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

>

>

>

>

>

```

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