Solve: `dy/dx = sin(x+y) + cos(x+y)`

Explanation

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

### Step 1: Substitute \( z = x + y \)
Let \( z = x + y \). Then, we can differentiate both sides with respect to \( x \):
\[ \frac{dz}{dx} = 1 + \frac{dy}{dx} \]
From this, we can express \(\frac{dy}{dx}\):
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