Link to actual problem [9096] \[ \boxed {y^{\prime }+\frac {\left (\ln \left (y\right ) x +\ln \left (y\right )-x \right ) y}{x \left (1+x \right )}=0} \]
type detected by program
{"unknown"}
type detected by Maple
[[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]
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 &= 0, \underline {\hspace {1.25 ex}}\eta &= \frac {y}{x}\right ] \\ \\ \end{align*}