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use the characteristic equation, do you know how?

Yes it's just the answer has sine and cosines in it and I don't know how they got it

that's because your answer are complex conjugated solutions. Have you dealt with them before?

No. All of the other questions were not like that

I was looking at it earlier under repeated roots and reduction order but it didn't help

Euler's identity? Yea we didn't cover that. I guess il try looking that up

Thank you both for your help