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Method of undetermined coefficients

  1. Jan 21, 2009 #1

    s7b

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    Hi,

    When using the method of undetermined coefficients to solve

    2y'' + y' = cos(2x) + 4x + 1

    I did it term by term. I figured out the first yp1 for the cos(2x). I'm just not sure what to "guess" as to the form of the yp2 for 4x+1

    Does anyone know what to use as the guess?
     
  2. jcsd
  3. Jan 21, 2009 #2

    rock.freak667

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    Homework Helper

    when you solved the auxilary equation if one root was 0, then for a polynomial, the particular integral would be a degree higher. For example if you solved and 0 was a root of the aux. eq'n. and the right side was ax+b, then the PI would be Ax^2+Bx+C
     
  4. Jan 21, 2009 #3

    lurflurf

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    It is easy to know what to guess.
    [D^2+2^2]cos(2x)=0
    [D^2](4x+1)=0
    Guess the solution to lcm{[2D^2+D],[D^2],[D^2+2^2]}=[D^2][2D+1][D^2+2^2]
     
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