The differential equation y(dy/dx) + x = c represents a family of:
The differential equation y(dy/dx) + x = c represents a family of:
- A. Straight lines
- B. Parabolas
- C. Circles
- D. Hyperbolas
Answer: C) Circles
Explanation: Rewriting as y dy = (c − x) dx. Integrating gives y²/2 = cx − x²/2 + k, which rearranges to x² + y² − 2cx = 2k. This is the general equation of a family of circles.
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