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