Answer: y = x²/2 + C.
- A y = x
- B y = x²/2 + C
- C y = 2x
- D y = x + C
Correct answer: B. y = x²/2 + C
Explanation: Integrate both sides: y = x²/2 + 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