(6)
Fig 9 2
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MATHEMATICS
388
The required differential equation is then obtained by eliminating a and b from
equations (4), (5) and (6) as
F (x, y, y′, y″) = 0 (7)
�Note  The order of a differential equation representing a family of curves is
same as the number of arbitrary constants present in the equation corresponding to
the family of curves Example 4 Form the differential equation representing the family of curves y = mx,
where, m is arbitrary constant