So-Called Cases of Failure in the Solution of Linear Differential Equations

Abstract

We turn now to the question of the generality of the solution of equation (2) obtainable by means of equation (3), that is, to the problem of the construction of integrals of the equationIn passing, we remark that it is shewn by the last example that integrals of equation (2) deduced from different functions satisfying the conditions of equation (3) may differ, so that a number of independent functions satisfying equations of the form of (3) may lead to an equivalent number of independent solutions of (2), or may lead to any smaller number other than zero.