Re: Change of function in an ODE

• To: mathgroup at smc.vnet.net
• Subject: [mg109082] Re: Change of function in an ODE
• From: dh <dh at metrohm.com>
• Date: Mon, 12 Apr 2010 22:58:31 -0400 (EDT)
• References: <hps1fg\$6l4\$1@smc.vnet.net>

```On 11.04.2010 10:32, Sam Takoy wrote:
> Hi,
>
> I'm solving
> DSolve[r^4 R''''[r] + 2 r^3 R'''[r] - r^2 R''[r] + r R'[r] -
>       L^4 r^4 R[r] == 0, R[r], r] // Simplify
>
> Now, I would like to make the substitution  R[r]=r^2 Log[r] G[r],
> formulate the equation for G[r] and solve it. What's the proper syntax
> for that?
>
> Thanks,
>
> Sam
>
Hi Sam,
the easiest way to write your equation in terms of G instead of R seems
to replace the symbol "R" by an anonymous function. Here is a simple
example:
t = R'[r];
t /. R -> (#^2 Log[#] G[#] &)
this will write R'' in terms o f G.
For your problem we would have:
t = r^4 R''''[r] + 2 r^3 R'''[r] - r^2 R''[r] + r R'[r] - L^4 r^4 R[r];
t /. R -> (#^2 Log[#] G[#] &)

cheers, Daniel

--

Daniel Huber
Metrohm Ltd.
Oberdorfstr. 68
CH-9100 Herisau
Tel. +41 71 353 8585, Fax +41 71 353 8907
E-Mail:<mailto:dh at metrohm.com>
Internet:<http://www.metrohm.com>

```

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