Link to actual problem [5807] \[ \boxed {\frac {y}{x}+\left (y^{3}+\ln \left (x \right )\right ) y^{\prime }=0} \]
type detected by program
{"exact"}
type detected by Maple
[_exact, [_1st_order, `_with_symmetry_[F(x),G(y)]`]]
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 {1}{y^{3}+\ln \left (x \right )}\right ] \\ \left [R &= x, S \left (R \right ) &= \frac {y^{4}}{4}+y \ln \left (x \right )\right ] \\ \end{align*}