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How to replace some variables and how to solve a differential equation?

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Dear all,

I am really new to Mathematica.

I have two questions, please.

1. How to replace a variable in a function?

I have defined:

f[r_] := Log[((2*\[Lambda])/(\[Kappa]*r*
        Cos[\[Lambda]*Log[(r/RM)]]))^2]

RM, lambda >0

I want to replace r with u given  by

u=log[Kappa*r]

I did it by hand but whant to check my result.


2. How to check or solve the differential equation:

f"[u]=0.5*exp[2*u+f[u]]

It would be sufficient for me to insert f[u] and see if both sides are 
the same. So far I failed.

Thank you for your help.

Regards
Blue

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How to replace some variables and how to solve a differential equation? bluesaturn <bluesaturn.at.kellnerweg.de@gmail.com> - 2014-02-20 07:56 +0000

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