You need to integrate both sides...
.
Now follow your instincts to use partial fractions... You can then simplify using logarithm rules.
dp/dt = P - P^2
ok i am supposed to separate the variables. im having a rough time with this problem..i know to get the p on one side and the dt on the other, and then i used partial fractions to try to integrate and thats when i had problems..
ln(p) + ln(1-p) = dt
i dont know im not even sure if thats right and suppose it is right, then when i raise it to e the p's cancel out?? any help would be appreciated.