Link to actual problem [9748] \[ \boxed {y^{\prime \prime }+\frac {a \left (-1+n \right ) \sin \left (2 x a \right ) y^{\prime }}{\cos \left (x a \right )^{2}}+\frac {n \,a^{2} \left (\left (-1+n \right ) \sin \left (x a \right )^{2}+\cos \left (x a \right )^{2}\right ) y}{\cos \left (x a \right )^{2}}=0} \]
type detected by program
{"second_order_change_of_variable_on_y_method_1"}
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 [R &= x, S \left (R \right ) &= \frac {\cos \left (x a \right )^{-n} \cos \left (x a \right ) y}{\sin \left (x a \right )}\right ] \\ \end{align*}