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Help finding the answer to DE using method of undetermined coefficients

  1. Feb 24, 2010 #1
    1. The problem statement, all variables and given/known data

    y'' - 5y' = 2x^3 - 4x^2 -x + 6




    3. The attempt at a solution

    I first found the m's on the left hand side. They are 0 and 5. I then found the m's on the right hand side. They are 0, 0, 0, and 0. I then wrote my interim equation:

    y = C1 + C2e^5x + Ax^4 + Bx^3 + Cx^2 + Dx. Because there already is a 0 on the left hand size for m, then there are x's for each part of the equation on the right side.

    This is where I'm confused. I have tried to find the coefficients by finding the first and second derivatives of Yp, but I get very odd numbers when I solve for the variables(B = 14/75 and C = 5.324 for example). Am I on the right track or did I screw up somewhere? We have never been presented with irrational coefficients before (as is the case with C), so I'm thinking I did something wrong somewhere...
     
  2. jcsd
  3. Feb 24, 2010 #2

    vela

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    It sounds like you're on the right track. I think you're just making algebraic errors when solving for A, B, C, and D, so double-check your work for mistakes. If you post your actual work in solving for them, others and I can see if we spot any mistakes as well.
     
  4. Feb 24, 2010 #3
    D'oh. You were right. Thank you!
     
  5. Feb 24, 2010 #4

    Mark44

    Staff: Mentor

    I don't see anything wrong, but don't use approximations, since that will foul things up. Instead of 5.324, use the exact value.
     
  6. Feb 24, 2010 #5
    There were no approximations, my algebra was just poor.
     
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