Re: DSolve with DiracDelta

• To: mathgroup at smc.vnet.net
• Subject: [mg75803] Re: DSolve with DiracDelta
• From: dimitris <dimmechan at yahoo.com>
• Date: Fri, 11 May 2007 05:20:35 -0400 (EDT)
• References: <f1unqt\$7si\$1@smc.vnet.net>

```I guess you use the new mathematica 6?

In[109]:=
DSolve[{Derivative[1][y][t] + o*y[t] == DiracDelta[t], y[0] == 0}, y,
t]

% /. o -> 7/10

Show[Block[{\$DisplayFunction = Identity}, (Plot[y[t] /. %[[1]], {t,
#1[[1]], #1[[2]]}, Axes -> False, Frame -> True] & ) /@
Partition[Range[-2, 2], 2, 1]]]

Out[109]=
{{y -> Function[{t}, (-1 + UnitStep[t])/E^(o*t)]}}

Out[110]=
{{y -> Function[{t}, (-1 + UnitStep[t])/E^((7*t)/10)]}}

Out[111]=
Graphics[]

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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