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.
Additional information
Notes on contributors
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R. Travis Kowalski
Travis Kowalski earned his Ph.D. in mathematics from the University of California at San Diego. His mathematical interests include power series theory and the intersections of mathematics, culture, history, and art. He currently serves as the head of the Department of Mathematics at the South Dakota School of Mines and Technology.