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Math Help - use the methods of frobenius to solve

  1. #1
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    Lightbulb use the methods of frobenius to solve

    use the methods of frobenius to solve:

    2xy"+y'+2y =0


    i want to know not just the answer but the steps how to answer it (explanation of the answer)
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  2. #2
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    Quote Originally Posted by compufatwa View Post
    use the methods of frobenius to solve:

    2xy"+y'+2y =0


    i want to know not just the answer but the steps how to answer it (explanation of the answer)
    The charachteristic equation is,
    2r(r-1) + r+0=0 thus, r=0,1/2.
    This means to look for solutions of the form:
    y=\sum_{n=0}^{\infty} a_n x^n and y=\sum_{n=0}^{\infty} a_n x^{n+1/2}
    Can you take it from there?
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  3. #3
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    Lightbulb

    ur point of view is not clear to me can u tell me more info about it
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  4. #4
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    Quote Originally Posted by compufatwa View Post
    ur point of view is not clear to me can u tell me more info about it
    Given the equation,
    x^2p(x)y''+xq(x)y'+r(x)y=0
    Where p(x),q(x),r(x) are analytic functions* on some open interval (-R,R).
    The method of Frobenius says that we can look for a solution of the form,
    y=\sum_{n=0}^{\infty}a_n x^{n+r} for some number r.
    Now to find this r we solve the equation,
    r(r-1)p(0) + rq(0) + r(0) = 0.
    So I told you what r has to be.


    *)"Analytic" on (-R,R) means the function can be expanded as its Taylor series about any point, in this case about 0.


    Yes, I got a question about Islam. Did you know that Halos (the floating circles around your head) were created by Christians. If so why would you use them?
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  5. #5
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    i do not think that the question is about islam ,but it's about the floating circles around icon head, it's just an icon i know that it's used in the art as in church and many famous art drawing .
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