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Differential Equations question.

  1. Apr 9, 2012 #1
    1. The problem statement, all variables and given/known data
    We have this DE:
    y(t)''+2y(t)'+y(t)=e^(-t)
    y(0)=1
    y(0)'=0
    2. Relevant equations
    We use LT
    L(y(t)'')=F(s)s^2-y(0)s-y(0)'
    L(y(t)')=F(s)s-y(0)
    L(y(t))=F(s)
    3. The attempt at a solution
    After calculus
    F(s)=(s^2+3s+3)/(s+1)^3=1/(s+1)+1/(s+1)^2+1/(s+1)^3
    => y(t)=e^(-t)(1+t+t^2/2)
    Which is a good result and y(0)=1 and y(0)`=0 http://www.wolframalpha.com/input/?i=%28+e^%28-t%29+%28t^2%2F2%2Bt%2B1%29%29%27%27%2B2*%28+e^%28-t%29+%28t^2%2F2%2B+t%2B1%29%29%27%2B%28e^%28-t%29+%28t^2%2F2%2B1+%2Bt%29%29
    Now, i use the formula that i was teached with residue
    We have a pole of order 3 = -1
    so y(t)=lim z=-1 (1/2!* (2 -- after we derivate 2 times))*e^(zt)) =e^(-t).
    Which is a wrong answer and i want to ask you why???
     
    Last edited: Apr 9, 2012
  2. jcsd
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