4. [018 Points] DETAILS PREVIOUS ANSWERS SCALCETB 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.) k _ a _ a _ 3 ' 3 X (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) + a cos(kt) a y' = Ak cos(kt) Bk sin(kt) :> y" = Ak2 sin(kt) Bkz cos(kt). The given differential equation 25y" = 9y is equivalent to 25y" + 9y = . Thus, LHS = 25y\" + 9y= 25(Ak2 sin(kt) BkZ cos(kt)) + 9( ) = 25Ak2 sin(kt) ZSBkZ cos(kt) + ( )sin(kt) + 95 cos(kt) = (9 25k2)A sin(kt) + ( )cos(kt) = since k2 =