Method of Inverse Operators

Consider a linear non-homogeneous ordinary differential equation with constant coefficients

where are all constants and . Let

the ODE can be rewritten as

Thus, the particular solution is

The particular solution can be easily obtained, if the effects of the inverse operator have been studied in advance.

Inverse Operation of Common Functions:

Inverse Operator Results

Pros and Cons of the Method of Inverse Operators: The method of inverse operators can systematically solve some tough problems. However, if contains products of several simple functions e.g., , the method of inverse operators may be more tedious than the method of undetermined coefficients.