Link to actual problem [14684] \[ \boxed {y^{\prime \prime \prime \prime }-10 y^{\prime \prime \prime }+38 y^{\prime \prime }-64 y^{\prime }+40 y=153 \,{\mathrm e}^{-t}} \]
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*} \\ \left [R &= t, S \left (R \right ) &= \frac {{\mathrm e}^{-2 t} y}{t}\right ] \\ \end{align*}
\begin{align*} \\ \left [R &= t, S \left (R \right ) &= \frac {{\mathrm e}^{-3 t} y}{\sin \left (t \right )}\right ] \\ \end{align*}
\begin{align*} \\ \left [R &= t, S \left (R \right ) &= \frac {{\mathrm e}^{-3 t} y}{\cos \left (t \right )}\right ] \\ \end{align*}
\begin{align*} \\ \\ \end{align*}
\begin{align*} \\ \\ \end{align*}