Solve the following differential equation: `y\ dx+xlog(y/x)dy=2x\ dy`

Explanation

To solve the differential equation \( y \, dx + x \log\left(\frac{y}{x}\right) \, dy = 2x \, dy \), we will first rearrange the equation and then simplify it.

### Step 1: Rearranging the Equation
We start with the given equation:
\[ y \, dx + x \log\left(\frac{y}{x}\right) \, dy = 2x \, dy \]
We can rearrange this to isolate terms involving \( dx \) and \( dy \):
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