Link to actual problem [5490] \[ \boxed {\sin \left (x \right ) y^{\prime \prime }-2 \cos \left (x \right ) y^{\prime }-y \sin \left (x \right )=0} \] With the expansion point for the power series method at \(x = 0\).
type detected by program
{"second order series method. Regular singular point. Difference is integer"}
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}{\cos \left (x \right )}\right ] \\ \end{align*}
\begin{align*} \\ \left [R &= x, S \left (R \right ) &= \frac {y}{\ln \left (\cos \left (x \right )+i \sin \left (x \right )\right ) \cos \left (x \right )-i \sin \left (x \right )}\right ] \\ \end{align*}