Answer: y = Cx.
- A y = x + C
- B y = Cx
- C y = Ce<sup>x</sup>
- D xy = C
Correct answer: B. y = Cx
Explanation: Separating variables gives ln y = ln x + c, so y = Cx.
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