Let $L$ be a self-adjoint differential operator given by $L=\frac{d}{dx}\left(a_2\frac{d}{dx}\right)+a_0$. If $u_1$ and $u_2$ are two solutions of $Lu=0$ and $J(u_1,u_2)=0$ for some $x$ for which $a_2(x)\not=0$, then show that $u_1$ and $u_2$ are linearly dependent.
I'm still learning about differential operators, but my knowledge of linear algebra is shaky. Linear dependence is $\exists c\in\mathbb{R}$ such that $u_1=cu_2$.
Any help on any of this would be greatly appreciated.