Link to actual problem [11729] \[ \boxed {y^{\prime \prime }-5 y^{\prime }+6 y=2-12 x +6 \,{\mathrm e}^{x}} \]
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*} \\ \\ \end{align*}
\begin{align*} \\ \\ \end{align*}
\begin{align*} \left [\underline {\hspace {1.25 ex}}\xi &= 1, \underline {\hspace {1.25 ex}}\eta &= 2 x +y -\frac {2}{3}\right ] \\ \left [R &= \frac {\left (3 y+6 x +4\right ) {\mathrm e}^{-x}}{3}, S \left (R \right ) &= x\right ] \\ \end{align*}