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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. I am having trouble figuring out how to find a particular solution to a differential equation using the method of undetermined coefficients. Everything I've found from other sites hasn't worked.
The central idea of the method of undetermined coefficients is this: Form the most general linear combination of the functions in the family of the nonhomogeneous term d(x), substitute this expression into the given nonhomogeneous differential equation, and solve for . The class of \(g(t)\)’s for which the method works, does include some of the more common functions, however, there are many functions out there for which undetermined coefficients simply won’t work. Second, it is generally only useful for constant coefficient differential equations. The method is .