Assume that the number of fish P(t) after t years grows according to the logistic equation

Question

dP/dt= P(a-bP) = bP(300 − P)

Find the solution of this DE (with the given initial value at t = 0) as a separable equation. Your solution formula will contain b as an unknown parameter.

I know you use partial fractions, but I get caught up by bP part. I didn't know if you carried it all the way to the end or what...

Answer 1

well, apparently

P(a-bP) = bP(300 − P)
aP - bP^2 = 300bP - bP^2
so, a = 300b

dP/dt = P(300b-bP) = bP(300-P)

Try plugging that in. You already know what the logistic growth function looks like, so that should guide your efforts some.