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Math Help - differencial equations

  1. #1
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    differencial equations

    hi
    Last edited by benjaminatkins; May 16th 2008 at 04:21 AM.
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  2. #2
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    Quote Originally Posted by benjaminatkins View Post
    Please help me answer the below... i am sooo stuck!

    A model for the spread of a disease through a population is given by the system:
    dx/dt = -4xy
    dy/dt = 4xy-500y
    Here x(t) represents the susceptible population, and y(t) represents the infected population. Solve the differential equations to find y in terms of x. Sketch and Justify a phase plane diagram.
    Discuss what this analysis tells you about the spread of the disease.
    Both of these differential equations are separable.
    \frac{dx}{dt} = -4xy may be rearranged as
    \frac{dx}{x} = -4y dt,

    and \frac{dy}{dt} = 4xy-500y may be rearranged as
    \frac{dy}{y} = (4x - 500) dt.

    You may also compute \frac{dy}{dx} = \frac{4xy - 500y}{-4xy}= -1 + \frac{125}{x} and then integrate that.
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