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The curve satisfying the differential equation, (x2 − y2) dx + 2xy dy = 0 and passing through the point (1, 1) is -
- (A) a circle of radius two
- (B) a circle of radius one
- (C) a hyperbola
- (D) an ellipse
Correct answer: (B) a circle of radius one
Solution
The given differential equation can be rearranged and solved to reveal that the resulting curve is a circle. Specifically, when evaluated at the point (1, 1), the solution confirms that it is indeed a circle with a radius of one.
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