Question

Find all critical points of the given plane autonomous system. (enter your answers as a comma-separated list.) x' = x + xy y' = −y − xy

Answer 1

$x'=x+xy=x(1+y)=0\implies x=0\text{ or }y=-1$

$y'=-y-xy=-y(1+x)=0\implies y=0\text{ or }x=-1$

There are 4 critical points: (0, 0), (0, -1), (-1, 0), and (-1, -1).