Important! The above table holds only when NO term in the trial function shows up in the complementary solution. If any term in the trial function does appear in the complementary solution, the trial function should be multiplied by to make the particular solution linearly independent from the complementary solution. If the modified trial function still has common terms with the complementary solution, another must be multiplied until no common term exists.
Pros and Cons of the Method of Undetermined Coefficients:The method is very easy to perform. However, the limitation of the method of undetermined coefficients is that the non-homogeneous term can only contain simple functions such as , , , and so the trial function can be effectively guessed.