The Pantograph Delay Differential Equation (PDDE), which incorporates a linear functional argument, is the subject of this study, which is a generalization of a functional differential equation. A new Novel Analytical Method (NAM) is used in this article to solve the Pantograph Delay Differential Equation. This approach uses simple calculus to perform long-term computations and is unrelated to any recurrence relation, therefore we must be cautious regarding its convergence. The resultant solutions are more physically realistic since they solve non-linear problems without needing linearization, discretization, or perturbation. Furthermore, iterations may be converged to Exact Solutions rather quickly, resulting in more accurate findings. Several illustrated examples are provided below to demonstrate the technique's efficacy and dependability, especially in non-linear scenarios.

Keywords: Pantograph Delay Differential Equations, Novel Analytical Method, Tylor Series, Convergence Analysis.