1-a. For what values of k does the function y = cos(kt) satisfy the differential equation 9y'' = 25y?

(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 equation 9y'' = 25y

is equivalent to 9y'' + 25y =?

thus, LHS = 9y'' + 25y= 9(Ak² sin(kt) Bk² cos(kt)) + 25( ? )

= 9Ak² sin(kt) 9Bk² cos(kt) +( ? ) sin(kt) + 25B cos(kt)

=(259k²)A sin(kt) + ( ?) cos(kt)

=( ? )since k² =( ?)