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Three of these four hold for a linear equation with constant coefficients. The exception is

  • A.its particular integral depends on the right-hand side
  • B.its general solution contains as many arbitrary constants as its degree
  • C.its general solution is the complementary function plus a particular integral
  • D.its complementary function is fixed by the auxiliary roots

Answer: B

The number of arbitrary constants matches the *order*, not the degree: a second-order equation carries two whatever powers appear. The other three are the standard structure of the solution, which is why the homogeneous and forced parts can be found independently and then added

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