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In general case, when Q
  0x , we have linear
heterogeneous differential equation (LNDE). We will consider
the methods of his solving.
1 Method of variation of arbitrary constant (Lagrange
method)
Lagrange suggested to search decision LNDR in a kind
 P  dxx

 Cy  ex (2.28)
that is in place of arbitrary constant C some function appears in
a formula   xC (1.42) .
We will find derivative
  P  dxx   P  dxx
y  C  ex  C  ex   P  
x

and we will put y and y in equation (2.25):
  P  dxx   P  dxx   P  dxx
C  ex  P    exCx  P    exCx  Q  x ,
Relatively unknown function   xC we get equation with
separated variables, which it is possible to write down in a kind
 C    Qx  ex  P  dxx ,
from where
~
  xC   Q  ex  P  dxx dx  C (2.29)
~
where through C the marked arbitrary became integration.
Putting expression in right part of formula (2.29) in a
formula (2.28) in place of  xC , we will get the formula of
common decision LNDE (for comfort of record constant we
mark integration again through C ):
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