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## Homework Statement

Problem: laplace transform of x"+2x'+x=sin(t) x=x'=0

## Homework Equations

## The Attempt at a Solution

Attempt at problem: I was able to get Y(s)=1/(s^2+1)(s^2+2s+5) and then i expanded it to get [s/10(s^2+2s+5)]-[s/10(s^2+1)]+[1/5(s^2+1)]. The last two terms are easy to transform the first term i completed the square and got 1/10*s/(s+1)^2+4

Question: from maple i know it will be a exp times a sin and cos function of some sort. I don't know how they got that even though i see it in the denominator.