In mathematics and its applications, a Sturm-Liouville problem is a second-order linear ordinary differential equation of the form:\(\frac{\mathrm{d}}{\mathrm{d} x}\left[p(x) \frac{\mathrm{d} y}{\mathrm{~d} x}\right]+q(x) y=-\lambda w(x) y\) for given functions \(p(x), q(x)\) and \(w(x)\), together with some boundary conditions at extreme values of \(x\).