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If y = (2x/pi - 1) cosec x is a solution of the differential equation dy/dx + P(x) y = (2/pi) cosec x on 0 < x < pi/2, find P(pi/4).

1. 1
2. 0
3. 1/2
4. sqrt(2)

Correct answer: 1

Solution

Substituting y and y' into the equation reduces P(x) to cot x, so P(pi/4) = cot(pi/4) = 1.

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