Diff-EQ: non-zero k so y = sin(kt) satisfies y'' + 9y = 0

[stellar]

For what nonzero values of "k" does the function y = sin(kt) satisfy the differential equation y" + 9y = 0 ?

Do I do the derivative twice, and plug it in?

[stapel_eliz]

That should do it:

y = sin(kt)

y' = k*cos(kt)

y" = -k^2*sin(kt)

Then y" + 9y is -k^2*sin(kt) + 9*sin(kt) = (9 - k^2)(sin(kt)).

For what values of "k" will this equal zero?