Find the function $\displaystyle f$ such that $\displaystyle f'(x) = f(x)(1 - f(x))$ and $\displaystyle f(0) = \frac{1}{2}$.

We are currently covering separable differentiable eq. and this problem is throwing me for a loop.

Any hints for a starting point?

I know $\displaystyle f(x) = \int(f(x)(1 - f(x)))$ thus $\displaystyle \frac{1}{2} = \int(f(0)(1 - f(0)))$. Then I am lost. How can you find f if you can't separate the x's and y's?