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Re: Re: PDE's with DSolve
*To*: mathgroup at smc.vnet.net
*Subject*: [mg6055] Re: [mg6045] Re: [mg5983] PDE's with DSolve
*From*: sherod at boussinesq.Colorado.EDU (Scott Herod)
*Date*: Sun, 16 Feb 1997 01:11:57 -0500
*Organization*: /usr/local/lib/rn/organization
*Sender*: owner-wri-mathgroup at wolfram.com
Perhaps I am misunderstanding your comments. If so please forgive my
explanation.
When I say "Solve the differential equation F(x,y(x),y'(x)) = 0"
I mean find the function y(x) such that F(x,y,y') is always zero on some
set (interval) of x's. For many functions F there are standard ways
to find such functions y(x).
In the case of the problem that I asked Mathematica to solve (in easy
notation)
d^2
---- y(x,t) = 0 (or y_{tt} = 0}
dt^2
the true solution is y(x,t) = a(x) + b(x) * t
where a and b are arbitrary functions of x.
Mathematica on the otherhand returns y(x,t) = a(x) + b(t) which
is wrong.
If you ask Mma to solve y_{xt} = 0 it appears to return
y = k x t + a(x) + b(t). I say appears because the actual result is
{{y[x[1],x[2]]\[Rule]-DSolve`DSolveDump`b$12 x[1] x[2]+C[1][x[1]]+C[2][x[2]]}}
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ (??)
At any rate this is also not correct.
Scott Herod
sherod at newton.colorado.edu
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
In article <5e0vt8$dlr at smc.vnet.net> "Christopher R. Carlen" <crobc at epix.net> writes:
>Scott Herod wrote:
>>
>> I was happy to see that DSolve can solve some quasi-linear partial
>> differential equations and was happily playing with it. I then tried
>> the following:
>>
>> DSolve[D[y[x,t], {t,2}] == 0, y[x,t], {x,t}].
>>
>> Rather distressing.
>>
>> Scott Herod
>
>Wouldn't it be necessary to have previously defined y[x,t] to be some
>explicit function?
>
>In other words, I cannot possibly solve even
>
>F(x,y,y')=0 without having knowledge of the function y(x) .
>
>Once y(x) is defined, then I can consider the means to find a solution.
>
>_____________________
>Christopher R. Carlen
>crobc at epix.net
>carlenc at cs.moravian.edu
>
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