Link to actual problem [14851] \[ \boxed {y^{\prime \prime }-6 y^{\prime }+13 y=3 \,{\mathrm e}^{-2 t}} \]
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*} \\ \left [R &= t, S \left (R \right ) &= \frac {{\mathrm e}^{-3 t} y}{\sin \left (2 t \right )}\right ] \\ \end{align*}
\begin{align*} \\ \left [R &= t, S \left (R \right ) &= \frac {{\mathrm e}^{-3 t} y}{\cos \left (2 t \right )}\right ] \\ \end{align*}
\begin{align*} \\ \\ \end{align*}