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From the differential equation of the fa...

From the differential equation of the family of ellipses
` (x^(2))/(a^(2)) + (y^(2))/(b^(2)) = 1` by eliminating arbitrary constants a and b.

Text Solution

Verified by Experts

The correct Answer is:
` xy(d^(2)y)/(dx^(2)) + x ((dy)/(dx))^(2) - y (dy)/(dx) = 0`
Which represents the differential equation of the family of elipses (1).
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