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Math Help - First Four nonzero terms in power series expansion

  1. #1
    Member diddledabble's Avatar
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    Post First Four nonzero terms in power series expansion

    Find the first Four nonzero terms in power series expansion about x=0

    y'-y=0

    or

    y''-2y'+y=0


    For an initial value system (x^{2}-x+1)y''-y'-y=0
    y(0)=0
    y'(0)=1
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  2. #2
    Moo
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    Hello,

    Consider the power series expansion of the solution (in any equation)

    y=\sum_{n\geq 0} a_nx^n

    Then y'=\sum_{n\geq 1} n \cdot a_nx^{n-1}

    etc...

    Then find a recursive relation between a_n and a_{n-1} (or possibly a_{n-2}, for the last equation)

    See here for an example : http://www.mathhelpforum.com/math-he...s-problem.html (take care of the steps, that's all)
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  3. #3
    Member diddledabble's Avatar
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    What about with initial values

    Like y''+(x-2)y'-y=0
    y(0)=-1
    y'(0)=0
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