       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:=
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
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:=
> 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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