Revised approach using the method of undetermined coefficients to determine the particular solution

We introduce a modification technique on the method of undetermined coefficients to explicitly find the particular solution of a second-order linear nonhomogenous differential equation when the coefficients are constant and the nonhomogenous part is either exponential, or polynomial, or sine, or cosine. We will state some sufficient conditions on the constant coefficients for this class of differential equations in order to find its particular solution more rapidly. We will provide some examples to show the validity of all results.