# Find equilibrium points given 2 differential equation

1. Mar 22, 2013

### fireychariot

1. The problem statement, all variables and given/known data

$\dot{x}$ = -pxy + qx, $\dot{y}$ = rxy - sy

where p,q,r and s are positive constants (p does not equal r)

Question is : Determine all the equilibrium points for the system of differential equations given above, expressing your answers in terms of p,q,r and s

3. The attempt at a solution

I do know one point is (0,0) however am stuck in finding out the others. I factorise them to get

x(-py + q) = 0
y(xr - s) = 0

Any hints will be much appreciated
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Mar 22, 2013

### HallsofIvy

Staff Emeritus
Okay, and then what? If you are taking a differential equations course, we should be able to assume that you can do basic algebra. You should know "if ab= 0 then either a= 0 or b= 0."

3. Mar 22, 2013

### fireychariot

-py+q=0 so do I say y = p/q how do I find the x coordinate from that? Is that when x =0 or do I substitute it into my second equation?

4. Mar 23, 2013

### fireychariot

I mean y = q/p sorry. What's confusing is the fact that it is variables as the constants instead of numbers so any more hints would be grateful.

5. Mar 23, 2013

### HallsofIvy

Staff Emeritus
?? Constants are numbers.