Functions with Nonzero Wronskian form a fundamental solution set

Abstract

This self-contained note could find classroom use in a course on differential equations. It is proved that if y1(x) and y2(x) are C 2 -functions whose Wronskian is never zero for α < x < β, then y1 and y2 form a fundamental solution set for a uniquely determined second-order linear homogeneous ordinary differential equation, y″ + p(x)y′ + q(x)y = 0, whose coefficients, p(x) and q(x), are continuous on (α, β).