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Find the values of ω for which y=cosωt satisfies d^2y/dt^2 +81y = 0

where ω1<ω2

I guess I'm just having a lot of problem even figuring out how to do these at all. Since it's a second degree problem, I found the derivative of y=cosωt, which is -sin(ωt)*ω, and I found the derivative of that to be cos(ωt)*ω. I then set ωcos(ωt)=81cos(ωt).

Am I going about this right at all?

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# Differential Equation, finding values

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