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Math Help - differential equation equilibria ?

  1. #1
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    Mar 2008
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    differential equation equilibria ?

    PLEASE HELP ME!!

    consider an interaction between two mutually inhibiting proteins with concentrations x and y, given by the differential equations:

    dx/dt = f(y)-x
    and
    dy/dt = g(x)-y

    where both f(y) and g(x) are decreasing functions.

    *show that equilibria occur when f[g(x)]=x

    how do i do the asterick part? any help would be very much appreciated..
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  2. #2
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    Joined
    Mar 2008
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    clarification

    Does equilibrium mean \frac{dx}{dt} = \frac{dy}{dt} = 0?
    Then f(y) = x and g(x) = y and you're done since substituting g(x) = y into the equation for f gives the desired result.
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