# Thread: differential equation equilibria ?

1. ## differential equation equilibria ?

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..

2. ## clarification

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