JEE Math Practice Question

Let $$y=y(x), y > 0$$, be a solution curve of the differential equation $$\left(1+x^{2}\right) \mathrm{d} y=y(x-y) \mathrm{d} x$$. If $$y(0)=1$$ and $$y(2 \sqrt{2})=\beta$$, then

1. A.$$e^{\beta^{-1}}=e^{-2}(3+2 \sqrt{2})$$
2. B.$$e^{3 \beta^{-1}}=e(5+\sqrt{2})$$
3. C.$$e^{3 \beta^{-1}}=e(3+2 \sqrt{2})$$
4. D.$$e^{\beta^{-1}}=e^{-2}(5+\sqrt{2})$$