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Inverse Laplace Question

  1. Jan 30, 2013 #1
    1. The problem statement, all variables and given/known data

    Could anyone please check my work, The answer is wrong. Correct Answer: e^2t(-t+e^t-1)

    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. jcsd
  3. Jan 30, 2013 #2

    Mark44

    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
  4. Jan 30, 2013 #3
    Gotcha, Thanks mate. This solves the mystery :) and yes i meant (s+2)^2
     
  5. Jan 30, 2013 #4

    Mark44

    Staff: Mentor

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