complicated differential equation problem

Question

(*The dot next to the N means N prime)

 

A lake is stocked with an initial population of fish N0 (at t = 0). Over time the fish

population N(t) grows according to the differential equation:
N(dot) = aN - (a/b)N^2 
,
where a and b are positive constants.
(a) Solve the differential equation to obtain the solution for N(t), using the initial
condition N(t = 0) = N0.
(b) What is the behaviour of N(t) as t → ∞?
(c) From your answer in part (a), determine the function t(N). Using this, evaluate how
long it takes for the fish population to reach 1000, given that the initial population
of fish is 10, and that a = 4 (in units of inverse years, i.e. year−1
) and b = 5000.

Answer 1

https://math.stackexchange.com/questions/1396099/how-to-find-the-solution-of-the-equation-y-ay-by2-a-b0