Link to actual problem [9555] \[ \boxed {\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -v \left (v -1\right ) y=0} \]
type detected by program
{"unknown"}
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 {LegendreP}\left (v -1, i x \right )}\right ] \\ \end{align*}
\begin{align*} \\ \left [R &= x, S \left (R \right ) &= \frac {y}{\operatorname {LegendreQ}\left (v -1, i x \right )}\right ] \\ \end{align*}