Answer: m² - 5m + 6 = 0.
- A m² - 5m + 6 = 0
- B m² + 5m + 6 = 0
- C m² - 5m - 6 = 0
- D 5m² - m + 6 = 0
Correct answer: A. m² - 5m + 6 = 0
Explanation: Replace d<sup>n</sup> y/dx<sup>n</sup> with m<sup>n</sup>: m² - 5m + 6 = 0. Roots: (m-2)(m-3) = 0, m = 2, 3.
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