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From the family of curves defined by (x² - y²) dx + 2xy dy = 0, identify the particular curve passing through the point (1, 1).
- A circle whose centre lies on the y-axis
- A circle whose centre lies on the x-axis
- An ellipse with its major axis along the y-axis
- A hyperbola with its transverse axis along the x-axis
Correct answer: A circle whose centre lies on the x-axis
Solution
The homogeneous ODE integrates to x² + y² = Cx; through (1,1) this is x² + y² = 2x, a circle centred on the x-axis.
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