The solution of sturm-liouville problems by D-C network analyzer

A GENERAL second-order ordinary differential equation occurring frequently in engineering analysis is ${d \over dx} \left [ f(x){d \phi \over dx} \right ]+ \lambda g(x) \phi = 0 \eqno{\hbox{(1)}}$ in which λ is a constant and f and g are arbitrary functions such that a finite solution exists in the interval of interest. It is the purpose of this paper to show how solutions satisfying this equation and various boundary conditions can be obtained by means of a simple d-c network analyzer. For such an equation, there exist only certain values of the parameter λ, the eigenvalues, which permit the solution to satisfy the boundary conditions. The first problem, then, is to determine one or more of these eigenvalues, whereupon the corresponding solutions can be obtained. This procedure presents considerable difficulty, and analytical solutions are available only for a few special cases.