Solve (i) `xdx +ydy + (xdy - ydx)/(x^(2) + y^(2)) = 0`
(ii) `y(1+xy) dx - xdy = 0`

Explanation

Let's solve the given differential equations step by step.

### Part (i): Solve the equation
\[ xdx + ydy + \frac{xdy - ydx}{x^2 + y^2} = 0 \]

**Step 1: Rewrite the equation**
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