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Math Help - Help with laplace tranforms question...

  1. #1
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    Help with laplace tranforms question...

    Here is the problem:
    Use laplace transforms to solve
    IVP
    Help with laplace tranforms question...-untitled.jpg

    How do I solve this? Should I do 2 separate equations or is there a theorem I use? Please help me get a few steps to get started.
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  2. #2
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    Quote Originally Posted by isu2014 View Post
    Here is the problem:
    Use laplace transforms to solve
    IVP
    Click image for larger version. 

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ID:	18164

    How do I solve this? Should I do 2 separate equations or is there a theorem I use? Please help me get a few steps to get started.
    Two seperate functions. Let LT[y(t)] = Y(s) and LT[x(t)] = X(s) and solve simultaneously for Y and X. Then invert each etc.
    Last edited by mr fantastic; July 11th 2010 at 03:13 AM.
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  3. #3
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    Quote Originally Posted by mr fantastic View Post
    Two seperate functions. Let LT[y(t)] = Y(s) and LT[x(t)] = X(s) and solve simultaneously for Y and X. Then invert each etc.
    Thanks, now I'm confused because I've only dealt with y', x' not y'', x''. How do I make equations with the double primes?
    Last edited by mr fantastic; July 11th 2010 at 03:14 AM.
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  4. #4
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    See here for a table that will show you the Laplace Transforms of second derivatives (and higher).
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  5. #5
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    Now I have:
    (s^2+4)Y(s) + 3X(s) = 0
    (s^2+1)X(s) + 4Y(s) = 0

    Determinate: -(s^4 - 5s^2 + 8)

    Is this correct? And what next?
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  6. #6
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    Quote Originally Posted by isu2014 View Post
    Now I have:
    (s^2+4)Y(s) + 3X(s) = 0
    (s^2+1)X(s) + 4Y(s) = 0

    Mr F says: The above equations are not correct.

    Determinate: -(s^4 - 5s^2 + 8)

    Is this correct? And what next?
    You have not correctly applied the formula for the Laplace transform of the double derivative of x and y. You need to go back and do this more carefully.

    Once you have the correct equations, you have to solve them simultaneously to get X and Y in terms of s. Then you have to get the inverse Laplace transform of each.
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