Link to actual problem [7569] \[ \boxed {2 y^{\prime \prime }+5 x y^{\prime }+\left (2 x^{2}+4\right ) y=0} \]
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*} \\ \\ \end{align*}
\begin{align*} \left [\underline {\hspace {1.25 ex}}\xi &= 0, \underline {\hspace {1.25 ex}}\eta &= {\mathrm e}^{-x^{2}} \operatorname {erf}\left (\frac {i \sqrt {3}\, x}{2}\right )\right ] \\ \left [R &= x, S \left (R \right ) &= \frac {{\mathrm e}^{x^{2}} y}{\operatorname {erf}\left (\frac {i \sqrt {3}\, x}{2}\right )}\right ] \\ \end{align*}