Wronskian test for linear independence of solutions

Statement

Let $I$ be an open interval, let $a_0, \dots, a_{n-1} : I \to \mathbb{R}$ be continuous, and let $y_1, \dots, y_n$ be solutions on $I$ of the homogeneous linear equation $y^{(n)} + a_{n-1}(x) y^{(n-1)} + \dots + a_0(x) y = 0$. Let $W = W(y_1, \dots, y_n)$ be their Wronskian. Then these three conditions are equivalent. (a) The functions $y_1, \dots, y_n$ are linearly independent on $I$. (b) There is a point $x_0 \in I$ with $W(x_0) \ne 0$. (c) For each $x \in I$, $W(x) \ne 0$.