Link to actual problem [8122] \[ \boxed {t y^{\prime \prime }+y^{\prime } t +2 y=0} \]
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}{\left (t -2\right ) t}\right ] \\ \end{align*}
\begin{align*} \\ \left [R &= t, S \left (R \right ) &= \frac {{\mathrm e}^{t} y}{\left (t^{2}-2 t \right ) \operatorname {expIntegral}_{1}\left (-t \right )+\left (-1+t \right ) {\mathrm e}^{t}}\right ] \\ \end{align*}