On generating relative and absolute invariants of linear differential equations

A general expression for a relative invariant of a linear ordinary differential equations is given in terms of the fundamental semi-invariant and an absolute invariant. This result is used to established a number of properties of relative invariants, and it is explicitly shown how to generate fundamental sets of relative and absolute invariants of all orders for the general linear equation. Explicit constructions are made for the linear ODE of order five. The approach used for the explicit determination of invariants is based on an infinitesimal method.