Link to actual problem [12277] \[ \boxed {\left (x^{2}-x \right ) y^{\prime \prime }+\left (2 x^{2}+4 x -3\right ) y^{\prime }+8 y x=0} \]
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 &= 0, \underline {\hspace {1.25 ex}}\eta &= \frac {1}{x^{2} \left (-1+x \right )^{2}}\right ] \\ \\ \end{align*}
\begin{align*} \left [\underline {\hspace {1.25 ex}}\xi &= 0, \underline {\hspace {1.25 ex}}\eta &= \frac {{\mathrm e}^{-2 x}}{\left (-1+x \right )^{2}}\right ] \\ \\ \end{align*}