For the differential equation, find all equilibrium solutions (if any) and determine if each is stable or unstable.
The equilibrium solutions are y = 0, y = -1, and y = 1.
When y > 1 all quantities are positive, so the slopes are positive also.
When 0 < y < 1 the quantity (y - 1) is negative and the others are positive, so the slopes are negative.
When -1 < y < 0 the quantities y and (y - 1) are negative, so the slopes are positive.
Finally, when y < -1 all quantities are negative, so the slopes are negative.
We conclude that 0 is the only stable equilibrium solution: