Solve `x\ dy-y\ dx=sqrt(x^2+y^2)dx`

Explanation

To solve the differential equation \( x \, dy - y \, dx = \sqrt{x^2 + y^2} \, dx \), we will follow these steps:

### Step 1: Rearranging the Equation
We start with the given equation:
\[ x \, dy - y \, dx = \sqrt{x^2 + y^2} \, dx \]
We can rearrange this to isolate \( dy \):
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