Solution Since 1 + y2 ≠ 0, therefore separating the variables, the given differential
equation can be written as
2
1
dy
+y
 =
2
1
dx
+x (1)
Integrating both sides of equation (1), we get
2
1
dy
∫+y
 =
2
1
dx
+x
∫
or
tan–1 y = tan–1x + C
which is the general solution of equation (1) Example 11 Find the particular solution of the differential equation 
2
4
dy
dx = −xy
 given
that y = 1, when x = 0 Solution If y ≠ 0, the given differential equation can be written as
dy2
y  = – 4x dx