Link to actual problem [9721] \[ \boxed {y^{\prime \prime }+\frac {2 y^{\prime }}{x}+\frac {c y}{x^{2} \left (x a +b \right )^{2}}=0} \]
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 [\underline {\hspace {1.25 ex}}\xi &= \frac {x^{2} a}{b}+x, \underline {\hspace {1.25 ex}}\eta &= 0\right ] \\ \\ \end{align*}