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Damnit! I am terrible at Partial Fractions!

  1. Mar 31, 2008 #1
    1. The problem statement, all variables and given/known data

    Solve y"+4y'=sin 3t subject to y(0)=y'(0)=0 using Laplace Transform

    3. The attempt at a solution

    So I got:


    [tex]\Rightarrow Y(s)=\frac{3}{(s^2+9)(s^2+4)}[/tex]

    Now it looks like two irreducible quadratics, which I know should not be too bad, but I have never dealt with more than one.

    Now am I correct to say that


    This is where I think I have the problem... the notation.

  2. jcsd
  3. Mar 31, 2008 #2


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    Homework Helper

    Given this transform:

    [tex]s^2Y(s)-sy(0)-y'(0)+4[sY(s)-y(0)]=\frac{3}{s^2+9}[/tex] ,

    shouldn't this be

    [tex]\Rightarrow Y(s)=\frac{3}{(s^2+9)(s^2+4*s*)}[/tex]

    Also, when you go to solve the partial fractions, you want to have 's' in the numerators:

  4. Mar 31, 2008 #3
    Oh crap...

    Yes, so I get:


    Thanks!!!! !
  5. Mar 31, 2008 #4

    Anyone know of a quick way to do this? I let s=0 and -4 to solve for C and D..... but what about A and B? Do I have to distribute this whole mess out? Or is there a more expedient way?
  6. Mar 31, 2008 #5
    Guess not.

    So now I have


    How do I simplify the 1st term?

    I can see that it looks like cosine. But...How do I get rid of all the crap?

    Hmm I guess I could....Oh!!! Break it up! I think that will work!
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