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A solution curve of (x² + x*y + 4x + 2y + 4)*dy/dx - y² = 0 with x > 0 passes through (1, 3). Which of the following is true for this solution curve?

1. intersects y = x + 2 exactly at one point
2. intersects y = x + 2 exactly at two points
3. intersects y = (x + 2)²
4. does NOT intersect y = (x + 3)²

Correct answer: intersects y = x + 2 exactly at one point

Solution

The curve (the official solution) meets y = x + 2 at exactly one point and does not intersect y = (x+3)²; the single-intersection statement is correct.

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