Thread: System of differential equations. No Clue

dx/dt= 0.02x(1-(x/80))+0.004xy

dy/dt= 0.04y(1-y/20)-0.0002xy

How can I Find all equilibrium points algebraically. I've tried setting them equal to zero but my equations make no sense. I got

x=8+16y and y=20-x

but i'm not sure i'm right. please help. Thanks

This is very much NOT linear. You are not expecting it to be nice and clean, are you?

You are on the right track. Set them back to zero and go carefully. You should get four solutions. Three are trivial. The fourth carries more interest unless everything must be non-negative for some reason.

yeah i was expecting them to be very nasty. that's why when they seem kind of easy, makes me wonder. I got those 2 solutions plus x=0 and y=0.
but i don't know if i should combine them or what else.

So, you have the three trivial solutions?

You have (80,0), (0,20), and (0,0)?

What about the one that isn't trivial?