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Find the differential equation satisfied by the family of conics given by ax² + by = 1, where a and b are arbitrary parameters:
- xy (d²y)/(dx²) + ((dy)/(dx))² - y (dy)/(dx) = 0
- xy (d²y)/(dx²) - ((dy)/(dx))² + y (dy)/(dx) = 0
- xy (d²y)/(dx²) - x ((dy)/(dx))² - y (dy)/(dx) = 0
- None of the above
Correct answer: None of the above
Solution
The family of conics defined by the equation ax² + by = 1 does not yield a differential equation that matches any of the provided options, indicating that none of them accurately represent the relationship derived from the original equation.
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