# Population Model

• September 20th 2007, 04:45 AM
fifthrapiers
Population Model
We have a population model given by the differential equation:

dP/dt = (k*cos(t))*P, where k is a pos. constant, and P(T) undergoes yearly seasonal changes.

Assume that P(0) = P_(0).

1.) Solve the Dif. Equation and graph the solution.
• September 20th 2007, 05:55 AM
topsquark
Quote:

Originally Posted by fifthrapiers
We have a population model given by the differential equation:

dP/dt = (k*cos(t))*P, where k is a pos. constant, and P(T) undergoes yearly seasonal changes.

Assume that P(0) = P_(0).

1.) Solve the Dif. Equation and graph the solution.

Did you notice that the differential equation is separable?

$\frac{dP}{dt} = (k~cos(t))P$

$\frac{dP}{P} = k~cos(t)~dt$

$\int \frac{dP}{P} = \int k~cos(t)~dt$

So integrate both sides and use your initial condition to evaluate the arbitrary constant in terms of $P_0$.

-Dan