Solve the initial value problem: `(xdy+ydx)=xy dx ,y(1)=1.`

Explanation

To solve the initial value problem \( (x dy + y dx) = xy dx \) with the condition \( y(1) = 1 \), we will follow these steps:

### Step 1: Rearranging the Equation
We start with the given equation:
\[ x dy - y dx = xy dx \]
Rearranging gives:
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