       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>
• Sender: owner-wri-mathgroup at wolfram.com

```Try the following

In:=
DSolve[{Derivative[y][x] - lamda2*y[x] ==
DiracDelta[x - d]*f, y == 0, y[l] == 0}, y[x],
x]

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:=
> DSolve[{y''[x] - lamda^2*y[x] == DiracDelta[x - d]*y[d], y == 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".
>
>
>
>
>
> 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:=
>>s = DSolve[{-y[x] + Derivative[y][x] == DiracDelta[d - x]*y[d], y
>>== 0, y[L] == 0}, y[x], x]
>>
>>From In:=
>>DSolve::"nvld" : "The description of the equations appears to be
>>ambiguous or \
>>invalid."
>>
>>Out=
>>{{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:=
>>DSolve::"nvld" : "The description of the equations appears to be
>>ambiguous or \
>>invalid."
>>
>>Extracting the solution to u[x]
>>
>>In:=
>>u[x_] = y[x] /. s[]
>>
>>you can Plot it, after assigning numeric values to all relevant
>>quantities:
>>
>>In:=
>>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,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
>>>
>>>
>>>
>>>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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```

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