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Math Help - Population Model

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    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.
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    Quote Originally Posted by fifthrapiers View Post
    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
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