       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)

```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 == Exp[-a]}, y[t], t][]

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}, 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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