Link to actual problem [2007] \[ \boxed {y+y^{3}+4 \left (x y^{2}-1\right ) y^{\prime }=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
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 &= \frac {1}{\left (y^{2}+1\right )^{2}}, \underline {\hspace {1.25 ex}}\eta &= 0\right ] \\ \\ \end{align*}