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Math Help - more unit step functions...

  1. #1
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    more unit step functions...

    ok im having a bit of a time solving this problem...

    y''-5y'+6y=U(t-1) y(0)=0, y'(0)=1

    the Unit step is giving me a problem...can i just make it e^-s and solve it?

    any help would be appreciated..

    thanks in advance!
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  2. #2
    MHF Contributor chisigma's Avatar
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    Quote Originally Posted by slapmaxwell1 View Post
    ok im having a bit of a time solving this problem...

    y''-5y'+6y=U(t-1) y(0)=0, y'(0)=1

    the Unit step is giving me a problem...can i just make it e^-s and solve it?

    any help would be appreciated..

    thanks in advance!
    Split the problem in two parts...

    a) find the solution of the initial values problem...



    ... and call \varphi this solution...

    b) find the solution of the initial values problem...



    Kind regards

    \chi \sigma
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  3. #3
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by slapmaxwell1 View Post
    ok im having a bit of a time solving this problem...

    y''-5y'+6y=U(t-1) y(0)=0, y'(0)=1

    the Unit step is giving me a problem...can i just make it e^-s and solve it?

    any help would be appreciated..

    thanks in advance!
    It looks like you are doing a Laplace transform? Note that
    \mathcal{L} \{ U(t - t_0) \} = \frac{e^{-st_0}}{s}

    Since t_0 = -1 what is the sign in the exponential?

    -Dan
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