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where a ( , i  2 , 1 ,..., ) n - the set material numbers, f (x )  0 -
i
the function.
The common decision of such equation, as known, is
determined by a formula

(xy )  ~ (x )  y ( * x ), (6.13)
y

~
where (xy )- common decision of proper LHDE, and *y (x ) -
some partial decision LNDE (6.12). Higher the algorithm of
construction of general decisions of LHDE with constant
coefficients was thoroughly considered.
In some case, when a function (xf ) has the special kind,
the method of selections of type of partial decision LNDE is
used after the type of this function - right part of equation (6.12).
Thus for determination of partial decision the method of
indefinite coefficients is used.
We will consider these cases.
1 Rights the part of LNDE (6.12) has a kind:

s
f ( x)  Q ( x) e  x  ( A x  A x s 1  ...  A e )  x . (6.14)
s 0 1 s

If  is not the root of characteristic equation of proper
LHDE, we search the decision part in a kind:

s
y*  P ( x) e  x  ( B x  B x s 1  ...  B e )  x . (6.15)
s 0 1 s

Here is P (x ) - polynomial of degree s with indefinite
s
coefficients B , B ,..., B .
0 1 s
If  is the root of characteristic equation of multiple r , we
search the decision part *y in a kind:

s
r
y*  x r P ( x) e  x  x ( B x  B x s 1  ...  B e )  x . (6.16)
s 0 1 s

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