Link to actual problem [9800] \[ \boxed {y^{\prime \prime \prime }+3 y^{\prime \prime } f \left (x \right )+\left (f^{\prime }\left (x \right )+2 f \left (x \right )^{2}+4 g \left (x \right )\right ) y^{\prime }+\left (4 g \left (x \right ) f \left (x \right )+2 g^{\prime }\left (x \right )\right ) y=0} \]
type detected by program
{"unknown"}
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*}