# Show that the differential equation is homogeneous and solve $\left\{x\cos\bigg(\large\frac{y}{x}\bigg)\normalsize+y\sin\bigg(\large\frac{y}{x}\bigg)\right\}ydx=\left\{y\sin\bigg(\large\frac{y}{x}\bigg)-\normalsize x\cos\bigg(\large\frac{y}{x}\bigg)\right\}\normalsize xdy$
$\begin{array}{1 1} C=\large\frac{1}{xy}\sec\big(\large\frac{y}{x}\big) \\ C=\large\frac{1}{xy}\tan \big(\large\frac{y}{x}\big) \\C=\large\frac{1}{xy}\sin \big(\large\frac{y}{x}\big) \\C=\large\frac{1}{xy}\cos \big(\large\frac{y}{x}\big) \end{array}$