For the differential equation, find all equilibrium solutions (if any) and determine if each is stable or unstable.
First we factor:
The equilibrium solutions are y = 0 and y = 1.
Since the quantity (y - 1)2 is always positive it won't affect the signs of the slopes.
When y > 0, the slopes are positive.
When y < 0, the slopes are negative:
Both equilibrium solutions are unstable.