On a universal differential equation for the analytic terms of C∞-superpositions on the real line

It is proved that every continuous function on the real line can be approximated uniformly (in the sense of a specific norm) by superpositions of analytic functions, which are solutions of a single universal differential equation. Every superposition is some function belonging to C∞(R). This improves a former result of the author, from which the superpositions are known to be continuous.  2004 Elsevier Inc. All rights reserved