Link to actual problem [7154] \[ \boxed {y^{\prime \prime }-2 y^{\prime }-y x=x^{2}+2} \]
type detected by program
{"second_order_airy"}
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 &= x, S \left (R \right ) &= \frac {{\mathrm e}^{-x} y}{\operatorname {AiryAi}\left (1+x \right )}\right ] \\ \end{align*}
\begin{align*} \\ \left [R &= x, S \left (R \right ) &= \frac {{\mathrm e}^{-x} y}{\operatorname {AiryBi}\left (1+x \right )}\right ] \\ \end{align*}
\begin{align*} \\ \\ \end{align*}