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Variation of parameters is preferred to the operator method when

  • A.the right-hand side is not of a form the operator method handles
  • B.the auxiliary equation has repeated roots
  • C.the equation has variable coefficients
  • D.the order of the equation exceeds two

Answer: A

The operator method has recipes for an exponential, a sine or cosine, a polynomial and their products. For something like \( \sec x \) or \( \ln x \) there is no such recipe, and variation of parameters builds the particular integral from the complementary function by integration instead. Repeated roots and higher order are handled by either method

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