Interpolation in asymptotic integration of second-order differential equations

For ordinary differential equations the equivalence concerning the common applicability domain is established for two known asymptotic integration methods, namely the method which reduces initial equation to nearly-diagonal Levinson type system and the approach based on reduction to Riccati-type equation. Besides the question is answered about the possibility of interpolation, i.e. treatment of both cases within the unified approach, that enables us to improve one result due to Hartman.