I have a problem regarding the equations dx/dt=x-xy and dy/dt=y+2xy. I need to find the critical points of this system and denote if they are stable or asymptotic or whatever. I flipped through the section on this and you can find the critical points by setting dx/dt and dy/dt to zero and solving for x and y. This gives (0,0) and (1,-1/2). But you still don't know what their nature is, so I tried to solve the system. I did this by dividing one by the other and getting dy/dx=y+2xy/x-xy. However I am stuck trying to solve this problem. I can't find a integrating factor for this in terms or either x or y (we haven't learnt anything beyond that) in order to make it exact. How else can I solve this? I gather I can turn this into a matrix and solve it somehow by I am not sure.(adsbygoogle = window.adsbygoogle || []).push({});

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Autonomous Systems and Stability

**Physics Forums | Science Articles, Homework Help, Discussion**