APPM 2360 Midterm: appm2360fall2016exam3_sol
Document Summary
Problem 1: (30 points; 6 points each) true/false questions. Answer true if the statement is always true. 6y = 0. of constants a and . (e) consider the de: (1) In the underdamped case, y(t) = 0 in nitely many times. (b) false. The forcing function is in resonance with the system, and so the amplitude of x(t) grows linearly with time. (c) true. Both e 2t and e 3t are solutions, hence so are y1 and y2 using linearity. For linear independence, you can either use the fact that {e 2t, e 3t} are linearly independent and that (cid:20)1. 1 1(cid:21) is an invertible matrix, or you can apply the wronskian test directly. (d) true. (e) false. Equation 1 is a third-order di erential equation, and so we need three linearly. 1 independent solutions to span its solution space.
