11.1.2 Sturm-Liouville problem

Problem: Find the solutions \( y=y(x) \) of the differential equation, that are non-identically zero in the indicated area and satisfy the given boundary conditions (the Sturm-Liouville problem). \[ \left\{\begin{array}{c} y^{\prime \prime}+\lambda y=0, \quad \pi \leq x \leq 2 \pi \\ y(\pi)=y^{\prime}(2 \pi)=0 \end{array} .\right. \]