Solve the following differential equation: `(sinx+cos x)dy+(cos x-sinx)dx=0`

Explanation

To solve the differential equation \((\sin x + \cos x) dy + (\cos x - \sin x) dx = 0\), we can follow these steps:

### Step 1: Rearranging the Equation
We start by rearranging the equation to isolate \(dy\) and \(dx\):
\[ (\sin x + \cos x) dy = -(\cos x - \sin x) dx \]
Dividing both sides by \((\sin x + \cos x)\) gives us:
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