Differential equations with a given set of solutions

Abstract

The aim of this paper is to study the following inverse problem of ordinary differential equations: For a given set of analytic functions ω={z1(t),…,zr(t)}, with zj(t)=xj(t)+iyj(t) and z¯j(t)=xj(t)−iyj(t) for j=1,…,r, defined in the open interval I⊆R, we want to determine the differential equation F(t,z¯,z,z˙,z¯˙,…,z(n),z¯(n))=0,where [Formula presented] for j=1,…,n, in such a way that the given set of functions ω is a set of solutions of this differential equation.