where the values of the constants A1 , A2 and B1, B2 are not simultaneously zero. Several methods have been proposed to determine the proper elements (i.e. eigenvalues and eigenfunctions) of Sturm-Liouville equations. Most of them have been reviewed by Kopal [1], but we shall examine one of them, the so called Rayleigh-Ritz method, in order to explain the main defect they have in common and to judge their general efficiency. This method was originally proposed by Ritz [2]. By transformations whose details will not be given here but which are described in many classical texts it leads to the solutions of equations of the form:
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M. Godart (1966) studied this question.