DSolve with DiracDelta
- To: mathgroup at smc.vnet.net
- Subject: [mg75764] DSolve with DiracDelta
- From: "Steffen Paul" <steffen.paul at item.uni-bremen.de>
- Date: Thu, 10 May 2007 05:10:20 -0400 (EDT)
- Organization: Universitaet Bremen, Germany
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