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b) We search the partial decision of heterogeneous Equation
in a kind:
x
*
y  C ( )x  C ( )x e ,
1 2

and functions C ( )x and C ( )x we search from the system of
1 1
equations
x
 C ( ) 1x   C ( )x e  0
 1 2
 x 1
 C 1 ( ) 0x   C 2 ( )x e  x ,
 1 e
from where
 C 1
 2 ( )x  e x (1 e x )


 C ( )x   1 .
  1 1 e x

Then
dx
C ( )x      x  ln(1 e x ) ,
1 x
1 e
C ( )x   e  x  x  ln(1 e x ) .
2

Constant integration we scorn (we search the partial
decision).
Consequently:
*
y    ln(1 e x ) 1 xe  x  e x ln(1 e x ).
x

c) the common decision of equation is:
*
x
y  y   x ln(1 e ) x ) 1 xe  x  e x ln(1 e x ) C  C e 
y   
1 2
 C  1 x  e x (C  x ) (1 e  x ) ln(1 e x ) .
1 2

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