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

Explanation

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

### Step 1: Simplify the Equation
We start with the equation:
\[ x(xdy + ydx) = ydx \]
Expanding this gives:
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