Let the solution curve y=y(x) of the differential equation (1+ e^2 x)((d y)/(d x)+y)=1 pass through the point (0, (π)/2). Then, lim_x → ∞ e^x y(x) is…

Let the solution curve $\displaystyle y=y(x)$ of the differential equation $\displaystyle \left(1+\mathrm{e}^{2 x}\right)\left(\frac{\mathrm{d} y}{\mathrm{~d} x}+y\right)=1$ pass through the point $\displaystyle \left(0, \frac{\pi}{2}\right)$. Then, $\displaystyle \lim _{x \rightarrow \infty} \mathrm{e}^x y(x)$ is equal to :