Expansions That Grow on Trees, Volume 49, Number 4

430 NOTICES OF THE AMS VOLUME 49, NUMBER 4 Linear Ordinary Differential Equations How to solve linear ordinary differential equations? Like many outstanding mysteries of mathematics, this question has the virtue of simplicity. Linear differential equations are the staple of every mathematical syllabus, familiar to all and sundry, and their investigation has informed much of the development of mathematical analysis in the last three hundred years. Needless to say, we can all provide partial answers to this question. Thus, the solution of the scalar equation y′ = a(t)y, y(0) = y0, is y(t) = e ∫ t 0y0, t ≥ 0, while the solution of the vector equation y′ = Ay, y(0) = y0 ∈ RN, where A is a constant N ×N matrix, is y(t) = ey0, t ≥ 0.