Solution
= Solution
Suppose $\varphi_2$ has no zero in $(x_1,x_2)$. It has a constant sign there, so replace it by its negative if needed and apply part (i). The conclusion is $q_1\equiv q_2$ on that interval. Taking the contrapositive proves the <Sturm comparison theorem>: unless the coefficients agree identically, $\varphi_2$ has a zero between the consecutive zeros of $\varphi_1$.