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An application of the spread relation to differential equations

If a differential equation with meromorphic coefficients has a certain form where the growth of one of the coefficients dominates the growth of the other coefficients in a finite union of angles, then we show that this puts restrictions on the deficiencies of any meromorphic solution of the equation. We use the spread relation in the proofs. Examples are given which show that our results are sharp in several ways. Most of these examples are constructed from the quotients of solutions of w″ + G(z)w = 0 for certain polynomials G(z) and from meromorphic functions which are extremal for the spread relation.