A) \[\log xy+x+y=c\]
B) \[\log \left( \frac{x}{y} \right)+x-y=c\]
C) \[\log xy+x-y=c\]
D) None of these
Correct Answer: C
Solution :
\[\frac{dy}{dx}=\frac{(1+x)y}{(y-1)x}\]can be written as \[\frac{y-1}{y}dy=\frac{(1+x)}{x}dx\] Þ \[\left( 1-\frac{1}{y} \right)dy=\left( 1+\frac{1}{x} \right)dx\] Þ \[(y-\log y)=(x+\log x)+c\]Þ\[x-y+\log xy=c\].
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