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We determine unknown numbers B , B ,..., B by the
0 1 s
method of indefinite coefficients, that is putting y and
*
)
(n
, * y  ..., y * in LNDE (2.35), equate coefficients at identical
degrees x . The upshots of the got system of Equations are
numbers B , B ,..., B .
0 1 s
2 Rights the part LNDE (6.12) has a kind:

f ( x)  e  x Q ( x cos) x   P ( x sin)  x  , (6.17)
s 1 s 2

where Q (x ), P (x ) are polynomials of degrees s , s
1 s 2 s 1 2
accordingly with the set coefficients max( s , s )  s .
1 2
If a complex number  i  is not present among the roots
of characteristic equation of proper LHDE, we search *y in a
kind:
y*  e  x u ( x cos)  x  ( x sin)  x  (6.18)
s s

where u (x ), (x ) - polynomials of degree s with indefinite
s s
coefficients.
If a number  i  is the root of characteristic equation of
multiple r we search *y in a kind:

e
y*  x r  x u ( x cos)  x  ( x sin)   x , (6.19)
s s

where u (x ), (x ) - polynomials of degree s with indefinite
s s
coefficients.
We will notice that type of decision (6.18) or (6.19) is kept
and in the case when in a formula (6) absent element, that
contains cos x  or sin x  .
If a function does not fall under the type of the resulted
functions, if it is possible, convert thus, that she was the sum of
elements, each of which has the special kind. Principle of
superposition of decisions is farther used.

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