Find the general solution of the differential equation \[x \frac{d y}{d x}-y+x \sin \frac{y}{x}=0 . \]

\[\begin{aligned} & x \frac{d y}{d x}-y+x \sin \frac{y}{x}=0 \\ & \Rightarrow \frac{d y}{d x}=\frac{y}{x}-\sin \frac{y}{x} \quad\left(\frac{y}{x}=v\right) \\ & \Rightarrow v+x \frac{d v}{d x}=v-\sin v \\ & \operatorname{cosec} v d v=-\frac{d x}{x} \\ & \Rightarrow \log |\operatorname{cosec} v-\cot v|+\log |x|=\log C \\ & \Rightarrow x\left(\operatorname{cosec} \frac{y}{x}-\cot \frac{y}{x}\right)=C \end{aligned} \]