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

Explanation

To solve the differential equation

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

we will follow these steps:

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