This chapter explores the D-operator (differential operator) method, a powerful algebraic framework designed to streamline the process of solving linear differential equations with constant coefficients. By substituting the derivative with the operator D, complex differential expressions are transformed into characteristic polynomials, allowing for a systematic approach to finding particular solutions. The text details specific theorems for handling a variety of forcing functions, including exponentials, trigonometric functions, and polynomials, while addressing specialized cases such as resonance—where the forcing function matches a root of the characteristic equation—and the use of Taylor series expansions for polynomial inputs. Complementing the theoretical derivations, the chapter provides extensive solved examples and integrates MATLAB verification to demonstrate how computational tools can validate analytical solutions and handle complex arithmetic. This method effectively reduces the calculus-heavy task of solving for the forced response of a system into a series of structured algebraic manipulations.