Consider the differential equation dy/dt = y + y^2/2. a. Find all equilibrium solutions, i.e. solutions of the form y(t) = C, where C is a constant. b. Choose the correct direction field for this equation. (UL) (UR) (LL) (LR) c. Show the solution curve for the initial value problem y(0) = -3 on the appropriate graph above and calculate lim y(t) as t approaches infinity. If using your own paper, redraw the appropriate direction field.