Show that the given differential equation `xdy-ydx=sqrt(x^(2)+y^(2))` dx is homogenous and solve it.

Explanation

To solve the differential equation \( x \, dy - y \, dx = \sqrt{x^2 + y^2} \, dx \), we will first rearrange and analyze the equation to show that it is homogeneous, and then we will solve it.

### Step 1: Rearranging the Equation
We start with the given equation:
\[ x \, dy - y \, dx = \sqrt{x^2 + y^2} \, dx \]
Rearranging gives:
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