Solution of the equation d/dx(pdu/dx)+qu=cu by a solution of the equation d/dx(pdu/dx)+qu=0

Abstract

We give a simple solution of the equation d/dx(pdu/dx)+qu=cu whenever a nontrivial solution of d/dx(pdu/dx)+qu=0 is known. The method developed for obtaining this result is based on the theory of pseudoanalytic functions and their relationship with solutions of the stationary two-dimensional Schrodinger equation. The final result, that is the formula for the general solution of the equation d/dx(pdu/dx)+qu=cu has a simple and easily verifiable form.