A) \[(1-{{x}^{2}})\frac{dy}{dx}-xy=0\]
B) \[(1-{{x}^{2}})\frac{dy}{dx}+xy=0\]
C) \[(1-{{x}^{2}})\frac{dy}{dx}-2xy=0\]
D) \[(1-{{x}^{2}})\frac{dy}{dx}+2xy=0\]
Correct Answer: B
Solution :
\[{{y}^{2}}=(1-{{x}^{2}})\] Þ\[2y\frac{dy}{dx}=-2x\] or \[\frac{dy}{dx}=\frac{-x}{y}=\frac{-xy}{(1-{{x}^{2}})}\] or \[(1-{{x}^{2}})\frac{dy}{dx}+xy=0\].
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