Exact Solutions of Linear Partial Differential Equations with Variable Coefficients

Bäcklund transformations relating the solutions of linear PDE with variable coefficients to those of PDE with constant coefficients are found, generalizing the study of Varley and Seymour 2]. Auto-Bäcklund transformations are also determined. To facilitate the generation of new solutions via Bäcklund transformation, explicit solutions of both classes of the PDE just mentioned are found using invariance properties of these equations and other methods. Some of these solutions are new.