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**!!!Solving a Differential Eq using Laplace and Unit-Step function**

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

I am having a terrible time just starting this. I need some explanation here. I have given up on the text I am using...

I need to solve the following piecewise function using Laplace and Unit-Step function:

y"+4y=f(t) y(0)=-1, y'(0)=0

where f(t)= t, t<2

5, t>2

**3. The attempt at a solution**

Now I condensed it to one line using the Unit Step function giving:

[itex]y''+4y=t-t*U(t-2)+5*U(t-2)[/itex]

Applying Laplace to the LHS is easy enough, but what is the Laplace of the unit step function? I am having a hard tome extrapolating it from the text.

So far I have

[itex]s^2Y(s)-sy(0)-y'(0)+4Y(s)=\frac{1}{s^2}-???[/itex]

Could somebody help me out with the "U" terms here?

Thank you