I'm struggling with this question: we have two differentiable functions $p, q$ in some interval $I$ and the equation $(p(x)y')'+q(x)y=0$, with given solutions $u$ and $1/u$. We're asked to show $u$ solves a first-order differential equation.
What I tried: I tried two things: plugging the solutions to the equation and differentiating, and plugging the solutions and integrating (to get rid of the 2nd order derivative). It didn't get me very far, though ...