Link to actual problem [9673] \[ \boxed {y^{\prime \prime }-\frac {\left (a +b \right ) y^{\prime }}{x^{2}}+\frac {\left (x \left (a +b \right )+a b \right ) y}{x^{4}}=0} \]
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 &= \frac {y}{x}, S \left (R \right ) &= -\frac {1}{x}\right ] \\ \end{align*}