Link to actual problem [11073] \[ \boxed {\left (a \,x^{n}+b x +c \right ) y^{\prime \prime }-a n \left (n -1\right ) x^{-2+n} y=0} \]
type detected by program
{"exact linear second order ode", "second_order_integrable_as_is"}
type detected by Maple
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
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}{a \,x^{n}+b x +c}\right ] \\ \end{align*}