- #1

jrsweet

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## Homework Statement

Consider the following initial value problem:

y''+4y = 9t, 0<=t<2

...0, t>=2

Find the equation you get by taking the Laplace transform of the differential equation and solve for Y(s)

## Homework Equations

## The Attempt at a Solution

I am just having trouble with the step function:

Say g(t)= 9t, 0<=t<2

...0, t>=2

g(t)= (1-u(t-2))9t ?

= 9t-u(t-2)9t

So, Laplace{g(t)} = (9-9e

^{-2s})/(s

^{2})

SO, s

^{2}Y(s) + 4Y(s) = (9-9e

^{-2s})/(s

^{2})

And, Y(s) = (9-9e

^{-2s})/((s

^{2})(s

^{2}+4))

There is something wrong with this. If anyone could help me out that would be much appreciated! Thanks!

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