Link to actual problem [2210] \[ \boxed {y^{\prime \prime \prime }-y={\mathrm e}^{x}} \]
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 &= x, S \left (R \right ) &= -\frac {\ln \left (-3 y+x \,{\mathrm e}^{x}\right )}{3}\right ] \\ \end{align*}