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

Explanation

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

### Step 1: Start with the given equation
\[ (x - y)e^{\frac{x}{x - y}} = a \]

### Step 2: Take the natural logarithm of both sides
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