(2)
If h(y) ≠ 0, separating the variables, (2) can be rewritten as
1
( )
h y  dy = g(x) dx (3)
Integrating both sides of (3), we get
1
( ) dy
∫h y
=
( )
∫g x dx (4)
Thus, (4) provides the solutions of given differential equation in the form
H(y) = G(x) + C
Here, H (y) and G (x) are the anti derivatives of 
1
( )
h y  and g(x) respectively and
C is the arbitrary constant Example 9 Find the general solution of the differential equation 
1
2
dy
x
dx
+y
=
−
, (y ≠ 2)
Solution We have
dy
dx  =
1
x2
−+y