Mathematics

Problem

x=f(y)

is the solution of the differential equation

(1+y^2) + (x-2e^{\tan^{-1}y})\frac{dy}{dx}=0, \quad y\in\left(-\frac{\pi}{2},\frac{\pi}{2}\right)

with

f(0)=1

, then

f\left(\frac{1}{\sqrt{3}}\right)

is equal to: (a)

e^{\pi/4}

(b)

e^{\pi/12}

(c)

e^{\pi/3}

(d)

e^{\pi/6}