# Show that the differential equation is homogeneous and solve $y\: dx+x\log\bigg(\large\frac{y}{x}\bigg)$$dy-2x\;dy=0$
$\begin{array}{1 1}\log(\large\frac{y}{x}) - 1 = Cy \\\log(\large\frac{x}{y}) - 1 = Cy \\ \log(\large\frac{y}{x}) + 1 = Cy \\\log(\large\frac{x}{y}) +1 = Cy \end{array}$