Answer: y = C·e kx.
- A y = C·e<sup>kx</sup>
- B y = kx + C
- C y = C/x + k
- D y = k/x + C
Correct answer: A. y = C·e<sup>kx</sup>
Explanation: Separating variables gives dy/y = k dx, so ln y = kx + c and y = C e<sup>kx</sup>.
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