Consider the nonlinear first order DE - = f(t, y ) = . 12+ yz - 4 dt , with slope field t as shown at the right below. a. Find the two nullclines (f (t, y) = 0, t * 0) and sketch them carefully on the given direction field. b. By analyzing the sign of f (t, y), justify the behaviour of the direction field in relation to the nullcline on the region t > 0, and hence predict two different types of solution behaviour. c. Sketch the solutions with ICs (1,0), (-1,0), (1,2), (-1,2), (2,-2), (-2,-2), (3,3), (-3,3), following the direction field carefully, and extending each solution to the boundaries of the window. [HINT: Use symmetry.] (Continued...) (Continued...) d Again analyzing f(t, y), explain what happens once a solution enters the region 12 + y?