Link to actual problem [7204] \[ \boxed {y^{\prime \prime \prime }+y^{\prime }+y=x} \] With initial conditions \begin {align*} [y^{\prime }\left (0\right ) = 0, y \left (0\right ) = 0, y^{\prime \prime }\left (0\right ) = 1] \end {align*}
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*} \\ \\ \end{align*}