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Homework Help: 2nd ODE constant coeff, quick question

  1. Feb 17, 2008 #1

    rock.freak667

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    1. The problem statement, all variables and given/known data
    Solve:
    [tex]\frac{d^2y}{dx^2}+\frac{dy}{dx}=3x^2+2x+1[/tex]

    3. The attempt at a solution

    Well the C.F. is [itex]y=C_1e^{-x}[/itex]
    the P.I. is of the form [itex]y_{PI}=Ax^3+Bx^2+Cx+D[/itex]

    I can find the values of A,B and C bu differentiating it and substituting it into the equation. But How would I find D since there is no 'y' in the ODE given and differentiating [itex]y_{PI}[/itex] makes the constant disappear.



    (Note: I can find the answer by integrating it w.r.t x and then using the integrating factor but I would like to know how to find it by adding the PI and CF together)
     
  2. jcsd
  3. Feb 17, 2008 #2
    The D is redundant since one of the solutions to the natural equation is a constant function.

    Therefor the constant function is determined by the initial conditions rather then the forcing function.
     
  4. Feb 17, 2008 #3

    rock.freak667

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    Ah...thanks then,I thought I was really doing something wrong.
     
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