Practice Problems: Annihilator Method

The annihilator method is a technique used to solve nonhomogeneous linear differential equations. It is particularly useful when dealing with functions on the right-hand side that are composed of products, sums, or compositions of elementary functions. The method involves finding the differential operator commonly denoted using the big [latrex]D[/latex] notation that, when applied to the left-hand side of the equation, produces the homogeneous version of the equation.

This operator is called the annihilator of the nonhomogeneous term. Once the annihilator is found, the original equation is “multiplied” by it, which results in a homogeneous differential equation that can be easily solved using standard techniques. The particular solution to the original equation is then obtained by applying the solution found for the annihilated homogenous differential to the original differential equation. In this essay, we will explore the technique of the annihilator method in detail and provide examples to illustrate the process.