Case III. Conjugate Complex Roots

  1. Suppose that the auxiliary equation has a nonrepeated complex root α + . Then, since the coefficients are real, the conjugate complex number α is also a non-repeated root. Thus, the solution given in (79) becomes

     

    image

     

    where k1 = c1 + c2, k2 = i(c1c2).

  2. If two pairs of imaginary roots are equal, then

     

    m1 = m2 = a + iβ and m3 = m4 = α.

     

    Using Case II, the complete solution is

     

    image

     

EXAMPLE 15.83

Solve

 

Solution.   The symbolic form of the given equation is

 

(D3 + D2 + 4D + 4)y = 0.

 

Therefore ...

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