The equation y' = f(x,y) with

   f(x,y) = 2 + 2x + y^2 + x y^2

implies

   f_x = partial f on variable x = 2 + y^2

and then

   f_x/f = (2+y^2)/(2+2x+y^2+(x)y^2)

This fraction looks like it depends on y, but it does not.

Experiment, if you will, setting x=0, x=1, x=-1, x=2 to see
if variable y appears. It does not, because common factors cancel.
Example: For x=0, the fraction equals 1, which is independent of y.

THE LESSON: Just because you see variable y in the fraction does not
mean it can't cancel out, due to common factors. Always substitute values
for x, to make sure the y does not cancel out.