# Laplace Transform

1. Nov 6, 2007

### EugP

1. The problem statement, all variables and given/known data
Find the Laplace Transform of the following:

$$5{\delta (t-3)}+4{u(t-2)}+3{e^{-5(t-3)}u(t-4)}$$

3. The attempt at a solution
I know how to do the first and second terms, but I'm having trouble with the third.

$$5e^{-3t}+4\frac{1}{s}e^{-2t} + ?$$

I think I should be using either

$$L\{ f(t-t_0)u(t-t_0) \} = e^{-st_0}F(s)$$

or

$$L\{ e^{-\alpha t}u(t) \} = \frac{1}{s+\alpha}$$

or both.

The problem is, in the first one, I don't know what to put for $$F(s)$$.

Any help would be appreciated.

Last edited: Nov 6, 2007
2. Nov 6, 2007

### SlideMan

Unfortunately, you can't use your first equation because $$t_0$$ in f and u are not the same.

Try breaking up the exponential using algebra first.