Link to actual problem [11162] \[ \boxed {\left (x^{2}+y^{2}+2 y\right ) y^{\prime }=-2 x} \]
type detected by program
{"exactWithIntegrationFactor"}
type detected by Maple
[_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]
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 {x^{2}+y^{2}}{x^{2}+y^{2}+2 y}\right ] \\ \\ \end{align*}