Question

(1+x²)xydy/dx=(1+y²)(1+x+x²)

Answer 1

I'm picking up my maths again after a number of years of rust and I'm having some trouble.

Obtain the solution to the DE:
dy/dx = (1+y2) / (1+x2)

My solution:
dy / (1+y2) = dx / (1+x2) 
knowing that dx/(1+x2) = arctan(x) (I believe this is a standard result? I've followed some trig to make myself comfortable with it in any case.)
arctan(y) = arctan(x) + A
y = x + C

The question I'm trying to solve is multiple choice and all the options I have are mixed fractions such as Cx/(1-Cx) or (1-Cx) / (x+C).
Intuitively it seems like y = x + C isn't an appropriate solution as that leads to dy/dx = 1 which seems contradictory.
Where am I going wrong?!