Answer: y = 2/x.
- A y = 2/x
- B y = 2x
- C y = 2e<sup>-x</sup>
- D xy = 2
Correct answer: A. y = 2/x
Explanation: Separating variables: dy/y=−dx/x. Integrating both sides: ln|y|=−ln|x|+C₁, so y=A/x. Applying IC y(1)=2: A=2. Solution: y=2/x (equivalently xy=2).
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