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 (1)
Integrating both sides of equation (1), we get
y∫dy2
 =
4 x dx
− ∫
or
−y1
 = – 2x2 + C
or
y =
212
x −C (2)
Substituting y = 1 and x = 0 in equation (2), we get,  C = – 1