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Math Help - Solving Differential Equation - series solution

  1. #1
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    Solving Differential Equation - series solution

    Hi All;
    let a_{0} $\neq$0 and a_{3} $\neq$0 and

    a_{n} =\frac{(n-3)a_{n-1}}{(n-2)(n-1)-2};n\geq1
    I need the general formula for the following summation in terms of a_{0} and a_{3}

    y=\sum_{i=1}^{\infty}a_{n}x^{n-2}<br />
    Thanks
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  2. #2
    A Plied Mathematician
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    I would simplify the expression multiplying the a_{n-1}. I think you'd find everything much easier to deal with.
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  3. #3
    MHF Contributor Also sprach Zarathustra's Avatar
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    Like the man before me...

    said...

    a_n=\frac{(n-3)a_{n-1}}{(n-1)(n-2)-2}=\frac{(n-3)a_{n-1}}{n^2-3n}=\frac{a_{n-1}}{n}
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