Link to actual problem [9578] \[ \boxed {\left (-a^{2}+x^{2}\right ) y^{\prime \prime }+8 y^{\prime } x +12 y=0} \]
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 &= y \left (-a^{2}+x^{2}\right )^{\frac {3}{2}}, S \left (R \right ) &= \frac {\ln \left (x -a \right )-\ln \left (x +a \right )}{2 a}\right ] \\ \end{align*}