Link to actual problem [2203] \[ \boxed {y^{\prime \prime }+3 y=3 \,{\mathrm e}^{-4 x}} \]
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 [\underline {\hspace {1.25 ex}}\xi &= 0, \underline {\hspace {1.25 ex}}\eta &= {\mathrm e}^{i \sqrt {3}\, x}\right ] \\ \left [R &= x, S \left (R \right ) &= {\mathrm e}^{-i \sqrt {3}\, x} y\right ] \\ \end{align*}
\begin{align*} \\ \\ \end{align*}