I.F. for y ln y $\frac{dx}{dy}$ + x − ln y = 0 is :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $ln\, y$
$y\, ln\, y\frac{dx}{dy} + x - ln\, y = 0$
$⇒y\, ln\, y\frac{dx}{dy} + x=ln\, y$
$⇒\frac{dx}{dy}+\frac{1}{y\, ln\, y}+x=\frac{1}{y}$
$I.F.=e^{\int P\,dy}$
$=e^{\int \frac{1}{y\, ln\, y}dy}$
$=e^{ln|ln\,y|}=ln\,y$