Now substituting the value of C in equation (2), we get the particular solution of the
given differential equation as 
212
1
y
x
=
+ Example 12 Find the equation of the curve passing through the point (1, 1) whose
differential equation is x dy = (2x2 + 1) dx (x ≠ 0) © NCERT
not to be republished
MATHEMATICS
394
Solution The given differential equation can be expressed as
dy* =
22
1
*
x
dx
x
 
 
 
 
 
 
 
or
dy =
1
2x
xdx
⎛
⎞
+
⎜
⎟
⎝
⎠ (1)
Integrating both sides of equation (1), we get
∫dy
 =
1
2x
xdx
⎛
⎞
+
⎜
⎟
⎝
⎠
∫
or
y = x2 + log |x| + C