MATH 024 Midterm: math24_2006s_exam3_soln
Document Summary
Math 24 exam 3 solutions: consider the equation y + 2. Solution (a) making the guess y = ert gives r2 + 2. Hence yh = c1 cos 0t + c2 sin 0t. (b) since 1 6= 0, this is a regular case for uc. Hence the guess is yp = a cos 1t + Substituting this guess in the equation gives ( 2. 0)(a cos 1t + b sin 1t) = cos 1t . The solution is b = 0 and a = 1 (c) if 1 = 0 this is an exceptional case for uc. Therefore, the suitable guess is multiplied by t as yp = at cos 1t + bt sin 1t. (d) as 1 approaches 0, the yp in part (b) has oscillations that grow without bound. When 1 = 0, i. e. , part (c), this is the case of resonance, where the additional factor t corresponds to the unbounded growth of the amplitude.
