Link to actual problem [12527] \[ \boxed {y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y=2 x +3} \]
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 &= 1, \underline {\hspace {1.25 ex}}\eta &= \frac {x}{4}+\frac {y}{4}\right ] \\ \left [R &= \left (x +y+4\right ) {\mathrm e}^{-\frac {x}{4}}, S \left (R \right ) &= x\right ] \\ \end{align*}