(a) For what values of k does the function y = cos(kt) satisfy the differential equation 36y''=49y? (Enter your answers as a comma-separated list.)k = (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 equation36y''=49y is equivalent to36y''+49y = . Thus,LHS =36y''+49y=36(Ak2 sin(kt) Bk2 cos(kt))+49=36Ak2 sin(kt)36Bk2 cos(kt)+sin(kt)+49B cos(kt)=(4936k2)A sin(kt)+cos(kt)= since k2= .