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Inverse laplace factoring

  1. Jan 29, 2013 #1
    1. The problem statement, all variables and given/known data

    see attachment

    2. Relevant equations



    3. The attempt at a solution
    I don't get the part where it says "Solving this equation for X(s), we obtain ..."
    Specifically jumping from 3/s(s2+3s+5) to (3/5)(1/s)-(3/5)[(s+2)/(s2+2s+5)].

    How did the problem break up this fraction into separate subtracting fractions?? Is there a trick or something? I'm completely lost here. Thanks.
     

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  2. jcsd
  3. Jan 29, 2013 #2

    Ray Vickson

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    It is just partial fractions. However, the expression given above is wrong: Maple 11 gets:

    gs:=3/s/(s^2+3*s+5):lprint(%);
    3/s/(s^2+3*s+5)

    (Maple uses notation A/B/C to stand for A/(B*C), etc, and uses A/B*C to mean (A/B)*C, etc.)

    g1:=convert(gs,parfrac,s): lprint(%);
    3/5/s + 1/5*(-3*s-9)/(s^2+3*s+5)

    So, Maple gets -(3/5)(s+3) instead of -(3/5)(s+2) in the numerator of the second term. You can easily check that (s+2) gives the wrong answer when you combine the two terms.

    BTW: "partial fractions" is a standard tool in calculus, often used in computing integrals. Just Google 'partial fractions' if you have not seen this material before, or consult a calculus textbook.
     
  4. Jan 29, 2013 #3
    i get it thx
     
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