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 F =
e∫x2 dx
= e2 log x = 
log2
2
x
e
=x
log
( )
[
( )]
f x
as e
f x
=
Therefore, solution of the given equation is given by
y