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
>
>
>
>
>