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## Homework Statement

question is attached

## Homework Equations

L(1) = 1 /s

L(t^n) = n!/s^(n+1)

L{f '(t)} = s F(s) - f(0)

L{f ''(t)} = s^2 F(s) - s f(0) - f '(0)

## The Attempt at a Solution

okay so i laplace transformed both sides and i got:

(s^2) Y(s) + 5s -5 -5s Y(s) -25 - 6Y(s) = -84exp(-5s) / s

Y(s) [s^2 - 5s - 6] + 5s - 30 = -84exp(-5s) / s

Y(s) = ((-exp(-5s)(5s(s-6)*exp(5s) +84)) / (s^3 - 5s^2 - 6s)

but thats so long and complicated that im wondering if i've stuffed up because I can't even seem to find the inverse laplace of the function.

#### Attachments

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