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The solution curve of the differential equation y' = (x² + y²)/(2xy) that goes through the point (2, 1) is a hyperbola whose eccentricity is:
- √2
- √3
- 2
- √5
Correct answer: √2
Solution
The differential equation describes a relationship between x and y that leads to a hyperbolic solution. By analyzing the characteristics of the hyperbola formed and calculating its eccentricity, we find that it equals √2, which is consistent with the properties of hyperbolas derived from the given equation.
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