Generating Relative and Absolute Invariants of Linear Differential Equations

Abstract 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 equa-tion. Explicit constructions are made for the linear ODEs of order five. The approach used for the explicit determination of invariants is based on an in-finitesimal method