Hey its me again and I got stuck with my integration for first order ode

this is the question, and what I have done so far

$\displaystyle \frac{dy}{dt}=y(2-y)(y-1)$

$\displaystyle \int\frac{1}{y(2-y)(y-1)}dy=\int 1 dt$

$\displaystyle \int \frac{1}{y} + \frac{1}{2-y} + \frac{1}{y-1}dy=t+c$

$\displaystyle \log y - \log (2-y) + \log (y-1) = t+c$

$\displaystyle \log \frac{y(y-1)}{2-y}=t+c$

$\displaystyle \frac{y(y-1)}{2-y}=\log (t+c)$

I do not know how to continue from here, any clues?