Re: DSolve with DiracDelta
- To: mathgroup at smc.vnet.net
- Subject: [mg75801] Re: DSolve with DiracDelta
- From: dh <dh at metrohm.ch>
- Date: Fri, 11 May 2007 05:19:31 -0400 (EDT)
- References: <f1unqt$7si$1@smc.vnet.net>
Hi Steffen,
Either, get the general solution by eliminating y[0] == 0 and set the
integration constant to zero.
Or choose the initial condition so that the wanted solution is uniquely
defined, e.g. y[-1]==0.
Hope this helps, Daniel
Steffen Paul 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
>
>
>
>
>