Link to actual problem [9978] \[ \boxed {y^{\prime \prime }-2 a \left (c +b x +y\right ) \left ({y^{\prime }}^{2}+1\right )^{\frac {3}{2}}=0} \]
type detected by program
{"unknown"}
type detected by Maple
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]]
Maple symgen result This shows Maple’s found \(\xi ,\eta \) and the corresponding canonical coordinates \(R,S\)\begin{align*} \\ \\ \end{align*}