Link to actual problem [14743] \[ \boxed {x^{3} y^{\prime \prime \prime }+10 x^{2} y^{\prime \prime }-20 x y^{\prime }+20 y=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 0, y^{\prime }\left (1\right ) = -1, y^{\prime \prime }\left (1\right ) = 1] \end {align*}
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*}