Find the equation of a curve passing through the point (0, 2) given that the sum of the coordinates of any point on the curve exceeds the magnitude of the slope of the tangent to the curve at that point by 5.

Explanation

To find the equation of the curve passing through the point (0, 2) given the condition that the sum of the coordinates of any point on the curve exceeds the magnitude of the slope of the tangent to the curve at that point by 5, we can follow these steps:

### Step 1: Set up the relationship
Let the coordinates of a point on the curve be (x, y). According to the problem, we have:
\[ x + y = \text{magnitude of the slope} + 5 \]
The slope of the tangent to the curve at any point is given by \(\frac{dy}{dx}\). Therefore, we can write:
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