# Piecewise continuous - step function

1. Dec 6, 2009

### jrsweet

1. The problem statement, all variables and given/known data
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)

2. Relevant equations

3. 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)/(s2)

SO, s2Y(s) + 4Y(s) = (9-9e-2s)/(s2)

And, Y(s) = (9-9e-2s)/((s2)(s2+4))

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

Last edited: Dec 6, 2009