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Math Help - [SOLVED] Finding the Particular Integral

  1. #1
    Member Altair's Avatar
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    [SOLVED] Finding the Particular Integral

    The question asks to evaluate the following :-

    \frac{e^x}{D^3 - D^2 - D +1}

    Its an example.

    Book has done it directly by telling that at {(D-1)}^2 this can't be solved as F(b) = 0 and thus we will apply the following rule :-

    \frac{ae^{bx}x^r}{\phi{(b)} r!}

    And thus the answer comes out to be :-

    \frac {x^2e^x}{4}

    The difficulty is that our calculus teacher told us that you will first do the following step to that factor for which F(b) <> 0 .

    y = e^{-bx}\int{e^{bx}f(x)dx}

    and then apply the above stated rule for that factor for which F(b) = 0.

    This was working all right till this question. If I solve it by what we are told by our teacher then the answer comes out to be

    \frac {x^2e^x}{8}

    Any comments? What should be the procedure for solving such questions ?
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  2. #2
    GAMMA Mathematics
    colby2152's Avatar
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    Is D a function of x?
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  3. #3
    Member Altair's Avatar
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    Its the Differential Operator.
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  4. #4
    Member Altair's Avatar
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    Found the mistake.
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