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  P  dxx  P  dxx
y  e ( Q  ex dx  C ) . (2.30)


We will write down a formula (2.30) in a kind



 P  dxx  P  dxx  P  dxx
y  Сe  e  Q  ex dx . (2.31)

We will find out maintenance of each terms in right part of
this equality:

 P  dxx
y  Сe – it is the common decision of proper
0
LHDE

y   e  P  dxx  Q  ex  P  dxx dx – some partial decision of
given LNDR, that swims out from formulas (2.28) and (2.29).
We will formulate a conclusion about the structure of
common decision LNDE: the common decision LNDE is the
sum of common decision of proper LHDE and some partial

decision LNDE: y  y  y .
0

Note 2.2 Formulas (2.30) or (2.31) optionally to memorize,
as a rule, it is simpler to do all process of method Lagrange
directly. However, the structure of common decision LNDE
needs to be well remembered.

Example 2.9 To find the common decision of equation
y 
1 x  y  cos . x

y cos x
 We will write down equation in a kind y    .
1  x 1  x
We will apply the method of variation arbitrary constant. We
y
will solve LHDE  y   0 at first, which is simultaneously
1 x
equation with the separated variables. We will separate variables

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