Excellent! How did you get that? I would be inclined to use "partial fractions" writing as . But integrating that should involve a "ln(1-x)" and I don't see that in your answer.
I'll actually give you the full question and hopefully someone can help me.
dy/dt= y(1-y) and they want us to find the general solution... I know its a seperable equation so I get dy/(y(1-y)) = 1 dt and we're ment to integrate it... though I dont know how. And the answer they give is y(t)= ke^t/(ke^t +1)