swered Question 1 29.3 / 33.3 pts Consider the differential equation dr dy = 3x + y. a) On the axes provided, sketch a slope field for the given differential equation at the 12 points indicated, and sketch a solution curve that passes through the point (0, 1). b ) Find dy in terms of x and y and evaluate it at the point (0, 1). Your Answer: $ % V & CKed Question 2 33.3 / 33.3 pts Consider the differential equation da dy = yz ( 2x + 2). Lety = f (x) be the particular solution to the differential equation with f (0) = 2. a) Find limx-0 f(I) -2 sin x -. Show the work that leads to your answer. b) Use Euler's method, starting at x = 0 with two steps of equal size, to approximate f (1). c) Find y = f (), the particular solution to the differential equation with initial condition f (0) = 2. Your Answer: ed Question 3 33.4 / 33.4 pts (Calculator Aanveld Question 3 33.4 / 33.4 pts (Calculator Active) Let P (t) represent the number of red wolves in North Carolina at time t years where t _ 0. The population P (t) is increasing at a rate proportional to 400 - P (t), where the constant of proportionality is k. a) If P(O) = 150, find P(t) in terms of t and k. b) If P(2) = 250, find k. c) Find limt-+co P (t). Your