The largest internal for which solution of differential equation $\large\frac{dy}{dx}=\sqrt {\large\frac{1-y^2}{(1+x^2)^2}}$ where $y(0)= \large\frac{1}{\sqrt 2}$ holds good is

Question

$(a)\;x \in [0, \infty] \\ (b)\;x \in (-\infty, 1] \\ (c)\;x \in (-\infty, \infty) \\ (d)\;x \in [-1,1] $