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
+ (1)
Clearly, (1) is a homogenous differential equation