Hi, I'd just like to have a quick clarification with regards to the method of undetermined coefficients. I know that if a characteristic equation has the form (r-4)3 = 0 then the characteristic solution will be yc = e4t + te4t + t2e4t + t3e4t and the particular solution ought to be Y = At4e4t That all makes sense to me. But I was wondering how the particular solution is to be found if the characteristic solution isn't entirely one root. Like if it was (r-4)2(r-2) =0 The characteristic solution would be yc = e4t + te4t + e2t My question then is two-fold. First, how do I structure the particular solution with regard to the method of undetermined coefficients? Because when all the roots repeat then the particular is just one power of t greater than the greatest one in the solution, like in my first example. But with two different roots out of 3 (or think of any other example), I'm not sure what to do. Can I even use that method, or is a particular solution even necessary when the characteristic equation has more than just repeated roots? Hopefully I wrote this clear enough to convey what I'm asking.