(1)
Substituting y = 0 and 
2
x
=π
 in equation (1), we get
0 =
2
sin
C
2
2
π
π
⎛
⎞
⎛
⎞ +
⎜
⎟
⎜
⎟
⎝
⎠
⎝
⎠
or
C =
2
4
−π
Substituting the value of C in equation (1), we get
y sin x =
2
2 sin
4
x
x
π
−
or
y =
2
2
(sin
0)
4 sin
x
x
πx
−
≠
which is the particular solution of the given differential equation Example 23 Find the equation of a curve passing through the point (0, 1) If the slope
of the tangent to the curve at any point (x, y) is equal to the sum of the x coordinate
(abscissa) and the product of the x coordinate and y coordinate (ordinate) of that point Solution We know that the slope of the tangent to the curve is dy
dx