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Non-homogenous differential Equation

  1. Feb 27, 2013 #1
    1. The problem statement, all variables and given/known data
    solve:
    y""+6y'+9y=e-3x/x3


    2. Relevant equations

    y=yc+yp


    3. The attempt at a solution

    I found yc=C1e-3x+C2xe-3x
    and am having difficulties finding yp. I am wondering which method would be the best to determine yp:

    - annihilators
    - undetermined coefficients
    - variation of paramaters.
     
  2. jcsd
  3. Feb 27, 2013 #2
    Since it is in the form [itex]e^{ax}/x^k[/itex] try using [itex]Ae^{-3x}/x[/itex]
     
  4. Feb 27, 2013 #3
    Thanks, it worked out. I have a hard time knowing what 'guess' to use for the derivative. How did you know to put it over x instead of x-3? I have a test tomorrow, so I want to make sure that I can do things properly.
     
  5. Feb 27, 2013 #4
    I usually always try the simplest first. This doesn't pertain to this question, but if [itex]Ae^{ax}[/itex] didn't work I would try [itex]Axe^{ax}[/itex], and if that didn't work I would try [itex]Ax^2e^{ax}[/itex]. It can be rather tedious for some questions but eventually you start to notice patterns.
     
  6. Feb 28, 2013 #5

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Is that really a fourth degree equation or is the second '' a typo?

    "Undetermined coefficents" works when the right side of the equation is one of the types of solutions you can get as solutions to homogenous differential equations with constant coefficients: exponentials, sine or cosine, and polynomials, as well as combinations of those. That is not the case here. I recommend "variation of parameters".
     
  7. Feb 28, 2013 #6
    I think he accidentally hit the quotation mark key.
     
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