ON THE CHOICE OF STANDARD SOLUTIONS FOR A HOMOGENEOUS LINEAR DIFFERENTIAL EQUATION OF THE SECOND ORDER

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Abstract
In this paper principles are set up for the choice of a pair of standard solutions of a homogeneous linear differential equation of the second order, suitable both for mathematical theory and for numerical tabulation. The equation is taken in the normal form and, in general, two cases arise: (i) with intervals of x called exponential regions, in which solutions behave roughly like positive and negative exponentials and are convex to the x-axis; (ii) with intervals of x called oscillatory regions, in which solutions cross and recross the x-axis as they oscillate, and are concave towards the axis.

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