A) \[xy+\log x=C\]
B) \[xy+\log y=C\]
C) \[xy-\log y=C\]
D) \[xy-\log x=C\]
Correct Answer: C
Solution :
Given, equation can be written as \[xy\,\,dy+{{y}^{2}}dx-dy=0\] On multiplying by\[\frac{1}{y}\], we get \[x\,\,dy+y\,\,dx-\frac{1}{y}dy=0\] \[\Rightarrow \] \[d(xy)-\frac{1}{y}dy=0\] On integrating, we get \[\Rightarrow \] \[\int{d}(xy)-\int{\frac{dy}{y}}=0\] \[\Rightarrow \] \[xy-\log y=C\]
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