Solve the following differential equations: `(dy)/(dx)=(x+y)/(x-y)`

Explanation

To solve the differential equation \(\frac{dy}{dx} = \frac{x+y}{x-y}\), we can follow these steps:

### Step 1: Identify the Type of Differential Equation
The given equation is a homogeneous differential equation because it can be expressed in the form \(\frac{dy}{dx} = \frac{f(y/x)}{g(y/x)}\).

### Step 2: Substitute \(y = vx\)
Let \(y = vx\), where \(v\) is a function of \(x\). Then, we can differentiate \(y\) with respect to \(x\):
\[
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