On almost-periodical solutions of an equation

Abstract

Sufficient conditions are considered for existance of almost-periodical solutions of differential equation $\frac{dy}{dx}=p(x)y+q(x)$, where functions $p(x)$, $q(x)$ are $Sp$-almost periodical solutions in the sense of Stepanoff. A numerical-analytical algorithm of constructing almost-periodical solutions of such equations is proposed.