MUTUA’S METHOD: PARTICULAR POLYNOMIAL AND COEFFICIENTS OF PARTICULAR INTEGRALS OF THE FORMcxn eAx

Abstract

In many problems involving solutions to ordinary differential equations, students and researchers in the field of applied mathematics are faced with challenges of obtaining the particul ar integrals. In particular, when the defined problem is formulated wit h non-homogeneous Ordinary Differential Equations wi th constant coefficients, Methods of Undetermined coefficients prove to be lengthy. Solutions to this will be reached by us e of a polynomial, which we shall call particular polynomial whose v alues at given ins tants will be us ed to determine the coefficients of thes e particular integrals. We will define the polynomial)(tp q of degreeq fornq n, been the order of the given ODE, by))()...()(()( 121 qqq mtmtmtmttp   .s m being the root of the characteristic function all not equal toc (in the exponenti al). Ifk are the number of roots all equal toc , then the particular i ntegral is,cxk kn p ex cPk y )(! 1  nk ,...,2,1,0