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Partial fractions/Laplace

  1. Nov 4, 2009 #1
    1. The problem statement, all variables and given/known data

    Got stuck doing the transform on a partial fraction thats giving me trouble


    2. Relevant equations

    y" + 2y' + 2y = 0 IC: F(0) = 1 F'(0) = -3

    3. The attempt at a solution

    Im getting stuck with a partial fraction of (s-1) / (s^2 + 2s + 2)
    the only thing i can think of is As+b = 1s-1 A = 1 B = -1 and i know if i change D(s) to (s+1)^2 +1 i can get e^(-t).
    (s - a)^2 + b^2 means a = -1 and b = +/- 1 then As+b / s^2 + 2s + 2 = [b - (s + a)] / [(s-a)^2 +b^2] and i get e^-t * [sin(-t) - cos(-t)] I don't think it is right tho
     
  2. jcsd
  3. Nov 5, 2009 #2

    tiny-tim

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    Welcome to PF!

    Hi ihatelaplace! Welcome to PF! :smile:

    (try using the X2 tag just above the Reply box :wink:)

    Your solution is nearly right, but I don't follow how you got there. :confused:

    Why not just use the standard -b ± √(b2 - ac) solution to the characteristic equation …

    that'll give you roots of the form p ± iq, for which the solutions are … ? :smile:
     
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