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A particular solution to the differential equation y'' + 2y' + y = t^2 + 3?

  1. Oct 6, 2012 #1
    A particular solution to the differential equation y'' + 2y' + y = t^2 + 3?
    is t^2 - 4t +7 in the answers, but i get t^2 - 4t + 9 so where am i going wrong.....

    y = Ay^2 + by + c
    y' = 2Ay + B
    y'' = 2A

    2A + 2(2Ay + B) + Ay^2 +By + c = t^2 + 3
    A(y^2) + (4A+B)y +(2A +2B+c) = t^2 + 0t + 3

    A = 1

    B + 4A = 0 → b = -4

    C + 2B + 2A = 3 → b = 9

    Sorry if it's just an arithmetical error i'm pretty tired
     
  2. jcsd
  3. Oct 6, 2012 #2

    SammyS

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    Shouldn't those be t's & not y' in:

    y = At2 + Bt + C

    y' = 2At + B

    y'' = 2A

    I also get:
    C + 2B + 2A = 3  →  C = 3 -2B -2A  →  C = 3 - 2(-4) - 2(1) = 9

    Did you copy the problem wrong?
     
  4. Oct 6, 2012 #3
    I did copy it right the answers must just be wrong
     
  5. Oct 6, 2012 #4

    LCKurtz

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    You could plug your ##y_p## in and see if it works. That would settle it.
     
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