Submit neatly written solutions to the following questions. you do not have to type your solutions, just submit solutions that are clear, and easily read. show sufficient work for full credit. (1) classify the following equation as to its order and whether or not it is linear or nonlinear. ry"(x) + (1) - ty(x) = 3.r - 1 (2) verify that y(x) = 3 is a solution to y'= 22,2 is a solution to =y-y? . find the value of c associated (3) the one-parameter family y = with y(-1) = 2.

If p(x) is the total value of the production when there are x workers in a plant, then the average productivity of the workforce at the plant is a(x) = p(x) x . (a) find a'(x). a'(x) = xp'(x) − p(x) x a'(x) = xp'(x) − p(x) x2 a'(x) = p'(x) − p(x) x a'(x) = xp'(x) − p'(x) x2 a'(x) = p'(x) − xp(x) x2 why does the company want to hire more workers if a'(x) > 0? a'(x) > 0 ⇒ a(x) is ; that is, the average productivity as the size of the workforce increases. (b) if p'(x) is greater than the average productivity, which of the following must be true? p'(x) − xp(x) > 0 p'(x) − xp(x) < 0 xp'(x) − p'(x) > 0 xp'(x) − p(x) < 0 xp'(x) − p(x) > 0