Let y=y(x) be a solution curve of the differential equation (y+1) tan^2 x d x+ tan x d y+y d x=0, x ∈(0, (π)/2). If lim_x → 0+ x y(x)=1, then the…

Let $\displaystyle y=y(x)$ be a solution curve of the differential equation $\displaystyle (y+1) \tan ^2 x \mathrm{~d} x+\tan x \mathrm{~d} y+y \mathrm{~d} x=0$, $\displaystyle x \in\left(0, \frac{\pi}{2}\right)$. If $\displaystyle \lim _{x \rightarrow 0+} x y(x)=1$, then the value of $\displaystyle y\left(\frac{\pi}{4}\right)$ is :