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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 3) is
2
2
2
2
x
y
a
+b
 = 1 (1)
Differentiating equation (1) with respect to x, we get 
2
2
2
2
0
x
y dy
dx
a
+b
=
or
y
dy
x
⎛dx
⎞
⎜
⎟
⎝
⎠ =
2
−ab2