First Order Separable Differential equation

Hello,

I'm in Differential Equations and I have my midterm tomorrow... I can do most everything on my review sheet, but I'm a bit confused when it comes to a very simple initial value problem:

y' = x*y^3, y(0)=1

Here is what I'm doing:

I figure I can use separation of variables like so:

dy/y^3 = x*dx

..and after integrating both sides:

-1/(2*y^2) = (x^2)/2

solving for y gives:

y = 1/x

...which the initial condition y(0) = 1 does not hold.

Can somebody point out what I'm doing wrong? I'm quite confused and I'm running out of time...

Thanks in advance,

- Jeff