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Engineering Mathematics
book

Engineering Mathematics

by Babu Ram
June 2009
Intermediate to advanced content levelIntermediate to advanced
1100 pages
42h 22m
English
Pearson India
Content preview from Engineering Mathematics

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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Publisher Resources

ISBN: 9789332515611