A) \[y({{x}^{2}}+1)=4\]
B) \[y({{x}^{2}}+1)+4=0\]
C) \[y({{x}^{2}}-1)=4\]
D) None of these
Correct Answer: A
Solution :
\[\frac{dy}{dx}=\frac{-2xy}{({{x}^{2}}+1)}\] Þ \[\frac{dy}{y}=-\frac{2x}{{{x}^{2}}+1}dx\] On integrating, we get \[\log y=-\log (1+{{x}^{2}})+\log c\]Þ\[y(1+{{x}^{2}})=c\] Since curve passes through (1, 2), we have \[c=2(1+{{1}^{2}})\] Þ \[c=4\] Hence solution is \[y({{x}^{2}}+1)=4\].
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