We have, $ \frac{dy}{dx} = \frac{y+x \tan \frac{y}{x}}{x}$ ...(i)
Given differential equation is in homogeneous form
$\therefore $ Put $y = vx$ in (i), we get
$ v + x \frac{dv}{dx} = v + \tan \, v$
$\Rightarrow \frac{1}{\tan v} dv =\frac{dx}{x} $
Taking integration on both sides, we get
$ \log \, (\sin \, v ) = \log \, x + \log \, c$
$\Rightarrow \log \frac{\sin v}{x} = \log c $
Solution of the differential equation is $ \sin\left(\frac{y}{x} \right) =xc $