Answer: y'' + y = 0.
- A y'' − y = 0
- B y'' + y = 0
- C y' + y = 0
- D y'' + y' = 0
Correct answer: B. y'' + y = 0
Explanation: Differentiating twice gives y'' = −y, i.e. y'' + y = 0.
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