This function g(x) = 
e∫P dx
 is called Integrating Factor
(I F )  of the given differential equation Substituting the value of g (x) in equation (2), we get
P
P
P
dx
dx
dy
e
e
y
dx
 
 
 
 =
P
Q
e  dx
 
or
Pdx 
d
dxy e
 
 =
P
Q
dx
e  
Integrating both sides with respect to x, we get
y e  Pdx
 
 =  
 
P
Q
dx
e
dx
  
 
or
y =
 
P
P
Q
C
dx
dx
e
e
dx
  
 
 
 
 
which is the general solution of the differential equation