Title: Commutativity and Commutative Pairs of Some Differential Equations,
Abstract: In this study, explicit differential equations representing commutative pairs
of some well-known second-order linear time-varying systems have been derived.
The commutativity of these systems are investigated by considering 30
second-order linear differential equations with variable coefficients. It is
shown that the system modeled by each one of these equations has a commutative
pair with (or without) some conditions or not. There appear special cases such
that both, only one or neither of the original system and its commutative pair
has explicit analytic solution. Some benefits of commutativity have already
been mentioned in the literature but a new application for in cryptology for
obscuring transmitted signals in telecommunication is illustrated in this
paper.