Link to actual problem [1255] \[ \boxed {\left (x +3\right ) y^{\prime \prime }+\left (1+2 x \right ) y^{\prime }-\left (2-x \right ) y=0} \] With initial conditions \begin {align*} [y \left (-1\right ) = 1, y^{\prime }\left (-1\right ) = 0] \end {align*}
With the expansion point for the power series method at \(x = -1\).
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*}
\begin{align*} \\ \left [R &= \frac {y \,{\mathrm e}^{x}}{x^{3}+9 x^{2}+27 x +27}, S \left (R \right ) &= -\ln \left (-x -3\right )\right ] \\ \end{align*}