JEE Math Practice Question

Let $$y=y(x)$$ be the solution of the differential equation $$\left(1+x^2\right) \frac{d y}{d x}+y=e^{\tan ^{-1} x}$$, $$y(1)=0$$. Then $$y(0)$$ is

1. A.$$\frac{1}{4}\left(e^{\pi / 2}-1\right)$$
2. B.$$\frac{1}{2}\left(1-e^{\pi / 2}\right)$$
3. C.$$\frac{1}{4}\left(1-e^{\pi / 2}\right)$$
4. D.$$\frac{1}{2}\left(e^{\pi / 2}-1\right)$$