Re: Re: Re: newbie question DSolve (revisited)

*To*: mathgroup at smc.vnet.net*Subject*: [mg52140] Re: [mg52118] Re: [mg52090] Re: newbie question DSolve (revisited)*From*: Oleksandr Pavlyk <pavlyk at phys.psu.edu>*Date*: Fri, 12 Nov 2004 02:13:53 -0500 (EST)*Organization*: Penn State University; Department of Physics*References*: <cmppui$mll$1@smc.vnet.net> <200411100945.EAA11259@smc.vnet.net> <200411110952.EAA28827@smc.vnet.net>*Reply-to*: pavlyk at phys.psu.edu*Sender*: owner-wri-mathgroup at wolfram.com

Try the following In[26]:= DSolve[{Derivative[2][y][x] - lamda2*y[x] == DiracDelta[x - d]*f, y[0] == 0, y[l] == 0}, y[x], x] instead. f would be just another parameter in your equation. Once the solution is found, see if y[d] can be made equal to f by say choosing a special value of lambda. Regards, Sasha Pratik Desai wrote: > 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 > To: mathgroup at smc.vnet.net > Subject: [mg52140] [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 :) >>> >>> >>> >>> >> > -- Office: 6H Osmond Web: http://www.pavlyk.com ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ No trees were destroyed to send this mail, but a lot of electrons were terribly disturbed.

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

**Re: Re: newbie question DSolve (revisited)***From:*"Pratik Desai" <pdesai1@umbc.edu>