If x=f(y) is the solution of the differential equation (1+y^2)+(x-2 e^tan^-1 y ) (d y)/(d x)=0, y ∈(-(π)/2, (π)/2) with f(0)=1, then f(1/(√ 3)) is…

If $\displaystyle x=f(y)$ is the solution of the differential equation $\displaystyle \left(1+y^2\right)+\left(x-2 \mathrm{e}^{\tan ^{-1} y}\right) \frac{\mathrm{d} y}{\mathrm{~d} x}=0, y \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$ with $\displaystyle f(0)=1$, then $\displaystyle f\left(\frac{1}{\sqrt{3}}\right)$ is equal to: