A) \[{{x}^{2}}+1\]
B) \[\frac{2x}{{{x}^{2}}+1}\]
C) \[\frac{{{x}^{2}}-1}{{{x}^{2}}+1}\]
D) None of these
Correct Answer: A
Solution :
\[\frac{dy}{dx}+\frac{2x}{1+{{x}^{2}}}y=\frac{{{x}^{2}}-1}{{{x}^{2}}+1}\] I.F. \[={{e}^{\int{\frac{2x}{1+{{x}^{2}}}dx}}}={{e}^{\log (1+{{x}^{2}})}}\]\[=1+{{x}^{2}}\].
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