Re: Re: newbie question DSolve (revisited)

*To*: mathgroup at smc.vnet.net*Subject*: [mg52118] Re: [mg52090] Re: newbie question DSolve (revisited)*From*: "Pratik Desai" <pdesai1 at umbc.edu>*Date*: Thu, 11 Nov 2004 04:52:33 -0500 (EST)*References*: <cmppui$mll$1@smc.vnet.net> <200411100945.EAA11259@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Thank you Dr. Hintze for your response, I tried your suggestion unfortunately, Mathematica gives me another error it is as follows In[10]:= DSolve[{y''[x] - lamda^2*y[x] == DiracDelta[x - d]*y[d], y[0] == 0, y[l] == 0}, y[x], x] (DSolve::"litarg"), "To avoid possible ambiguity, the arguments of the dependent variable in (the equation) should literally match the independent variables". Thanks again for your reply again Dr Hintze, Pratik Desai ----- Original Message ----- From: "Dr. Wolfgang Hintze" <weh at snafu.de> To: mathgroup at smc.vnet.net Subject: [mg52118] [mg52090] Re: newbie question DSolve > If you replace DiracDelta[d - x]*y[x] by the equivalent DiracDelta[d - > x]*y[d] then your equation can be solved as follows (with just one minor > error message appearing twice, which can be ignored) > > In[1]:= > s = DSolve[{-y[x] + Derivative[2][y][x] == DiracDelta[d - x]*y[d], y[0] > == 0, y[L] == 0}, y[x], x] > > From In[1]:= > DSolve::"nvld" : "The description of the equations appears to be > ambiguous or \ > invalid." > > Out[1]= > {{y[x] -> 1/2*E^(-d - x)*(-((E^(2*x)*((-1 + E^(2*d))*UnitStep[-d] - > (E^(2*d) - E^(2*L))*UnitStep[-d + L])*y[d])/ > (-1 + E^(2*L))) + ((E^(2*L)*(-1 + E^(2*d))*UnitStep[-d] - > (E^(2*d) - E^(2*L))*UnitStep[-d + L])*y[d])/ > (-1 + E^(2*L)) - E^(2*d)*UnitStep[-d + x]*y[d] + > E^(2*x)*UnitStep[-d + x]*y[d])}} > > From In[2]:= > DSolve::"nvld" : "The description of the equations appears to be > ambiguous or \ > invalid." > > Extracting the solution to u[x] > > In[4]:= > u[x_] = y[x] /. s[[1]] > > you can Plot it, after assigning numeric values to all relevant > quantities: > > In[6]:= > L = 1; d = 0.5; y[d] = 1; > Plot[u[x], {x, -1, 4}, PlotRange -> {{-1, 5}, {-2, 1}}]; > > Hope this hepls > Wolfgang > > > Pratik Desai wrote: > >> Hello all >> >> I am trying to use DSolve to solve a ode with discontinuity in it (wave >> equation with a viscous damper injected at a location d) >> >> This is what i am using >> >> DSolve[{y''[x]-lamda^2*y[x]==DiracDelta[x-d]*y[x],y[0]==0,y[L]== >> =0},y[x],x] >> >> the problem I am facing is that >> >> y[x] on the right hand side (next the delta function) varies w.r.t to >> the location >> >> y[x]==y[x]&& 0<=x<=d >> y[x]==y[L-x]&&d<=x<=L >> >> I can solve the above equation without the y[x] coupled to the delta >> function >> >> Please advise and thanks in advance, >> >> >> Pratik Desai >> >> >> ps: This is my third attempt at posting my query, I hope this time it >> makes it to the list :) >> >> >> >> >

**Follow-Ups**:**Re: Re: Re: newbie question DSolve (revisited)***From:*Oleksandr Pavlyk <pavlyk@phys.psu.edu>

**Re: Re: Re: newbie question DSolve (revisited)***From:*yehuda ben-shimol <benshimo@bgu.ac.il>

**References**:**Re: newbie question DSolve***From:*"Dr. Wolfgang Hintze" <weh@snafu.de>