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 (1)
Separating the variables in equation (1), we get
(2 – y) dy = (x + 1) dx (2)
Integrating both sides of equation (2), we get
(2
)
∫−y dy
=
(
1)
x
dx
+
∫
or
2
2
y −y2
 =
2
C1
x2
+x
+
or
x2 + y2 + 2x – 4y + 2 C1 = 0
or
x2 + y2 + 2x – 4y + C = 0, where C = 2C1
which is the general solution of equation (1) © NCERT
not to be republished
DIFFERENTIAL EQUATIONS
393
Example 10 Find the general solution of the differential equation 
2
2
11
dy
y
dx
x
=+
+