Link to actual problem [9855] \[ \boxed {f^{\prime }\left (x \right ) y^{\prime \prime }+f \left (x \right ) y^{\prime \prime \prime }+g^{\prime }\left (x \right ) y^{\prime }+g \left (x \right ) y^{\prime \prime }+h^{\prime }\left (x \right ) y+h \left (x \right ) y^{\prime }+A \left (x \right ) \left (y^{\prime \prime } f \left (x \right )+g \left (x \right ) y^{\prime }+h \left (x \right ) y\right )=0} \]
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 \(R,S\)