A) \[xy=c\]
B) \[x+y=c\]
C) \[\log x\,\,\log y=c\]
D) \[{{x}^{2}}+{{y}^{2}}=c\]
Correct Answer: A
Solution :
Differential equation \[\frac{dx}{x}+\frac{dy}{y}=0\]. Integrating, we get \[\int{\frac{dx}{x}+\int{\frac{dy}{y}=0}}\] or \[\log x+\log y=\log c\] or \[\log (xy)=\log c\] or \[xy=c\].
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