In the preface of Advanced Engineering Mathematics, 2nd Ed. by Zill and Cullen, it is claimed that the function relating the width of the Eiffel Tower as to the distance from its top, $x \mapsto f(x)$, is given by the solution of the following equation:
$$ af(x)\int_0^{x}f(t)^2\,dt=x\int_0^x f(t)\,dt - \int_0^x tf(t)\,dt $$
The authors invite readers who can solve this equation to email them the solution, and I have always wondered why they do this. Is it an open problem?