Link to actual problem [7000] \[ \boxed {x \left (x -2\right )^{2} y^{\prime \prime }-2 \left (x -2\right ) y^{\prime }+2 y=0} \] With the expansion point for the power series method at \(x = 0\).
type detected by program
{"second order series method. Regular singular point. Repeated root"}
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 [R &= x, S \left (R \right ) &= \frac {y}{-2+x}\right ] \\ \end{align*}
\begin{align*} \\ \left [R &= \frac {y}{-2+x}, S \left (R \right ) &= \frac {\ln \left (-2+x \right )}{2}-\frac {\ln \left (x \right )}{2}\right ] \\ \end{align*}