Link to actual problem [10175] Solve \begin {gather*} \boxed {9 \left (y^{\prime \prime }\right )^{2} y^{\left (5\right )}-45 y^{\prime \prime } y^{\prime \prime \prime } y^{\prime \prime \prime \prime }+40 y^{\prime \prime \prime }=0} \end {gather*}
type detected by program
{"unknown"}
type detected by Maple
[[_high_order, _missing_x], [_high_order, _missing_y], [_high_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*} \\ \left [R &= x, S \left (R \right ) &= \frac {y}{x}\right ] \\ \end{align*}
\begin{align*} \\ \left [R &= y-\frac {x^{2}}{2}, S \left (R \right ) &= x\right ] \\ \end{align*}
\begin{align*} \left [\underline {\hspace {1.25 ex}}\xi &= \frac {x}{3}, \underline {\hspace {1.25 ex}}\eta &= y\right ] \\ \left [R &= \frac {y}{x^{3}}, S \left (R \right ) &= 3 \ln \left (x \right )\right ] \\ \end{align*}