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Math Help - LaPlace transforms

  1. #1
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    LaPlace transforms

    Bear with me here, I took DIFF EQ 3 semesters ago and laplace transforms have come up again in a new class and I need to help
    Solve the following using Laplace transforms:
    x''+x'+x=1 where x '(0)= 0 and x(0)=0

    I get the equation down to X(s)=X(s^2+s+1)=\dfrac 1s
    then  X(s) = \dfrac 1{s(s^2+s+1)}
    next I went to partial fractions: \dfrac As + \dfrac{Bs+C}{(s^2+s+1)}
    then finding a common denominator and setting it equal to 1 i get 1 = s^2(A+B) + s(A+C) + A
    Solving that I get A=1,B=-1 and C=-1

    Plugging these back in I get \dfrac 1s - \dfrac {s+1}{(s^2+s+1)}
    Now this is where I am stuck....I my table I cannot find a tranfer related to \dfrac{s+1}{(s^2+s+1)} and I do not know how to manipulate it so I can use the tables.
    Last edited by tactical; January 27th 2011 at 12:08 PM.
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Deleted.
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    deleted
    Last edited by tactical; January 27th 2011 at 12:33 PM.
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    With all due respect to FernandoRevilla, I think the OP has the correct X(s). [EDIT]: FR has deleted his post. My advice to the OP'er is to complete the square in the denominator of the right-hand fraction, and also break up that fraction into the sum of two simpler fractions. The result will lead you, I think, to trig functions.
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  5. #5
    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by tactical View Post
    in which step is this mistake?
    The mistake was mine .

    Express:

    s^2+s+1=\left(s+1/2\right)^2+3/4
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  6. #6
    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by Ackbeet View Post
    With all due respect to FernandoRevilla, I think the OP has the correct X(s). [EDIT]: FR has deleted his post.
    Editing and answering sometimes have non empty intersecction.


    Fernando Revilla
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  7. #7
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    Quote Originally Posted by FernandoRevilla View Post
    Editing and answering sometimes have non empty intersecction.
    Aha.
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  8. #8
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    Quote Originally Posted by FernandoRevilla View Post
    The mistake was mine .

    Express:

    s^2+s+1=\left(s+1/2\right)^2+3/4
    okay that make sense now. Thank you
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  9. #9
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    You're certainly welcome for my contribution.
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