Related non-homogeneous partial differential equations

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Abstract
The author's technique for relating the solutions of pairs of homogeneous partial differential equations is extended to nonhomogeneous equations. This method is first developed for a canonical class of non-homogeneous equations having homogeneous terms which resemble generalized hypergeometric operator equations. Transformations are obtained which connect pairs of non-homogeneous terms and pairs of solutions. Formulas involving shifts on parameters are also developed. Numerous important equations from applied mathe¬matics can be reduced to some one of these canonical types (through changes of variables) and their solution properties can be readily inferred. The theory developed is employed to treat (i) shifting relations on solutions of non-homogeneous GASPT equations, (ii) a projection technique for elliptic equations and (iii) solutions of higher order homogeneous equations through a factorization procedure

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