# First order differential equation

What method would you use to solve:

$$(1+x^2)\frac{\mathrm{d}y}{\mathrm{d}x}=1+y^2 \;; \qquad y(2)=3$$

I am asking this because I only know two methods of solving the DEs - separation of variables and integrating factor. Since the separation of variables does not work here, I tried integrating factor, however, I don't know what to do with the $y^2$, because for the IF to work I need to get y on its own ($\frac{\mathrm{d}y}{\mathrm{d}x} + P(x)y = Q(x)$)

What method do I use to solve this?

• I think that separation of variables works fine. – Claude Leibovici Feb 12 '15 at 12:24

Why not separation? I get $$\frac{1}{1+y^2} \frac{\mathrm{d}y}{\mathrm{d}x} = \frac{1}{1+x^2}$$