A) ? x
B) \[-\frac{x}{(1-{{x}^{2}})}\]
C) \[\sqrt{(1-{{x}^{2}})}\]
D) \[\frac{1}{2}\log (1-{{x}^{2}})\]
Correct Answer: C
Solution :
\[(1-{{x}^{2}}).\frac{dy}{dx}-xy=1\] Þ \[\frac{dy}{dx}-\frac{x}{1-{{x}^{2}}}.y=\frac{1}{1-{{x}^{2}}}\] I.F. \[={{e}^{\int{p.dx}}}={{e}^{\int{\frac{-x}{1-{{x}^{2}}}dx}}}\]\[={{e}^{\frac{1}{2}\log (1-{{x}^{2}})}}=\sqrt{1-{{x}^{2}}}\].
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