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 > > > > >