Solve the given differential equation by separation of varia

Solve the given differential equation by separation of variables. dP/dt = p - p^2 p=

dP / (P - P^2) = dt

dP/(P(1 - P)) = dt

dP/(P(P - 1)) =-dt

A/P + B/(P-1) = 1/(P(P-1))

A(P-1) + BP = 1

(A+B)P - A = 1

So, A = -1

Thus, B = 1

So, it becomes :

-1/(P) + 1/(P-1) * dP = -dt

ln|P - 1| - ln|P| = -t + C

ln|(P - 1)/P| = -t + C

ln|1 - 1/P| = -t + C

1 - 1/P = Ce^(-t)

1/P = 1 - Ce^(-t)

P = 1 / (1 - Ce^(-t)) ----> ANSWER