  We give a simple proof of a fairly flexible comparison theorem for equations
of the type $-(p(u'+su))'+rp(u'+su)+qu=0$ on a finite interval where $1/p$,
$r$, $s$, and $q$ are real and integrable. Flexibility is provided by two
functions which may be chosen freely (within limits) according to the situation
at hand. We illustrate this by presenting some examples and special cases which
include Schr\"odinger equations with distributional potentials as well as
Jacobi difference equations.

Classical Analysis and ODEs