Abstract
The study of the symmetric properties of differential equations is essential for identifying effective methods for solving them. In this paper, we examine the oscillatory behavior of solutions of Emden-Fowler-type mixed non-linear neutral differential equations with both canonical and non-canonical operators. By utilizing integral conditions and the integral averaging method, we present new sufficient conditions to ensure that all solutions are oscillatory. Our results enhance and extend previous findings in the literature and are illustrated with suitable examples to demonstrate their effectiveness.