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An integrating factor of the differential equation $y \log y \frac{d x}{d y}+x-\log y=0$, is |
$\log (\log y)$ $\log y$ $\frac{1}{\log y}$ $\frac{1}{\log (\log y)}$ |
$\log y$ |
We have, $\frac{d x}{d y}+\frac{1}{y \log y} x=\frac{1}{y}$ Integrating factor = $e^{\int \frac{1}{y \log y}} d y=e^{\log (\log y)}=\log y$ |
