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Math Help - Two LaPlace Transform problems

  1. #1
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    Two LaPlace Transform problems

    can i have the complete solution for these problems ??

    i don't know how to start solving !!

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  2. #2
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    Quote Originally Posted by Hossam View Post
    can i have the complete solution for these problems ??

    i don't know how to start solving !!

    For the first one you will need to combine three different theorems

    \mathcal{L}\{ f'(t)\}=sF(s)-f(0)

     \mathcal{L}\{ t^nf(t)\}=(-1)^n\frac{d^n}{ds^n}F(s)

     \mathcal{L}\{ e^{at}f(t)\}=F(s-a)

    See if you can combine them to get the answer.

    for 2 use the convolution theorem

    \mathcal{L}\{ \int_{0}^{t}f(t-\tau)g(\tau)d\tau\}=F(s)G(s)
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  3. #3
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    for problem 2 , convolution theorem says f(t-u) .. and here it's e^(x-t) .. so i have to take the ( - ) common so it becomes e^-(t-x) ??? is this right ?
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  4. #4
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    Quote Originally Posted by Hossam View Post
    for problem 2 , convolution theorem says f(t-u) .. and here it's e^(x-t) .. so i have to take the ( - ) common so it becomes e^-(t-x) ??? is this right ?
    Yes that is correct!
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  5. #5
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    Quote Originally Posted by TheEmptySet View Post
    Yes that is correct!
    Okay , Thanks much
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