If `(x-y) \ e^(x/(x-y))=a` , prove that `y(dy)/(dx)+x=2y` .

Explanation

To prove that \( y \frac{dy}{dx} + x = 2y \) given that \( (x - y) e^{\frac{x}{x - y}} = a \), we will differentiate both sides of the equation and manipulate the resulting expression. Here’s a step-by-step solution:

### Step 1: Differentiate both sides
We start with the equation:
\[ (x - y) e^{\frac{x}{x - y}} = a \]
Since \( a \) is a constant, the derivative of the right-hand side is zero. We will use the product rule on the left-hand side.
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