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Thread: 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 $\displaystyle \varphi$ this solution...

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



    Kind regards

    $\displaystyle \chi$ $\displaystyle \sigma$
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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
    $\displaystyle \mathcal{L} \{ U(t - t_0) \} = \frac{e^{-st_0}}{s}$

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

    -Dan
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