Link to actual problem [1246] \[ \boxed {\left (2+x \right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }+3 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 4, y^{\prime }\left (0\right ) = 3] \end {align*}
With the expansion point for the power series method at \(x = 0\).
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 &= x, S \left (R \right ) &= \frac {{\mathrm e}^{x} y}{x \left (x -4\right ) \left (2+x \right )^{2}}\right ] \\ \end{align*}
\begin{align*} \\ \left [R &= x, S \left (R \right ) &= \frac {{\mathrm e}^{x} y}{{\mathrm e}^{-2} x \left (x -4\right ) \left (2+x \right )^{2} \operatorname {Ei}_{1}\left (-2-x \right )+\left (x^{3}-x^{2}-10 x -6\right ) {\mathrm e}^{x}}\right ] \\ \end{align*}