EVALUATION OF THE INDEX AND SINGULAR POINTS OF LINEAR DIFFERENTIAL-ALGEBRAIC EQUATIONS OF HIGHER ORDER

摘要

We study linear systems of ordinary differential equations of higher order with an identically singular matrix at the higher derivative of the required vector-valued function in the domain of definition. We give definitions of the index and singular points for these systems, formulate the conditions of solvability, and deduce a formula for the general solution. The algorithms for finding the index and singular points are presented.