Link to actual problem [7542] \[ \boxed {\left (x^{2}+1\right ) y^{\prime \prime }-8 x y^{\prime }+20 y=0} \]
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 &= \frac {x^{2}}{5}+\frac {1}{5}, \underline {\hspace {1.25 ex}}\eta &= y x\right ] \\ \left [R &= \frac {y}{\left (x^{2}+1\right )^{\frac {5}{2}}}, S \left (R \right ) &= 5 \arctan \left (x \right )\right ] \\ \end{align*}