Show that the given differential equation is homogeneous and solve each of them.`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: Rewrite the Differential Equation
We start by rewriting the given equation in a more manageable form. We can rearrange it as follows:

\[ x \, dy = y \, dx + \sqrt{x^2 + y^2} \, dx \]
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