Question:

Let $y=y(x)$ be the solution of the differential equation $\dfrac{dy}{dx}+\dfrac{2x}{(1+x^2)^2}y=xe^{\frac{1}{1+x^2}}$; $y(0)=0$. Then the area enclosed by the curve $f(x)=y(x)e^{-\frac{1}{1+x^2}}$ and the line $y-x=4$ is ________.