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Diff eq - LT Discontinuous Sources HW

  1. Aug 8, 2016 #1
    1. The problem statement, all variables and given/known data
    15whzic.png

    2. Relevant equations
    2j495qh.png
    3. The attempt at a solution
    this is my attempt, I figured this would be easier than typing.
    2hhipmq.jpg

    any how, I find partial fraction method is so time consuming and very algebraically complicated, is there a trick or another method I could use to make this easier?

    thanks
     
  2. jcsd
  3. Aug 8, 2016 #2

    Ray Vickson

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    Convert ##Y_1(s) = \frac{1}{(s+3)(s-4)(s-8)}## to partial fractions, then multiply by ##5 e^{-9s}## later; better still, find the inverse of ##Y_1(s)## as ##y_1(t)##; the solution is then ##5 u(t-9)y_1(t-9)##.

    The partial fractions can be found easily (but still with some algebra) by applying successively the identities
    $$\frac{1}{(s-a)(s-b)} = \frac{1}{a-b} \left[ \frac{1}{s-a} - \frac{1}{s-b} \right] \: \text{if} \; a \neq b$$
     
  4. Aug 10, 2016 #3
    That was so much help
    I used this and worked like miracles for few questions, I was just confused of changing to and from the t-c.
     
  5. Aug 10, 2016 #4

    Ray Vickson

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