11.1.1 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). \[ \left\{\begin{array}{c} y^{\prime \prime}+\lambda y=0, \quad \frac{3}{4} \leq x \leq 1 \\ y\left(\frac{3}{4}\right)=y^{\prime}(1)=0 \end{array} \quad y \not \equiv 0 .\right. \]