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MathGroup Archive 2007

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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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