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.