Phase Analysis of a Linear Second Order O.D.E.

In order to give a more complete answer to the first question on page about the oscillatory nature of the solutions to the S-L d.e., and to the second question about the spectrum of allowed eigenvalues, we shall use the method of the Poincaré phase plane. It is particularly desirable to employ this method to linear ordinary differential equations (o.d.e.'s) of second order not only for the breadth and the depth of the obtained results, but also for the ease with which these results are obtained. A major contributing factor to the latter is that the method is capable of characterizing the solutions to any such differential equation, and it can do so geometrically.