Abstract: This paper is devoting to study the growth of solutions of some types of higher-order linear differential equations with entire coefficients. One of its coefficients is an entire function extremal for Denjoy's conjecture. By using the value distribution theory of meromorphic functions and the asymptotic value theory of entire functions, and comparing the size of the module of each item appeared in such equations, the estimation on the growth order of its solutions are obtained. It is proved that any nontrivial solution of the equation with one dominant coefficient is of infinite, when there exists one coefficient satisfying the second-order differential equation. The same result also holds for the equation with coefficients having the same growth order and the exponential expressions. The obtained results are the generalization and supplement of some previous results in linear differential equations.

Key words: differential equation, entire function, Denjoy's conjecture, order of growth