# Math Help - Laplace Transforms of DE II

1. ## Laplace Transforms of DE II

Another Problem

$D^{2}y + 2Dy -3y = e^{-3t}$

All initial condtions are 0. I am having a problem with the partial fraction part

This is how far I got

$Y(s)= \frac{1}{((s+1)^{2}-4)(s+3)}$

I dont think I am decomposing it properly hence I ma not getting the correct answer

2. Your work is correct... what is difficult to undestand however is why the term $s^{2} + 2s -3 = (s+3) (s-1)$ is written as $(s+1)^{2} -4$...

... anyway you can proceed 'step by step' exactly as in your previous post...

Kind regards

$\chi$ $\sigma$

3. Thx Chi Sigma

The lecturer started the solution that way, so I didn't bother checking :-(