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A curve passes through (1, pi/6) and at every point (x, y) (with x > 0) its slope equals y/x + sec(y/x). Find the equation of the curve.
- sin(y/x) = log x + 1/2
- cosec(y/x) = log x + 2
- sec(2y/x) = log x + 2
- cos(2y/x) = log x + 1/2
Correct answer: sin(y/x) = log x + 1/2
Solution
With v = y/x the equation becomes x dv/dx = sec v, giving sin v = ln x + C; the point fixes C = 1/2.
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