Mathematics - Differential Equation Question with Solution | TestHub

Let $y=y(x)$ be the solution of the differential equation $\frac{\mathrm{d}y}{\mathrm{d}x}+\frac{2x}{{\left(1+x^2\right)}^2}y=x{\mathrm{e}}^{\frac{1}{\left(1+x^2\right)}};y(0)=0.$
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__________