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I'm working through some example question and the memo leaves out this question. I was hoping someone can help me out.

**The question:**

Construct a differential equation of the form y'' + by' + cy = 0 which has y(t) = e^t cos(3t) as one of its solutions.

What I did:

First I found the y'(t) and y''(t)

Plugged that into the DE.

My answer:

b = -2

c = -6

y'' - 2y' - 6y = 0