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initial condition in using dsolve

• To: mathgroup at smc.vnet.net
• Subject: [mg64316] initial condition in using dsolve
• From: rudy <rud-x at caramail.com>
• Date: Sat, 11 Feb 2006 03:32:46 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

Hello,
I'm trying to use DSolve tu obtaine the solution of the PDE:
eq={D[f[x, t], t]+ v*D[f[x, t], x]==0, f[x, 0]==fo[x]}

but with the instruction

DSolve[eq, f, {x, t}]

Mathematica doesn't resolve.
It's strange because the solution is known:

f[x,t] = f[x- v t,0]

If I do:

eq={D[f[x, t], t]+ v*D[f[x, t], x]==0}
and
DSolve[eq, f, {x, t}]
it works:

out > {f -> Function[{x, t}, C[1][(t v - x)/v]]}

I don't understand why it works in the second case and not in the first...
can anybody help?
Regards
Rudy

• Follow-Ups:
  • Re: initial condition in using dsolve
    • From: Devendra Kapadia <dkapadia@wolfram.com>