Link to actual problem [10009] \[ \boxed {y^{\prime \prime } x^{4}-x \left (x^{2}+2 y\right ) y^{\prime }+4 y^{2}=0} \]
type detected by program
{"unknown"}
type detected by Maple
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
Maple symgen result This shows Maple’s found \(\xi ,\eta \) and the corresponding canonical coordinates \(R,S\)\begin{align*} \left [\underline {\hspace {1.25 ex}}\xi &= \frac {x}{2}, \underline {\hspace {1.25 ex}}\eta &= y\right ] \\ \left [R &= \frac {y}{x^{2}}, S \left (R \right ) &= 2 \ln \left (x \right )\right ] \\ \end{align*}
\begin{align*} \\ \left [R &= -\frac {\left (x^{2}-y\right ) \ln \left (x \right )}{x^{2}}, S \left (R \right ) &= \ln \left (\ln \left (x \right )\right )\right ] \\ \end{align*}