Link to actual problem [10171] Solve \begin {gather*} \boxed {y^{\prime \prime } y^{\prime \prime \prime }-a \sqrt {\left (y^{\prime \prime }\right )^{2} b^{2}+1}=0} \end {gather*}
type detected by program
{"unknown"}
type detected by Maple
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]
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 [R &= x, S \left (R \right ) &= \frac {y}{x}\right ] \\ \end{align*}