Originally Posted by

**penney21** 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:

P'(t)=(b-kP)P-hP

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

equals:

(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.