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Math Help - Solving an I.V.P. with Laplace transforms.

  1. #16
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    Re: Solving an I.V.P. with Laplace transforms.

    Quote Originally Posted by romsek View Post
    I'm just going to show you how it's done.

    \frac{1}{(s+3)^2}\Longleftrightarrow \left(t e^{-3 t} u(t)\right)

    s F(s)\Longleftrightarrow \left(\frac{d}{dt}f(t)\right)

    \frac{d}{dt}t e^{-3 t} u(t)=\delta (t) t e^{-3 t}+\left(e^{-3 t}-3 t e^{-3 t}\right) u(t) = \left(e^{-3 t}-3 t e^{-3 t}\right) u(t)

    I'll let you mess with getting the constants right.
    I'm still not really following you. I don't have a rule lying around that says;
    s F(s)\Longleftrightarrow \left(\frac{d}{dt}f(t)\right)

    The closest I have is;

    {\Lapl}{\mathcal{L}}{(f^\prime)}(s) = s{\Lapl}{\mathcal{L}}(f)(s) - f(0)

    And I know that f(0)=-1

    Do you know a general name for that property so i can dig up a proof? Or is it on one of the lists and I'm just not seeing it?
    Attached Thumbnails Attached Thumbnails Solving an I.V.P. with Laplace transforms.-laplace-table-1.png   Solving an I.V.P. with Laplace transforms.-laplace-table-2.png  
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  2. #17
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    Re: Solving an I.V.P. with Laplace transforms.

    I apologize I should have spelled out the full form of the property. You just get used to saying f'(t) <--> s F(s)

    It's #4 on your 2nd page. The one you identified. You have f(0) so use it.
    Last edited by romsek; December 9th 2013 at 01:52 PM.
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  3. #18
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    Re: Solving an I.V.P. with Laplace transforms.

    Quote Originally Posted by romsek View Post
    I apologize I should have spelled out the full form of the property. You just get used to saying f'(t) <--> s F(s)

    It's #4 on your 2nd page. The one you identified. You have f(0) so use it.
    Oh OK good.

    Don't I need to dig up a -1 someplace? Do I need to completely rearrange the problem?
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  4. #19
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    Re: Solving an I.V.P. with Laplace transforms.

    Quote Originally Posted by bkbowser View Post
    Oh OK good.

    Don't I need to dig up a -1 someplace? Do I need to completely rearrange the problem?
    no. Just compute f(t) the way I outlined below and then at the end subtract off f(0) = -1
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