About solves asymptotic form of ordinary differential equations

Solutions asymptotic behavior of $k$-order ordinary differential equations ($k=2,3,\dots$) is investigated. Sufficient conditions, in which solutions have a asymptotic form $x^{(r)}(t)=C_rt^{k-1-r}+o(t^{k-1-r})$, $r=0,1,\dots\,k-1$ as $t\to+\infty$, are received