A) \[xy+y\log y=c\]
B) \[xy+y\log y-y=c\]
C) \[xy+\log y-x=c\]
D) None of these
Correct Answer: B
Solution :
\[xdy+ydx+\log ydy=0\] Þ \[xdy+ydx=-\log ydy\] \[y\frac{dx}{dy}+x=-\log y\] Þ \[\frac{dx}{dy}+\frac{x}{y}=-\frac{\log y}{y}\] I.F. =\[{{e}^{\int{\frac{1}{y}dy}}}=y\] Hence solution is \[x.y=-\int{y.\frac{\log ydy}{y}+c}\] Þ \[xy=-(y\log y-y)+c\] Þ \[xy+(y\log y-y)=c\].
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