Issue with answer given to problem.

Question from pg 32 of Barron's AP Calculus

The solution of the differential equation $\frac{\mathrm{d}y}{\mathrm{d}x}=2xy^2$ for which $y = -1$ when $x = 1$ is

(A) $y = -\frac{1}{x^2}$ for $x \neq 0$

(B) $y = -\frac{1}{x^2}$ for $x > 0$

I think A is a possible solution; however the answer given is

This function is discontinuous at $x=0$. Since the particular solution much be differentiable in an interval containing the inital value $x = 1$, the domain is $x > 0$.

Giving (B) as the correct answer.

Even from the answer given in the book, should not (A) be an acceptiable answer as well because its domain contains the domain of (B)?

via Recent Questions - Mathematics - Stack Exchange http://math.stackexchange.com/questions/289655/issue-with-answer-given-to-problem