Solve: `(xcosy-ysiny)dy+(x siny+ycosy)dx=0`

Explanation

To solve the differential equation \((x \cos y - y \sin y) dy + (x \sin y + y \cos y) dx = 0\), we will follow these steps:

### Step 1: Rewrite the equation
We start by rewriting the equation in a more manageable form:
\[ (x \cos y - y \sin y) dy + (x \sin y + y \cos y) dx = 0 \]
This can be rearranged as:
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