x2 =
( ) (2
)
C
x
x
dx +
∫
 = 
3
x dx +C
∫
or
y =
2
2
C
x4
x−
+
which is the general solution of the given differential equation © NCERT
not to be republished
DIFFERENTIAL EQUATIONS
411
Example 21 Find the general solution of the differential equation y dx – (x + 2y2) dy = 0 Solution The given differential equation can be written as
dx
x
dy
−y
 = 2y
This is a linear differential equation of the type 
1
1
P
Q
dx
x
dy +
=
, where 1
1
P
= −y
 and
Q1 = 2y Therefore 
1
1
log
log( )
1
I