(adsbygoogle = window.adsbygoogle || []).push({}); !!!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

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Solving a Differential Eq using Laplace and Unit-Step function

**Physics Forums | Science Articles, Homework Help, Discussion**