Link to actual problem [9403] \[ \boxed {y^{\prime \prime }+2 a y^{\prime } \cot \left (x a \right )+\left (-a^{2}+b^{2}\right ) y=0} \]
type detected by program
{"kovacic"}
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}{\sin \left (b x \right ) \csc \left (x a \right )}\right ] \\ \end{align*}
\begin{align*} \\ \left [R &= x, S \left (R \right ) &= \frac {y}{\cos \left (b x \right ) \csc \left (x a \right )}\right ] \\ \end{align*}