On the asymptotic behavior of the solution of the second order linear differential equation

In work the problem of finding of the decision of one of kinds of the differential equation of the second order is considered. In this equation maximum wide assumption concerning factor of the equation that is the sum of a polynomial and almost periodic function of some kind is made. With the help of so-called method VKBJ it is constructed formal asymptotic decomposition of the decision that according to A. M. Iljin’s theorem is also the present decomposition.