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On the Applications of a New Technique to Solve Linear Differential Equations, with and without Source ⋆

By N. Gurappa, Pankaj K. Jha and Prasanta K. Panigrahi

Abstract

Abstract. A general method for solving linear differential equations of arbitrary order, is used to arrive at new representations for the solutions of the known differential equations, both without and with a source term. A new quasi-solvable potential has also been constructed taking recourse to the above method. Key words: Euler operator; monomials; quasi-exactly solvable models 2000 Mathematics Subject Classification: 33C99; 81U15 1 A new procedure for solving linear differential equations Linear differential equations play a crucial role in various branches of science and mathematics. Second order differential equations routinely manifest in the study of quantum mechanics, in connection with Schrödinger equation. There are various techniques available to solve a given differential equation, e.g., power series method, Laplace transforms, etc. Not many general methods applicable to differential equations of arbitrary order exist in the literature (see [1] and references therein). We make use of a general method for solving linear differential equations of arbitrary order to construct new representations for the solutions of the known second order linear differential equations, both without and with a source term. This method has foun

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