|Method of Inverse Operators|
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:
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.