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
