(3)
Eliminating a and b from equations (1), (2) and (3), we get
2
d y2
y
dx
+
 = 0 (4)
which is free from the arbitrary constants a and b and hence this the required differential
equation © NCERT
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DIFFERENTIAL EQUATIONS
389
Example 6 Form the differential equation
representing the family of ellipses having foci on
x-axis and centre at the origin Solution We know that the equation of said family
of ellipses (see Fig 9