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Math Help - Laplace transform

  1. #1
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    Laplace transform

    How do i find the general solution of this equation using laplace transform?? its a practice problem for my exam but im not sure how to solve it.

    y'''-4y'=0 when y(0)=1, y'(0)=2, y(0)''=-20
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  2. #2
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    Quote Originally Posted by Juggalomike View Post
    How do i find the general solution of this equation using laplace transform?? its a practice problem for my exam but im not sure how to solve it.

    y'''-4y'=0 when y(0)=1, y'(0)=2, y(0)''=-20
    The laplace transform of

    \frac{d^ny}{dt^n}=s^nY-\sum_{k=0}^{n-1}s^{n-k-1}y^{k}(0)

    So in your case

    \mathcal{L}\{y'''\}=s^3Y-s^2y(0)-sy'(0)-y''(0)=s^3Y-s^2-2s+20

    and

    \mathcal{L}(y')=sY-1

    This gives the algebraic equation

    s^3Y-s^2-2s+20-4(sY-1)=0

    Now just solve for Y and invert the transform
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  3. #3
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    ah great, thanks alot, was doing the y''' wrong.
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