Solve the differential equation `(x dy-y dx)ysin(y/x)=(y dx+x dy)xcos(y/x)`.

Explanation

To solve the differential equation

\[ (x \, dy - y \, dx) \, y \sin\left(\frac{y}{x}\right) = (y \, dx + x \, dy) \, x \cos\left(\frac{y}{x}\right), \]

we will follow these steps:

...