4. [7/8 Points] DETAILS PREVIOUS ANSWERS SCALCET8 9.1.004. (a) For what values of k does the function y = cos(kt) satisfy the differential equation 25y" = -9y? (Enter your answers as a comma-separated list. ) CO K = CT / CO 5 (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. y = A sin(kt) + B cos(kt) y' = Ak cos(kt) - BK sin(kt) y" = -Ak2 sin(kt) - BK2 cos(kt). The given differential equation 25y" = -9y is equivalent to 25y" + 9y = 0 Thus , LHS = 25y" + 9y= 25(-Ak2 sin(kt) - BK2 cos(kt)) + 9 Asin (kt ) + Bcos(kt) = -25Ak2 sin(kt) - 25BK2 cos(kt) + 9A sin ( kt ) + 9B cos (kt ) = (9 - 25k2)A sin(kt) + (9 - 2542) B cos ( kt ) = (9 - 2512) ( Asin (kt ) + Bcos(kt) ) since k- = 9 25 X