Link to actual problem [2751] \[ \boxed {y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y=9 \,{\mathrm e}^{-x}} \]
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 [\underline {\hspace {1.25 ex}}\xi &= 0, \underline {\hspace {1.25 ex}}\eta &= \frac {4 y}{9}+{\mathrm e}^{-x}\right ] \\ \left [R &= x, S \left (R \right ) &= \frac {9 \ln \left (4 \,{\mathrm e}^{x} y+9\right )}{4}\right ] \\ \end{align*}