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MathGroup Archive 1999

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Re: Manipulating differential equations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg18609] Re: [mg18552] Manipulating differential equations
  • From: "Andrzej Kozlowski" <andrzej at tuins.ac.jp>
  • Date: Tue, 13 Jul 1999 01:01:33 -0400
  • Sender: owner-wri-mathgroup at wolfram.com

Here is one possible way.

In[1]:=
dg1 = c''[x] + g c'[x];

In[2]:=
Block[{c = Function[x, Exp[-a x]]}, dg1]
Out[2]=
  2
 a     a g
---- - ----
 a x    a x
E      E

In[3]:=
Block[{c = Function[x, Sin[a x]]}, dg1]
Out[3]=
                2
a g Cos[a x] - a  Sin[a x]

In[4]:=
dg1
Out[4]=
g c'[x] + c''[x]
--
Andrzej Kozlowski
Toyama International University
JAPAN
http://sigma.tuins.ac.jp
http://eri2.tuins.ac.jp


----------
>From: Martin Heimann <martin.heimann at bgc-jena.mpg.de>
>To: mathgroup at smc.vnet.net
>Subject: [mg18609] [mg18552] Manipulating differential equations
>Date: Sat, Jul 10, 1999, 3:18 PM
>

> Dear colleagues,
>
> I would like to insert test functions into an expression that contains
> differentials:
>
> dg1 = c''[x] + g c'[x]
>
> I would like e.g. to replace c[x] by Exp[-a x]:
>
> dg1/.c[x]->Exp[-a x]
>
> but this doesn't work; one has to put substitution rules for each of the
> derivatives explicitly. Is there a more elegant way to achieve this?
>
> Cheers,
> Martin Heimann
> ------------------------------------------------------------------
> Max-Planck-Institut fuer Biogeochemie
> Postfach 100164, D-07701 Jena, Germany
> (Street Address: Tatzendpromenade 1a)
>
> Tel.:  +49-3641-64-3773/3701,  Fax.: +49-3641-64-3710
> Email: martin.heimann at bgc-jena.mpg.de


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