Substitution method for exact differential equation help I'm trying to use the substitution method to solve for a differential equation. The equation is 
$y'=(x+y-3)^2 $, $ y(0) = 0$ 
I used substitution to get $u=x+y-3$ and $u'=1+y'$. So the final equation is $$u'-1=u^2$$ However, I am unsure how to get the final y= equation with the initial value included. I would really appreciate someone's help on how to solve.

After rearranging, the equation is separable:
$$u' = u^2 + 1 \implies \frac{u'}{u^2 + 1} = 1 \implies \int \frac{u'(x)}{u(x)^2 + 1} dx = \int dx$$
The left-hand integral is then simply $\arctan u$.
