dy/dx = x+y^2
Do I use the intergrating factor and if so when I take y^2 to the other side to make it in the form p(x)y is the x just 1
This is a non-trivial DE. Here is WolframAlpha's solution in terms of Bessel functions. My copy of Mathematica Version 4 yields a solution in terms of Airy functions. I should also point out that the substitution
$\displaystyle u=y-\dfrac{x^{2}}{2}$
changes the DE into the Ricatti equation
$\displaystyle u'=\dfrac{x^{4}}{4}+x^{2}u+u^{2}.$
You could do a series solution method.