This chapter explores the Method of Variation of Parameters, a robust and versatile analytical technique used to determine particular solutions for non-homogeneous linear differential equations. Unlike the Method of Undetermined Coefficients, this approach is universally applicable to any continuous non-homogeneous term and does not require constant coefficients, provided the solutions to the corresponding homogeneous equation are known. The chapter details the use of the Wronskian to ensure the linear independence of homogeneous solutions and introduces the formula for reduction of order to find a second independent solution when only one is initially provided. Through a comprehensive suite of solved examples, the text demonstrates how to construct particular solutions by integrating variable parameters, while also integrating MATLAB applications to perform symbolic differentiation, integration, and verification of complex results. This chapter effectively bridges theoretical derivation with computational practice, offering a complete framework for solving higher-order linear equations that defy simpler methods.