Link to actual problem [1264] \[ \boxed {\left (10-2 x \right ) y^{\prime \prime }+\left (x +1\right ) y=0} \] With initial conditions \begin {align*} [y \left (2\right ) = 2, y^{\prime }\left (2\right ) = -4] \end {align*}
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 {WhittakerM}\left (-\frac {3 \sqrt {2}}{2}, \frac {1}{2}, \sqrt {2}\, \left (x -5\right )\right )\right ] \\ \left [R &= x, S \left (R \right ) &= \frac {y}{\operatorname {WhittakerM}\left (-\frac {3 \sqrt {2}}{2}, \frac {1}{2}, \sqrt {2}\, \left (x -5\right )\right )}\right ] \\ \end{align*}
\begin{align*} \left [\underline {\hspace {1.25 ex}}\xi &= 0, \underline {\hspace {1.25 ex}}\eta &= \operatorname {WhittakerW}\left (-\frac {3 \sqrt {2}}{2}, \frac {1}{2}, \sqrt {2}\, \left (x -5\right )\right )\right ] \\ \left [R &= x, S \left (R \right ) &= \frac {y}{\operatorname {WhittakerW}\left (-\frac {3 \sqrt {2}}{2}, \frac {1}{2}, \sqrt {2}\, \left (x -5\right )\right )}\right ] \\ \end{align*}