Answer: x + y dy/dx = 0.
- A x + y dy/dx = 0
- B x dy/dx - y = 0
- C x dy/dx + y = 0
- D x² + y² = r²
Correct answer: A. x + y dy/dx = 0
Explanation: x² + y² = r². Differentiate: 2x + 2y(dy/dx) = 0, so x + y(dy/dx) = 0.
The general solution y=Ax² represents an entire FAMILY of curves, one for each value of the arbitrary constant A; a particular solution (fixed by an initial condition) selects exactly one curve from this family.
Concept context
Equations involving derivatives and their solutions