Link to actual problem [8121] \[ \boxed {t^{2} y^{\prime \prime }+\left (t^{2}-3 t \right ) y^{\prime }+3 y=0} \]
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 [R &= t, S \left (R \right ) &= \frac {{\mathrm e}^{t} y}{t^{3}}\right ] \\ \end{align*}
\begin{align*} \\ \left [R &= t, S \left (R \right ) &= \frac {{\mathrm e}^{t} y}{t \left (\operatorname {expIntegral}_{1}\left (-t \right ) t^{2}+{\mathrm e}^{t} t +{\mathrm e}^{t}\right )}\right ] \\ \end{align*}