The problem is...
$$ \frac{dp}{dt} = 10p(1-p),$$ $p(0)=0.1$.
Solve and show that $p(t) \to 1$ as $t\to \infty.$
I know this is probably really simple, I was trying to go down the line of finding a general solution and then imposing the boundary condition. But I can't even see how to find the general solution... Then for the second bit taking the limit of the general solution $p(t)$?