I'm having some trouble with a Differential Equations Population problem.
Here is the background for the question..
The DE governing a fish pop. P(t) with harvesting proportional to the population is given by:
where b>0 is birthrate, kP is deathrate, where k>0, and h is the harvesting rate. Model assumes that the death rate per individual is proportional to the pop. size. An equilibrium point for the DE is a value of P so that P'(t)=0.
I worked out the integral to be the following:
1 / [(b-h)-kP]P dp = dt
(lnP - ln(b-h-kP)) / (b-h) + C
However, I'm having trouble answering this part of the question..
Determine h so that Y is maximized, and find this Y. This is the maximum sustainable yield.
How would I go about solving that part? Any help would be greatly appreciated.