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Math Help - ODE Method of Variation of Parameters help

  1. #1
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    ODE Method of Variation of Parameters help

    ODE Method of Variation of Parameters help-ode-problem.pdf
    Above is my problem sorry that it's a link but It was to hard to convert from latex into here (i used some packages)
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  2. #2
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    You're missing a term in your variation of parameters formula. Given an nth order linear ODE

    a_n(x)y^{(n)} + a_{n-1}(x)y^{(n-1)} + \cdots + a_1(x)y' + a_0(x)y = f(x)

    with independent solutions y_1, \cdots , y_n the variation of parameters formula is

    \displaystyle y_p = \sum_{k=1}^n y_k \int \dfrac{W_k}{W} \dfrac{f(x)}{a_n(x)}dx.

    With what you have you set a_n = 1 where it should be a_n = x^3. With this assignment things work out giving you the desired y_p.
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