  We present an approach how to obtain solutions of arbitrary linear operator
equation for unknown functions. The particular solution can be represented by
the infinite operator series (Cyclic Operator Decomposition), which acts the
generating function. The method allows us to choose the cyclic operators and
corresponding generating function selectively, depending on initial problem for
analytical or numerical study. Our approach includes, as a particular case, the
perturbation theory, but generally does not require inside any small parameters
and unperturbed solutions. We demonstrate the applicability of the method to
the analysis of several differential equations in mathematical physics, namely,
classical oscillator, Schr\"odinger equation, and wave equation in dispersive
medium.
