Link to actual problem [7546] \[ \boxed {\left (x^{2}+1\right ) y^{\prime \prime }-10 x y^{\prime }+28 y=0} \]
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 &= 1+\frac {7 x^{2} \left (5 x^{2}-6\right )}{3}\right ] \\ \left [R &= x, S \left (R \right ) &= \frac {y}{1+\frac {35}{3} x^{4}-14 x^{2}}\right ] \\ \end{align*}
\begin{align*} \\ \left [R &= x, S \left (R \right ) &= \frac {y}{x \left (x^{6}+21 x^{4}-105 x^{2}+35\right )}\right ] \\ \end{align*}