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**23.) y'' + 2y' + y = 4e**

^{-t}; y(0) = 2, y'(0) = -1Y(s) = [(as + b) y(0) + a y'(0) + F(s)]/(as

^{2}+ bs + c)

My attempt:

a = 1, b = 2, c = 1

F(s) = 4 L{ e

^{-t}} = 4/(s+1) (From Laplace Transform Table)

Plugging and simplifying:

Y(s) = (2s

^{2}+ 5s + 7)/[(s + 1)(s

^{2}+ 2s + 1)

Here is where I get stuck. I've tried Partial Fraction Decomposition a couple times, with no real luck. The numerator also doesn't factor. I need to get it to match something in my table (sorry I have no way to post it). I do find it peculiar that the denominator is a perfect cube. Any help would be greatly appreciated!