I'm having some problems recognizing duplication when using the undetermined coefficients method to solve homogeneous type differential equations. http://college.cengage.com/mathematics/larson/calculus_early/3e/shared/chapter15/clc7eap1504.pdf Example 2 on Page 1119, could someone explain to me why there is duplication in that problem because I am just not seeing it. And when there is duplication, do you multiply each term in the particular solution by the variable, t, or just a select few? This is my main concern with undetermined coefficients. To check for duplication, do you look [itex]g(t)[/itex] and [itex]y_c(t)[/itex] and see if there are any alike terms then move on to your initial guess and multiply through by t if there are any like terms? I'm just having some trouble with this concept. If someone could explain it to me in some detail that would be great, as the sites I've found just don't explain it well enough, though the site linked above is the best one I've come across so far. My textbook doesn't even mention duplication sadly.