Link to actual problem [9681] \[ \boxed {y^{\prime \prime }-\frac {\left (2 x^{2}-1\right ) y^{\prime }}{x^{3}}+\frac {2 y}{x^{4}}=0} \]
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 &= -5+\frac {1}{x^{2}}\right ] \\ \left [R &= x, S \left (R \right ) &= \frac {x^{2} y}{-5 x^{2}+1}\right ] \\ \end{align*}