Differential Equations

Let \(y=y(x)\) be the solution of the differential equation

\(\frac{\mathrm{d} y}{\mathrm{~d} x}+\frac{2 x}{\left(1+x^2\right)^2} y=x \mathrm{e}^{\frac{1}{\left(1+x^2\right)}} ; y(0)=0.\)

Then the area enclosed by the curve \(f(x)=y(x) \mathrm{e}^{-\frac{1}{\left(1+x^2\right)}}\) and the line \(y-x=4\) is ________.