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Laplace Transform IVP (Easy I think)

  1. Dec 7, 2013 #1
    1. The problem statement, all variables and given/known data
    Use Laplace transforms to solve the initial value problems.
    ##y''+4y=0;## ##y(0)=5;## ##y'(0)=0##

    2. Relevant equations

    3. The attempt at a solution
    $$y''+4y=0$$ $$L(y'')+L(4y)=L(0)\implies s^{2}Y(s)-sy(0)-y'(0)+4(sY(s)-y(0))=0\implies s^{2}Y(s)+4sY(s)-5s-20=0$$ $$Y(s)(s^{2}+4s)=5s+20\implies Y(s)=\frac{5}{s}$$
    Now I'm supposed to take the inverse laplace of that which would just be 5. I'm not sure what to do with this now.
    Last edited: Dec 7, 2013
  2. jcsd
  3. Dec 7, 2013 #2
    Found my mistake, it's not 4y'...
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