Solving ay'' + by' + cy = 0 with a Simple Product Rule Approach

摘要

When elementary ordinary differential equations (ODEs) of first and second order are included in the calculus curriculum, second-order linear constant coef-ficient ODEs are typically solved by a method more appropriate to differential equations courses. This method involves the characteristic equation and its roots, complex-valued solutions, and some method (often mysterious, unnatural, or simply left unjustified) for establishing te~(rt) as a solution when r is the only real root. Here we outline a seldom used but more natural approach better suited to the calculus curriculum. Complex numbers are not needed, and the solution te~(rt) arises constructively.