$ \text{Let the solution curve } y=y(x) \text{ of the differential equation } (1+e^{2x})!\left(\dfrac{dy}{dx}+y\right)=1 \text{ pass through the point } \left(0,\dfrac{\pi}{2}\right). $ $ \text{Then } \lim_{x\to\infty} e^{x}y(x) \text{ is equal to:} $