Solve:
`xdy+ydx= (xdy-ydx)/(x^(2)+y^(2))`

Explanation

To solve the differential equation \( x \, dy + y \, dx = \frac{x \, dy - y \, dx}{x^2 + y^2} \), we will follow these steps:

### Step 1: Rearranging the Equation
We start with the given equation:
\[ x \, dy + y \, dx = \frac{x \, dy - y \, dx}{x^2 + y^2} \]
Multiply both sides by \( x^2 + y^2 \) to eliminate the fraction:
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