factor"}
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*} \\ \left [R &= t, S \left (R \right ) &= \frac {{\mathrm e}^{2 t} x}{t}\right ] \\ \end{align*}
\begin{align*} \\ \\ \end{align*}