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 xf  ,  y   k f  yx,  (2.15)

In particular, if k  0 , we have the homogeneous function
of the zero measuring. For example, such is a function
2
x  y 2
f  yx,  
2 xy
2
2
( x)  ( y) 2 2 x  y 2 0
f  x,  y      f  yx, ,
2 x y   2 xy

2
and function  yxf ,   x  xy – is the homogeneous function
of the 2-th measuring, because of

2
2
f  x,  y  ( x)   x y   2 x (  2  y )   2 f  yx, 

We will notice that in the case when two functions
P  yx, ; Q  yx,  are homogeneous identical measuring, their
P  yx, 
relation  yxf ,   is the homogeneous function of the
Q  yx, 
zero measuring. It can always represent the homogeneous
function of the zero measuring as a function of relation of
y x
variables or .
x y

Definition 2.3 Homogeneous in relation to variables x and
y differential Equation of the first order of kind is named
 y 
.  y     (2.16)
 x 
or kind
 , yxP dx  Q  , yx dy  0 ,

where functions  yxP , ; Q  yx,  is homogeneous identical
measuring. This case is taken to previous (2.15) after

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