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equation we will get the complete differential of some function
in left part  yxu , :
 Pdx  Qdy  du ,
where a condition is executed

  P   Q 
.  (2.11)
y  x 

It is easily to find an integrating cofactor in such two case:
1   P  Q 
1)      F  x , then there is an integrating

Q  y  x  
cofactor      x which depends on a variable only and can be
found from differential Equation

 P  Q

d ln  y  x 
.  (2.12)
dx Q

1   Q  P 
2)     F  y , then there is an integrating
P  x  y   1


cofactor      y which depends on a variable only and can be
found from differential equation

 Q  P

d ln  x  y 
.  (2.13)
dy P

1   P  Q 
3)     F  x , then there is an integrating
Q  y  x    2

cofactor     x which depends on a variable only and can be
found from differential equation

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