Mathematics

Problem

y = y(x)

is the solution curve of the differential equation

\frac{dy}{dx} + y \tan x = x \sec x

0 \le x \le \frac{\pi}{3}

y(0) = 1

, then

y\left(\frac{\pi}{6}\right)

is equal to : [JEE MAINS - ONLINE - 2023] (1)

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

(2)

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

(3)

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

(4)

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