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.

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- Sep 20th 2007, 04:45 AMfifthrapiersPopulation 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. - Sep 20th 2007, 05:55 AMtopsquark
Did you notice that the differential equation is separable?

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

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

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

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

-Dan