Example 20  Find the general solution of the differential equation 
2
2
(
0)
xdy
y
x
x
dx +
=
≠ Solution The given differential equation is
2
xdy
dx +y
 = x2 (1)
Dividing both sides of equation (1) by x, we get
2
dy
y
dx
+x
 = x
which is a linear differential equation of the type 
P
Q
dy
dx +y
=
, where 
2
P
=x
 and Q = x So
I