Consider the following methods of finding the particular integral for a non-homogeneous differential equation. Discuss the reasoning and answers of the given questions.
(a) Methods of undetermined coefficient (Superposition approach and Annihilator approach)
(b) Method of variation of parameters.
1) For which particular forms of the input function g(x), the methods of undetermined coefficients are used? Also, discuss the reason to restrict to those particular forms of g(x).
2) In what way do you think the method of variation of parameters has an advantage over the methods of undetermined coefficients.