Re: DSolve with DiracDelta

*To*: mathgroup at smc.vnet.net*Subject*: [mg75835] Re: [mg75764] DSolve with DiracDelta*From*: Bob Hanlon <hanlonr at cox.net>*Date*: Fri, 11 May 2007 05:37:41 -0400 (EDT)*Reply-to*: hanlonr at cox.net

It appears that you need a boundary condition at a time other than zero. Clear[soln]; soln[t_]=y[t]/. DSolve[{y'[t] + a y[t] == DiracDelta[t], y[1] == Exp[-a]}, y[t], t][[1]] UnitStep[t]/E^(a*t) Bob Hanlon ---- Steffen Paul <steffen.paul at item.uni-bremen.de> 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 > > > > >