Abstract
Summary The usual process for solving a nonhomogeneous system of linear differential equations is to find the general complementary homogeneous solution first and then construct a particular solution from it. When can we flip the script on this process and compute a particular solution first? This paper argues this is possible when the nonhomogeneous forcing function is analytic. It presents two different series expansions for this particular particular solution using power series methods, and reveals a surprising connection to the more familiar variation of parameters formula.
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