holds. Equation (13.75) is called the auxiliary equa-
tion (AE) or subsidiary equation of the difference
equation. Since the degree of the equation (13.75) is
m it has m roots l
1
, l
2
, …,
l
m
(say). Solving the AE
(13.75) we can write the Complementary Function
(CF) of the difference equation (13.70) as shown in
the table below.
13.8.1(b) Particular Integral
Operating equation (13.70) by the inverse operator
1()Ef
we get the particular integral of equation
(13.58) as
y
n
=
1
()Ef
f ( n) (13.77)
13.8.2 Short Methods for Finding
the Particular Integral
Rule 1 f ( n) =a
n
and f(a) ≠ 0 (13.78)
(1) PI=
1
()Ef
a
n
=
1
()af
a
n
(replace ...
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