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in Differential equations by (52.5k points)

The differential equation representing the family of ellipses having foci either on the x-axis or on the y-axis, centre at the origin and passing through the point (0, 3) is

(A) xyy'' + x(y')2 - yy' = 0

(B) x + y'' = 0

(C) xyy' + y2 - 9 = 0

(D) xyy' - y2 + = 0

1 Answer

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Answer is (D) xyy' - y2 + = 0

We know that general equation of ellipse is

x2/a2 + y2/b2 = 1

and passes through the point (0, 3). Therefore,

x2/a2 + y2/9 = 1   (1)

Differentiating the Eq. (1) with respect to x, we get

From Eqs. (1) and (2), the differential equation is

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