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Auxiliary equation for d²y/dx² - 5dy/dx + 6y = 0 is:

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.

Family of Solution Curves: y = Ax²Each value of the constant A gives ONE particular curve from the family

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

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