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Solve how to eliminate variable

• To: mathgroup at smc.vnet.net
• Subject: [mg105269] Solve how to eliminate variable
• From: Petr Martinec <petr.martinec at gmail.com>
• Date: Wed, 25 Nov 2009 23:00:52 -0500 (EST)

Hi dears,
I am using Solve to get differential equation from set of linear  and
differential equation. When I use code like this

Solve[{
  Subscript[F, t] == g m \[Phi][t],
  l Subscript[k, p]
\!\(\*SuperscriptBox["\[Phi]", "\[Prime]",
MultilineFunction->None]\)[t] == Subscript[F, p],
  l m
\!\(\*SuperscriptBox["\[Phi]", "\[Prime]\[Prime]",
MultilineFunction->None]\)[t] == F,
  -F == -Subscript[F, p] + Subscript[F, t] + Subscript[F, v],
  }, \[Phi]''[t]]

I obtain result like

{{
\!\(\*SuperscriptBox["\[Phi]", "\[Prime]\[Prime]",
MultilineFunction->None]\)[t] -> F/(l m)}}

but my goal is get result containing Fv:

{{
\!\(\*SuperscriptBox["\[Phi]", "\[Prime]\[Prime]",
MultilineFunction->None]\)[t] -> (-Subscript[F, v] - g m \[Phi][t] +
    l Subscript[k, p]
\!\(\*SuperscriptBox["\[Phi]", "\[Prime]",
MultilineFunction->None]\)[t])/(l m)}}

Can somebody help me how to do this using Solve or witch function to
use. I wouldn't like to use Rule and Replace.

Thanks
Petr Martinec