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