Link to actual problem [2426] \[ \boxed {9 x^{2} y^{\prime \prime }+10 y^{\prime } x +y=x -1} \] With the expansion point for the power series method at \(x = 0\).
type detected by program
{"second order series method. Regular singular point. Complex roots"}
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*} \\ \left [R &= y-\frac {x}{11}, S \left (R \right ) &= \frac {\ln \left (x \right )}{11}\right ] \\ \end{align*}
\begin{align*} \\ \left [R &= \frac {y+1}{x}, S \left (R \right ) &= \ln \left (x \right )\right ] \\ \end{align*}