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MathGroup Archive 2007

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Re: DSolve with DiracDelta

  • To: mathgroup at smc.vnet.net
  • Subject: [mg75835] Re: [mg75764] DSolve with DiracDelta
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Fri, 11 May 2007 05:37:41 -0400 (EDT)
  • Reply-to: hanlonr at cox.net

It appears that you need a boundary condition at a time other than zero.

Clear[soln];
soln[t_]=y[t]/.
    DSolve[{y'[t] + a y[t] == DiracDelta[t], 
          y[1] == Exp[-a]}, y[t], t][[1]]

UnitStep[t]/E^(a*t)


Bob Hanlon

---- Steffen Paul <steffen.paul at item.uni-bremen.de> wrote: 
> 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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