Homework Help: Inverse Laplace Question

1. Jan 30, 2013

Desii

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

2. Relevant equations

Inverse Laplace

3. The attempt at a solution

Here's my solution, please point out my mistakes. One mistake i found after taking the picture is: Its -2te^-2t ( third last step), Then my answer is just e^-t+e^-2t

http://postimage.org/image/mfzr6aom5/ [Broken]

Last edited by a moderator: May 6, 2017
2. Jan 30, 2013

Staff: Mentor

You have a couple of mistakes near the beginning.

You have
$$\frac{1}{(s + 1)^2(s + 1)^2} = \frac{A}{s+ 1} + \frac{Bs + C}{(s + 2)^2}$$

The first mistake is minor and probably a typo - you wrote (s + 1)2 in the first fraction when I think you meant (s + 2)2.

The second mistake is one of understanding. To decompose a repeated linear factor such as (s + 2)2 you do it like this:
$$\frac{1}{(s + 1)^2(s + 2)^2} = \frac{A}{s+ 1} + \frac{B}{s + 2} + \frac{C}{(s + 2)^2}$$
The way you did it is for irreducible quadratics (i.e., quadratics with complex factors), not quadratics that are perfect squares.

After that I stopped looking.

Last edited by a moderator: May 6, 2017
3. Jan 30, 2013

Desii

Gotcha, Thanks mate. This solves the mystery :) and yes i meant (s+2)^2

4. Jan 30, 2013

Staff: Mentor

That's why they pay us the big bucks. Oh wait, they don't pay us at all!