A) \[x{{(\ell \,n\,y)}^{2}}=1\]
B) \[x(\ell \,n\,y)=1\]
C) \[{{(\ell \,n\,y)}^{2}}=x\]
D) \[(x+\ell \,n\,y)=2\]
Correct Answer: B
Solution :
\[x\frac{dy}{dx}+y(\ln \,y)=0\,\Rightarrow \,\int{\frac{dx}{x}+\int{\frac{dy}{y(\ln \,y)}}}=C;\] \[\ln \,(x\,\ln \,y\,)=C.\]. If \[x=1\] then \[y=e\] \[\Rightarrow \,\ln \,(\ln \,e)\,=C\Rightarrow \,C=0\]
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