Question: (a)For what values of k does the function y = cos(kt) satisfy the differential equation25y=49y?(Enter your answers as a comma-separated list.)k =75(b)For those values of

(a)For what values of k does the function y = cos(kt) satisfy the differential equation25y=49y?(Enter your answers as a comma-separated list.)k =75(b)For those values of k, verify that every member of the family of functionsy = 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=Ak2sin(kt)Bk2cos(kt)Note that the given differential equation25y=49yis equivalent to25y+49y =0.Now, substituting the expressions for y andyabove and simplifying, we haveLHS =25y+49y=25Asin(kt)+Bcos(kt)+49(A sin(kt)+ B cos(kt))=25Asin(kt)25Bk2 cos(kt)+49A sin(kt)+49B cos(kt)=(4925k2)Bcos(kt)+(4925k2) B cos(kt)=0since for all value of k found above,k2=4925.

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