       Re: Change of function in an ODE

• To: mathgroup at smc.vnet.net
• Subject: [mg109053] Re: Change of function in an ODE
• From: DrMajorBob <btreat1 at austin.rr.com>
• Date: Mon, 12 Apr 2010 06:51:44 -0400 (EDT)

```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 at 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 at yahoo.com

```