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Find the value(s) of [tex] \omega [\tex] for which [tex] y = \cos(\omega * t) [\tex] satisfies

[tex]\frac{d^2*y}{d*t^2} + 9y = 0[\tex]

I am trying to use latex but it doesn't seem to be working when I do "preview post" so I will rewrite what I am saying to make it more understandable in case Latex doesn't work upon posting.

Find the value(s) of omega for which y = cos(omega*t) satisfies:

(d^2t)/(dt^2) + 9y = 0

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I am not entirely sure what I am supposed to do here. My ideas have been

1.) switch 9y over to the right side

2.)Take the integral of both sides

3.)Take the integral of both sides again to solve for y(t)

This approach however left me lost in the dark and I feel is incorrect. I also tried substituting y = cos(omega*t) in for y but I can't solve the following equation. Could someone give me some ideas what I should do?