Link to actual problem [2741] \[ \boxed {y^{\prime \prime }+y^{\prime }-2 y=4 x^{2}+5} \]
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*} \\ \left [R &= \frac {\left (4 x^{2}+4 x +2 y+11\right ) {\mathrm e}^{-2 x}}{2}, S \left (R \right ) &= x\right ] \\ \end{align*}