Link to actual problem [15473] \[ \boxed {\ln \left (x \right ) y^{\prime \prime }-y \sin \left (x \right )=0} \] With initial conditions \begin {align*} [y \left ({\mathrm e}\right ) = {\mathrm e}^{-1}, y^{\prime }\left ({\mathrm e}\right ) = 0] \end {align*}
With the expansion point for the power series method at \(x = {\mathrm e}\).
type detected by program
{"second order series method. Ordinary point", "second order series method. Taylor series method"}
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*}