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For the differential equation dy/dx = y tan x - y² sec x, which of the following is an integrating factor?

1. tan x
2. sec x
3. cosec x
4. cot x

Correct answer: sec x

Solution

This is a Bernoulli equation. Dividing by y^2 and setting v = 1/y gives v' + v tanx = secx. The integrating factor is e^{integral tanx dx} = e^{ln secx} = sec x.

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