Show that the differential equation `xcos(y/x)(dy)/(dx)=ycos(y/x)+x`is homogeneous and solve it.

Explanation

To solve the differential equation \( x \cos\left(\frac{y}{x}\right) \frac{dy}{dx} = y \cos\left(\frac{y}{x}\right) + x \), we will follow these steps:

### Step 1: Show that the differential equation is homogeneous
A differential equation is homogeneous if it can be expressed in the form \( F(tx, ty) = t^n F(x, y) \) for some integer \( n \).

Let's rewrite the given equation:
\[
x \cos\left(\frac{y}{x}\right) \frac{dy}{dx} = y \cos\left(\frac{y}{x}\right) + x
...