Link to actual problem [9766] \[ \boxed {y^{\prime \prime }-\frac {\phi ^{\prime }\left (x \right ) y^{\prime }}{\phi \left (x \right )-\phi \left (a \right )}+\frac {\left (-n \left (1+n \right ) \left (\phi \left (x \right )-\phi \left (a \right )\right )^{2}+\frac {d^{2}}{d a^{2}}\phi \left (a \right )\right ) y}{\phi \left (x \right )-\phi \left (a \right )}=0} \]
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 \(R,S\)