Answer: y = x²/3 + C/x.
- A y = x²/3 + C/x
- B y = x² + C
- C y = x³/3 + C
- D y = x/3 + Cx
Correct answer: A. y = x²/3 + C/x
Explanation: IF = x, so (xy)' = x²; integrating xy = x³/3 + C, hence y = x²/3 + C/x.
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