Link to actual problem [14777] \[ \boxed {\left (x -2\right ) y^{\prime \prime }+y^{\prime }-y=0} \] With the expansion point for the power series method at \(x = -2\).
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 [\underline {\hspace {1.25 ex}}\xi &= 0, \underline {\hspace {1.25 ex}}\eta &= \operatorname {BesselI}\left (0, 2 \sqrt {-2+x}\right )\right ] \\ \left [R &= x, S \left (R \right ) &= \frac {y}{\operatorname {BesselI}\left (0, 2 \sqrt {-2+x}\right )}\right ] \\ \end{align*}
\begin{align*} \left [\underline {\hspace {1.25 ex}}\xi &= 0, \underline {\hspace {1.25 ex}}\eta &= \operatorname {BesselY}\left (0, 2 i \sqrt {-2+x}\right )\right ] \\ \left [R &= x, S \left (R \right ) &= \frac {y}{\operatorname {BesselY}\left (0, 2 i \sqrt {-2+x}\right )}\right ] \\ \end{align*}