Two questions in diophantine approximation

Abstract

The first question is about a possible variation on Dirichlet's approximation theorem for linear forms αx+βy+z, wherex,y are restricted topositive integers. The second question, which turns out to be related to the first, is about approximation to elements in a power series fieldk((t −1)) by solutions β of first order linear differential equationsxβ′+yβ+z=0, wherex,y,z are polynomials int.