(3)
Substituting x = 0 and y = 1 in equation (3), we get
2 e0 + log |1| = C ⇒ C = 2
Substituting the value of C in equation (3), we get
2
yx
e  + log |y | = 2
which is the particular solution of the given differential equation Example 18 Show that the family of curves for which the slope of the tangent at any
point (x, y) on it is  
2
2
2
x
y
+xy
, is given by x2 – y2 = cx Solution We know that the slope of the tangent at any point on a curve is dy
dx Therefore,
dy
dx  =
2
2
2
x
y
xy
+
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DIFFERENTIAL EQUATIONS
405
or
dy
dx  =
2
2
1
2
yxy
x
+