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Homework Help: 2nd Order inhomogeneous ODEs

  1. Mar 30, 2010 #1
    1. Using the complementary function and particular integral method find the solutio of the differential equation.

    d2y/dx^2 + 3 dy/dx +2y = 20cos2x

    Which satisfies y(0) = 1 y'(0) = 0

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Mar 30, 2010 #2
    there are different ways to solve this differential equation.
    I know you can solve it with the method of undetermined coefficients OR Variation of Parameters.
  4. Mar 30, 2010 #3
    I have already found the complementary function to be:

    y = Ae^(-t) + Be(-2t)

    Im just not sure how to find the particular integral!
  5. Mar 30, 2010 #4


    Staff: Mentor

    Try yp = Ccos(2x) + Dsin(2x) for your particular solution.

    Minor note: The independent variable should be x, not t, since x is the independent variable in your differential equation.
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