APPM 2360 Midterm: appm2360spring2015exam2_sol
Document Summary
On the front of your bluebook write: (1) your name, (2) your student id number, (3) lecture section (4) your instructor"s name, and (5) a grading table for ve questions. Text books, class notes, and calculators are not permitted. After you finish: turn in both your bluebook and a signed exam paper, and write your name on one of the sign out sheets. Problem 1: (30 points) consider the ode system in the rst quadrant (x 0, y 0) Solution: (a) the vector eld is given by v = [y x2, 4(x y)]. Thus the equilibrium points are determined according to. Thus y = y2 and y = x producing two eq. points (0, 0), (1, 1). (b) the horizontal nullcline is de ned as y = x such that v = [y y2, 0]. Therefore we nd right arrows for y < 1: v = [+, 0] and leftarrows y > 1: v = [ , 0].
