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 = -2 and y = 3.
For y > 3, both (y - 3) and (y + 2) are positive. The product (y - 3) (y + 2) is positive, as are the slopes.
For -2 < y < 3 the quantity (y - 3) is negative and (y + 2) is positive, so the slopes are negative.
For y < -2, both (y - 3) and (y + 2) are negative, so the slopes are positive.
We conclude that y = -2 is a stable equilibrium and y = 3 is an unstable equilibrium: