       dsolve?

• To: mathgroup at smc.vnet.net
• Subject: [mg57001] dsolve?
• From: Chris Chiasson <chris.chiasson at gmail.com>
• Date: Thu, 12 May 2005 02:32:49 -0400 (EDT)
• Reply-to: Chris Chiasson <chris.chiasson at gmail.com>
• Sender: owner-wri-mathgroup at wolfram.com

```Dear Mathematica Gurus:

In trying to find the area under a curve for polytropic compression of
an ideal gas, I have run into a problem with DSolve. I have two
workarounds, which are listed below, but I want to use DSolve. Any
suggestions?

Problem Code:
DSolve[{Derivative[W][V]==(P1*V1^k)/V^k,W[V1]==0},W,V]
"For some branches of the general solution, the given boundary conditions lead \
to an empty solution."

Workaround 1:
Assuming[{V1>V2>0},Integrate[(P1*V1^k)/V^k,{V,V1,V2}]]

Workaround 2:
First[DSolve[{Derivative[W][V]==(P1*V1^k)/V^k},W,V]]
First[Solve[W[V1]==0/.%,C]]
FullSimplify[W[V]/.%%/.%]

Thank you for your valuable time,
--
Chris Chiasson
http://chrischiasson.com/
1 (810) 265-3161

```

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