Abstract
In this paper we reveal the relationship between the coefficients of a linear differential equation and its fundamental solutions. The relation is a generalzation of the relation (Viete's formulae) of the coefficients of a polynomial and its roots. As direct applications of the relation we give elegant ways to develop the determinant formulas for some Vandermonde-like and generalized Vandermonde-like matrices. In addition, we introduce and prove Newton-Girard formulas for a fundamental set of solutions of a linear homogeneous differential equation.