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MathGroup Archive 2007

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Re: DSolve with DiracDelta correction

  • To: mathgroup at smc.vnet.net
  • Subject: [mg75805] Re: DSolve with DiracDelta correction
  • From: dimitris <dimmechan at yahoo.com>
  • Date: Fri, 11 May 2007 05:21:39 -0400 (EDT)
  • References: <f1unqt$7si$1@smc.vnet.net>

Ooops!

Mathematica 5.2 gives the solution with 6.

Ignore my answer.

Dimitris

=CF/=C7 Steffen Paul =DD=E3=F1=E1=F8=E5:
> Hi
> I tried to solve
> DSolve[{y'[t] + \[Alpha] y[t] == DiracDelta[t], y[0] == 0}, y, t]
>
> and got
>
> -\[ExponentialE]^(-t \[Alpha]) (1 - HeavisideTheta[t])
>
> which is zero for t >0.
>
> The solution is correct but I expected somthing else:
>
> exp( - alpha t) UnitStep(t)
>
> which is zero for t <0 and which is also a solution.
>
> In engineering, these solutions are called impulse responses.
>
> The last solution is physically more usefull , because the system responds
> after the excitation (DiracDelta).
>
>
>
> How can I force Mathematica to give only solutions with nonzero values for t
>  >0 ?
>
>
>
> Regards,
>
> Steffen



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