Show that the differential equation `x sin ((y)/(x))(dy)/(dx) = y sin ((y)/(x)) + x` is homogeneous. Also find its general solution.

Explanation

To show that the differential equation \( x \sin\left(\frac{y}{x}\right) \frac{dy}{dx} = y \sin\left(\frac{y}{x}\right) + x \) is homogeneous and to find its general solution, we will follow these steps:

### Step 1: Rewrite the Differential Equation
The given differential equation can be rewritten as:
\[ \frac{dy}{dx} = \frac{y \sin\left(\frac{y}{x}\right) + x}{x \sin\left(\frac{y}{x}\right)} \]

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