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