Solve `x(dy)/(dx)=y(logy-logx+1)`

Explanation

To solve the differential equation \( x \frac{dy}{dx} = y (\log y - \log x + 1) \), we can follow these steps:

### Step 1: Rewrite the Equation
We start with the given equation:
\[ x \frac{dy}{dx} = y (\log y - \log x + 1) \]
We can simplify the right-hand side using the property of logarithms:
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