Re: newbie question DSolve
- To: mathgroup at smc.vnet.net
- Subject: [mg52090] Re: newbie question DSolve
- From: "Dr. Wolfgang Hintze" <weh at snafu.de>
- Date: Wed, 10 Nov 2004 04:45:41 -0500 (EST)
- References: <cmppui$mll$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
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 :) > > > >
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- Re: Re: newbie question DSolve (revisited)
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- Re: Re: newbie question DSolve (revisited)