Link to actual problem [10170] Solve \begin {gather*} \boxed {\left (\left (y^{\prime }\right )^{2}+1\right ) y^{\prime \prime \prime }-\left (3 y^{\prime }+a \right ) \left (y^{\prime \prime }\right )^{2}=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], [_3rd_order, _reducible, _mu_poly_yn]]
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 &= \frac {y}{x}, S \left (R \right ) &= \ln \left (x \right )\right ] \\ \end{align*}
\begin{align*} \\ \left [R &= x^{2}+y^{2}, S \left (R \right ) &= -\arctan \left (\frac {x}{y}\right )\right ] \\ \end{align*}