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In this paper we study asymptotic properties of the third order trinomial delay differential equation $$y^{\text{'}\text{'}\text{'}}\left(t\right)-p\left(t\right)y^{\text{'}}\left(t\right)+g\left(t\right)y\left(\tau \left(t\right)\right)=0$$ by transforming this equation to the binomial canonical equation. The results obtained essentially improve known results in the literature. On the other hand, the set of comparison principles obtained permits to extend immediately asymptotic criteria from ordinary to delay equations.

The aim of this paper is to study asymptotic properties of the solutions of the third order delay differential equation $${\left(\frac{1}{r\left(t\right)}{y}^{\text{'}}\left(t\right)\right)}^{\text{'}\text{'}}-p\left(t\right)y^{\text{'}}\left(t\right)+g\left(t\right)y\left(\tau \left(t\right)\right)=0.*$$ Using suitable comparison theorem we study properties of Eq. () with help of the oscillation of the second order differential equation.