Function \( y=f(x) \) satisfies the differential equation \( \sqrt{1-x^{2} y^{2}} d x=x d y+y d ....

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Function \( y=f(x) \) satisfies the differential equation
\( \mathrm{P} \)
\( \sqrt{1-x^{2} y^{2}} d x=x d y+y d x \) with the condition
W.
\( \lim _{x \rightarrow 0} f(x)=1 \). The value of \( f\left(\frac{\pi}{2}\right) \) is equal to
(1) \( \frac{2}{\pi} \)
(2) \( \frac{\pi}{2} \)
(3) 0
(4) \( \frac{-\pi}{2} \)


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