Annihilator Method Problem

  1. 1. The problem statement, all variables and given/known data

    Solve the given differential equation using the annihilator method:

    (D-3)(D+2)y=x^2e^x

    2. Relevant equations

    D=dy/dx


    3. The attempt at a solution

    I think the annihilator would be (D-1)^3.

    so the solution would be in the form:

    y = Ae^x + Bxe^x + C(x^2)e^x + De^(3x) +Ee^(-2x)

    Solving for the particular solution yields:

    Ae^x+Bxe^x+C(x^2)e^x = (x^2)(e^x)

    Am I solving this correctly, and if so, where do I go from here?

    Thanks a bunch,

    John
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Mark44

    Staff: Mentor

    Everything looks fine, so far.

    Using your particular solution, y = Ae^x + Bxe^x + Cx^2e^x, calculate y' and y'' and substitute into your differential equation to find A, B, and C. Your differential equation is y'' - y' - 6y = x^2e^x

    Your general solution will still involve undetermined coefficients for the e^(3x) and e^(-2x) terms unless you have some initial conditions.
     
  4. Thanks for the quick reply. I'll repost my final solutions.
     
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