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 © NCERT
not to be republished
DIFFERENTIAL EQUATIONS
409
Steps involved to solve first order linear differential equation:
(i)
Write the given differential equation in the form 
P
Q
dy
dx +y
=
 where P, Q are
constants or functions of x only