Link to actual problem [10167] Solve \begin {gather*} \boxed {9 y^{\prime \prime \prime } y^{2}-45 y^{\prime } y^{\prime \prime } y+40 \left (y^{\prime }\right )^{3}=0} \end {gather*}
type detected by program
{"unknown"}
type detected by Maple
[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]]
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*} \\ \\ \end{align*}
\begin{align*} \left [\underline {\hspace {1.25 ex}}\xi &= -\frac {x^{2}}{3}, \underline {\hspace {1.25 ex}}\eta &= x y\right ] \\ \left [R &= x^{3} y, S \left (R \right ) &= \frac {3}{x}\right ] \\ \end{align*}