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From: Sam Takoy on 11 Apr 2010 04:32
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

From: DrMajorBob on 12 Apr 2010 06:46
eqn = Module[{R},
R[r_] = r^2 Log[r] g[r];
r^4 R''''[r] + 2 r^3 R'''[r] - r^2 R''[r] + r R'[r] -
L^4 r^4 R[r] == 0] // Simplify

r (L^4 r^3 g[r] Log[r]-3 (8+3 Log[r]) (g^\[Prime])[r]-r ((24+23 Log[r])
(g^\[Prime]\[Prime])[r]+r (2 (2+5 Log[r]) (g^(3))[r]+r Log[r]
(g^(4))[r])))==0

You still need initial conditions, and you can probably omit the factor
r... since the expression won't be useful near r == 0, due to the Log[r]
terms.

Bobby

On Sun, 11 Apr 2010 03:32:53 -0500, Sam Takoy <sam.takoy(a)yahoo.com> 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
>


--
DrMajorBob(a)yahoo.com

From: Christoph Lhotka on 12 Apr 2010 06:46
hello,

there is an straigthforward way to tell Mathematica to replace funtions
AND their derivatives in expressions/equations:

expr=r^4 R''''[r] + 2 r^3 R'''[r] - r^2 R''[r] + r R'[r] - L^4 r^4 R[r] == 0

expr/.Table[D[R[r]->r^2 Log[r] G[r],{r,i}],{i,0,4}]

which you can now try to solve..

christoph


From: dh on 12 Apr 2010 22:56
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(a)metrohm.com>
Internet:<http://www.metrohm.com>


From: Simon Pearce on 12 Apr 2010 22:58
I would use:

eqn ==
r^4 R''''[r] + 2 r^3 R'''[r] - r^2 R''[r] + r R'[r] - L^4 r^4 R[r];

Simplify[eqn /. R -> Function[{r}, r^2 Log[r] G[r]]]

Which works well for me.

Simon

-----Original Message-----
From: Sam Takoy [mailto:sam.takoy(a)yahoo.com]
Sent: 11 April 2010 09:33
Subject: Change of function in an ODE

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


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