Link to actual problem [15196] \[ \frac {d^{3}}{d x^{3}}y \left (x \right ) = \sqrt {1-\left (\frac {d^{2}}{d x^{2}}y \left (x \right )\right )^{2}} \]
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*}