Answer: y = C.
- A y = C
- B y = x
- C y = x + C
- D y = 0
Correct answer: A. y = C
Explanation: If the derivative is zero everywhere, y is a constant, so y = C.
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