Question

Solve $y\log ydx-xdy=0$

Answer 1

$y\log ydx-xdy=0$

$y\log ydx=xdy$

$\frac{dy}{y\log y}=\frac{dx}{x}$

Let $\log y=t$

$\frac{1}{y}dy=dt$

$\int \frac{dt}{t}=\int \frac{dx}{x}$

$\log t=\log x+\log c$

$\log y=cx$