Link to actual problem [7210] \[ \boxed {5 x^{5} y^{\prime \prime \prime \prime }+4 x^{4} y^{\prime \prime \prime }+x^{2} y^{\prime }+y x=0} \]
type detected by program
{"higher_order_ODE_non_constant_coefficients_of_type_Euler"}
type detected by Maple
[[_high_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 [R &= x, S \left (R \right ) &= \frac {y}{\moverset {4}{\munderset {\textit {\_a} &=1}{\sum }}x^{\operatorname {RootOf}\left (5 \textit {\_Z}^{4}-26 \textit {\_Z}^{3}+43 \textit {\_Z}^{2}-21 \textit {\_Z} +1, \operatorname {index} &=\textit {\_a} \right )} \textit {\_C}_{\textit {\_a}}}\right ] \\ \end{align*}
\begin{align*} \\ \\ \end{align*}
\begin{align*} \\ \left [R &= \frac {y}{x}, S \left (R \right ) &= \ln \left (x \right )\right ] \\ \end{align*}