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Re: newbie question DSolve

• To: mathgroup at smc.vnet.net
• Subject: [mg52152] Re: newbie question DSolve
• From: "Dr. Wolfgang Hintze" <weh at snafu.de>
• Date: Fri, 12 Nov 2004 02:14:16 -0500 (EST)
• References: <cmppui$mll$1@smc.vnet.net> <200411100945.EAA11259@smc.vnet.net> <cmvemo$sk6$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

At least for my Mathematica 4.0 I've found the cause of the error message:
it is the y[d] which makes the trouble.

Replace it by a constant called yd evrything works fine.

Wolfgang

DrBob wrote:

> That use of DSolve returns unevaluated in version 5.0.1, with a different error message:
> 
> DSolve::litarg
> 
> To avoid possible ambiguity, the arguments of the dependent variable in `1` \
> should literally match the independent variables.
> 
> Bobby
> 
> On Wed, 10 Nov 2004 04:45:41 -0500 (EST), Dr. Wolfgang Hintze <weh at snafu.de> wrote:
> 
> 
>>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 :)
>>>
>>>
>>>
>>>
>>>
>>
>>
>>
> 
> 
> 

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