To find equilibrium solutions we set the differential equation equal to 0 and solve for *y*. 0 = *y*^{2 }-* y* = *y*(*y* - 1) so the equilibrium solutions are *y* = 0 and *y* = 1. Now to figure out if the other solutions are trying to snuggle up to or run away from each of these equilibrium solutions. When *y* > 1 the quantity is positive, which means the slopes on the slope field will be positive when *y* > 1. Let's sketch this into our very rough slope field. When *y* is between 0 and 1, *y* is positive but (*y* - 1) is negative, so the product *y*(*y* - 1) is negative. This means the slopes on the slope field will be negative for 0 Finally, when *y* is less than 0 both *y* and (*y* - 1) are negative, so the product *y*(*y* - 1) is positive. This means the slopes will be positive for *y* < 0. The solutions above *y* = 1 are trying to get away from the equilibrium, so that's an unstable equilibrium. The other solutions are trying to get closer to *y* = 0, so that's a stable equilibrium: |