Solve the differential equation: . Find the particular solution satisfying the condition that when…

Solve the differential equation: $(x\\,dy - y\\,dx) y\sin\left(\frac{y}{x}\right) = (y\\,dx + x\\,dy) x\cos\left(\frac{y}{x}\right)$. Find the particular solution satisfying the condition that $y = \pi$ when $x = 1$. [Application]