Application of Laplace Transform Method to Solve Neutral-Type Delay Differential Equation

This study investigates the use of the Laplace transform method to resolve a particular class of second-order linear initial-value neutral delay differential equations, which are prevalent in fields such as physics and engineering. By employing this analytical approach, we derive exact solutions that facilitate a deeper awareness of the dynamics of the system and its stability characteristics. A thorough illustrative example is provided to illustrate the Laplace transform method's efficacy, showcasing its practical utility in addressing real-world problems. This study not only highlights the advantages of the Laplace transform in providing clear insights into complex delay systems but also emphasizes its relevance in both theoretical and applied contexts.