Link to actual problem [8271] \[ \boxed {2 \left (t^{2}-5 t +6\right ) y^{\prime \prime }+\left (2 t -3\right ) y^{\prime }-8 y=0} \]
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 &= 0, \underline {\hspace {1.25 ex}}\eta &= t^{2}-\frac {13}{3} t +\frac {37}{8}\right ] \\ \left [R &= t, S \left (R \right ) &= \frac {y}{t^{2}-\frac {13}{3} t +\frac {37}{8}}\right ] \\ \end{align*}