Annihilator method

Summary

The annihilator method finds a particular solution of a linear differential equation $L y = f$ with constant coefficients. It applies when the right side $f$ itself solves some homogeneous constant-coefficient equation $A f = 0$. Applying $A$ turns the problem into the homogeneous equation $A L y = 0$, whose solutions are known, and this tells exactly which trial functions to use. It is the systematic form of the method of undetermined coefficients.