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Differential Equations Method of Flexible guessing

  1. Feb 16, 2012 #1
    1. The problem statement, all variables and given/known data
    Find a particular solution Yp of the given equation. Primes denote deriviate with respect to x
    (method of flexible guess)

    2. Relevant equations
    4y''+4y'+y=3xe^x



    3. The attempt at a solution
    when I used y=Ae^x as guess my A depended on x
    So y=Axe^x gave me 12A+9Ax=3x
    12A=0
    9Ax=3x
    does not work,
    Before I go on to trying y=Ax^2e^x am I doing this right?
     
  2. jcsd
  3. Feb 16, 2012 #2

    Mark44

    Staff: Mentor

    I don't know what you mean by "my A depended on x." A is a constant, so is not dependent on any variable.
    Why don't you try yp = Aex + Bxex?
     
  4. Feb 16, 2012 #3
    Yp=3/9xe^x-4/9e^x right?
     
  5. Feb 16, 2012 #4

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Right.
     
  6. Feb 16, 2012 #5

    Mark44

    Staff: Mentor

    This is something you should get in the habit of checking for yourself. You've already done all the hard work. If 4yp'' + 4y' + yp [itex]\equiv[/itex] 3xex, then your solution is correct.
     
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