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General Solution to HDE

  1. Nov 28, 2009 #1
    1. The problem statement, all variables and given/known data

    (D^2 + 2D + 10)^2 * (D^2 - 2D -3)y = 0.

    2. Relevant equations

    D = d/dx

    3. The attempt at a solution

    Solving for the roots gives:

    -1 + 3i, -1 - 3i <== both of multiplicity 2
    and 3, -1.

    So the general solution should be:

    y = Ae^(3x) + Be^(-x) + Ce^(-x)cos(3x) + Dxe^(-x)cos(3x) + Ee^(-x)sin(3x) + Fxe^(-x)sin(3x)

    Am I handling this correctly?

    Thanks
     
  2. jcsd
  3. Nov 28, 2009 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Looks ok to me.
     
  4. Nov 28, 2009 #3
    Thanks for looking at it.
     
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