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

*To*: mathgroup at smc.vnet.net*Subject*: [mg132359] How to replace some variables and how to solve a differential equation?*From*: bluesaturn <bluesaturn.at.kellnerweg.de at gmail.com>*Date*: Thu, 20 Feb 2014 03:27:39 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-outx@smc.vnet.net*Delivered-to*: mathgroup-newsendx@smc.vnet.net

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