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If \(y=y(x)\) is the solution curve of the differential equation \(\frac{d y}{d x}+y \tan x=x \sec x, 0 \leq x \leq \fra…

Q1

If \(y=y(x)\) is the solution curve of the differential equation \(\frac{d y}{d x}+y \tan x=x \sec x, 0 \leq x \leq \frac{\pi}{3}, y(0)=1\), then \(y\left(\frac{\pi}{6}\right)\) is equal to

[JEE Main 2023, 1 Feb (Shift 1)]

a

\(\frac{\pi}{12}-\frac{\sqrt{3}}{2} \log _e\left(\frac{2}{e \sqrt{3}}\right)\)

b

\(\frac{\pi}{12}-\frac{\sqrt{3}}{2} \log _e\left(\frac{2 \sqrt{3}}{e}\right)\)

c

\(\frac{\pi}{12}+\frac{\sqrt{3}}{2} \log _e\left(\frac{2}{e \sqrt{3}}\right)\)

d

\(\frac{\pi}{12}+\frac{\sqrt{3}}{2} \log _e\left(\frac{2 \sqrt{3}}{e}\right)\)

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