Link to actual problem [12046] \[ \boxed {x^{\prime \prime \prime \prime }-5 x^{\prime \prime }+4 x={\mathrm e}^{t}} \]
type detected by program
{"higher_order_linear_constant_coefficients_ODE"}
type detected by Maple
[[_high_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*} \\ \\ \end{align*}
\begin{align*} \\ \left [R &= t, S \left (R \right ) &= \frac {\ln \left (t \,{\mathrm e}^{t}+6 x\right )}{6}\right ] \\ \end{align*}