A) \[\frac{1}{\log y}\]
B) \[\log (\log y)\]
C) \[1+\log y\]
D) \[\frac{1}{\log (\log y)}\]
E) \[\log y\]
Correct Answer: E
Solution :
Given differential equation can be rewritten as \[\frac{dx}{dy}=\frac{(\log y-x)}{y\log y}\] \[\Rightarrow \] \[\frac{dx}{dy}+\frac{x}{y\log y}=\frac{1}{y}\] \[\therefore \] \[IF={{e}^{\int{\frac{1}{y\log y}}dy}}\] \[={{e}^{\log \log y}}=\log y\]
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