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Re: Change of function in an ODE

  • To: mathgroup at smc.vnet.net
  • Subject: [mg109091] Re: Change of function in an ODE
  • From: Simon Pearce <Simon.Pearce at nottingham.ac.uk>
  • Date: Mon, 12 Apr 2010 23:00:15 -0400 (EDT)

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 at yahoo.com]
Sent: 11 April 2010 09:33
To: mathgroup at smc.vnet.net
Subject: [mg109091] [mg109043] 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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