Link to actual problem [12043] \[ \boxed {x^{\prime \prime \prime }-6 x^{\prime \prime }+11 x^{\prime }-6 x={\mathrm e}^{-t}} \]
type detected by program
{"higher_order_linear_constant_coefficients_ODE"}
type detected by Maple
[[_3rd_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 {\ln \left (24 x \,{\mathrm e}^{t}+1\right )}{24}\right ] \\ \end{align*}