(a) For what values of k does the function y k = = cos(kt) satisfy the differential equation 49y” = -16y? (Enter your answers as a comma-separated list.) (b) For those values of k, verify that every member of the family of functions y = A sin(kt) + B cos(kt) is also a solution. We begin by calculating the following. y = A sin(kt) + B cos(kt) ⇒ y' = Ak cos(kt) – Bk sin(kt) = y" = Note that the given differential equation 49y" = -16y is equivalent to 49y" + 16y = Now, substituting the expressions for y and y” above and simplifying, we have = LHS 49y" + 16y = 49( [ = -49 + 16(A sin(kt) + B cos(kt)) 49Bk2 cos(kt) + 16A sin(kt) + 16B cos(kt) + (16 − 49k²) B cos(kt) = (16-49k2) = 0 since for all value of k found above, k² =