Link to actual problem [4744] \[ \boxed {y^{\prime \prime }+{\mathrm e}^{2 x} y-n^{2} y=0} \]
type detected by program
{"second_order_bessel_ode_form_A"}
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 &= x, S \left (R \right ) &= \frac {y}{\operatorname {BesselJ}\left (n , {\mathrm e}^{x}\right )}\right ] \\ \end{align*}
\begin{align*} \\ \left [R &= x, S \left (R \right ) &= \frac {y}{\operatorname {BesselY}\left (n , {\mathrm e}^{x}\right )}\right ] \\ \end{align*}