Link to actual problem [10895] \[ \boxed {x y^{\prime \prime }+\left (2 a x +b \right ) y^{\prime }+a \left (a x +b \right ) y=0} \]
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}{a}, \underline {\hspace {1.25 ex}}\eta &= x y\right ] \\ \\ \end{align*}