Link to actual problem [1796] \[ \boxed {\left ({\mathrm e}^{t}-1\right ) y^{\prime \prime }+y^{\prime } {\mathrm e}^{t}+y=0} \] With the expansion point for the power series method at \(t = 0\).
type detected by program
{"second order series method. Regular singular point. Repeated root"}
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*} \\ \\ \end{align*}
\begin{align*} \\ \left [R &= t, S \left (R \right ) &= \frac {{\mathrm e}^{t} y}{{\mathrm e}^{t}+\ln \left ({\mathrm e}^{t}-1\right )}\right ] \\ \end{align*}