Link to actual problem [8123] \[ \boxed {t y^{\prime \prime }+\left (-t^{2}+1\right ) y^{\prime }+4 y t=0} \]
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 &= 1-t^{2}+\frac {1}{8} t^{4}\right ] \\ \left [R &= t, S \left (R \right ) &= \frac {y}{1-t^{2}+\frac {1}{8} t^{4}}\right ] \\ \end{align*}