Using FindRoot or interpolation function with symbolic argument

*To*: mathgroup at smc.vnet.net*Subject*: [mg92164] Using FindRoot or interpolation function with symbolic argument*From*: exoptery at gmail.com*Date*: Mon, 22 Sep 2008 05:26:07 -0400 (EDT)

I'd like to use NDSolve to integrate a pair of ODEs. Expressing the system as a set of explicit equations, however, requires the inverse of ArcTanh[x] / x. I thought I'd define a function for this as follows: f = Compile[{{y, _Real}}, x /. FindRoot[ArcTanh[x] == y x, {x, 99/100}]]; However, when I set, say, eqn1 = u'[R] == u[R] f[(u[R] (1 + v[R])^2)/(1 + v[R]^2)] Mathematica clearly dislikes the use of symbols instead of a numerical argument. Is there a way to define an NDSolve-digestible equation that calls FindRoot with symbolic arguments? Thank you for your attention. J.