Link to actual problem [6015] \[ \boxed {x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y=0} \]
type detected by program
{"higher_order_ODE_non_constant_coefficients_of_type_Euler"}
type detected by Maple
[[_3rd_order, _with_linear_symmetries]]
Maple symgen result This shows Maple’s found \(\xi ,\eta \) and the corresponding canonical coordinates \(R,S\)\begin{align*} \\ \left [R &= x, S \left (R \right ) &= \frac {y}{x}\right ] \\ \end{align*}
\begin{align*} \\ \\ \end{align*}
\begin{align*} \\ \left [R &= x, S \left (R \right ) &= \frac {y}{x^{2}}\right ] \\ \end{align*}
\begin{align*} \\ \\ \end{align*}
\begin{align*} \left [\underline {\hspace {1.25 ex}}\xi &= \frac {x^{2}}{3}, \underline {\hspace {1.25 ex}}\eta &= x y\right ] \\ \left [R &= \frac {y}{x^{3}}, S \left (R \right ) &= -\frac {3}{x}\right ] \\ \end{align*}