  We consider the phase-integral method applied to an arbitrary linear ordinary
second-order differential equation with non-analytical coefficients. We propose
a universal technique based on the Frobenius method which allows to obtain new
exact relation between connection matrices associated with its general
solution. The technique allows the reader to write an exact algebraic equation
for the Stokes constants provided the differential equation has at most one
regular singular point in a finite area of the complex plane. We also propose a
way to write approximate relations between Stokes constants in case of multiple
regular singular points located far away from each other. The well-known Budden
problem is solved with help of this technique as an illustration of its usage.
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