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Math Help - Help needed (Frobenius method)

  1. #1
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    Help needed (Frobenius method)

    any 1 can help me on solving the following question plz.

    Use Frobenius method to solve the following differential equation

    X2Y'' +X(2-X)Y'-2Y= 0
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  2. #2
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    just to remember

    No answer up tell now , plz. try again
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  3. #3
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    This is how I'd start it and I'm taking this right out of Rainville and Bedient on the chapter on power series solutions:

    2xy''+x(2-x)y'-2y=0

    Now convert it to the standard form y''+p(x)y'+q(x)y=0:

    y''+\frac{x(2-x)}{2x} y'-\frac{1}{x}y=0

    with p(x)=1-x/2 and q(x)=1/x. That means p_0=0 and q_0=0 leaving for the indicial equation c^2-c=0 giving roots of 0 and 1. So I'd next go to the section dealing with difference of roots a positive integer by first substituting y(x)=\sum_{n=0}^{\infty} a_n x^{n+c} into the original differential equation and continuing.
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  4. #4
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    Razem, I had some problems going further with this as I've been away from it for some time but I do know the route if I had to solve it: Open the book to the first page of that chapter on power series, start reading, do all of the examples, do a few problems in each section, let it simmer over several days, maybe I don't know about 5-10 problems in all. Eventually, I'd get to the point where I could then go back to this problem and work it. That's really in my opinion how to successfully approach a problem you can't solve in math and elsewhere: put it on the back-burner and work some simpler ones first and then "scale-up" .
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  5. #5
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    Quote Originally Posted by shawsend View Post
    Razem, I had some problems going further with this as I've been away from it for some time but I do know the route if I had to solve it: Open the book to the first page of that chapter on power series, start reading, do all of the examples, do a few problems in each section, let it simmer over several days, maybe I don't know about 5-10 problems in all. Eventually, I'd get to the point where I could then go back to this problem and work it. That's really in my opinion how to successfully approach a problem you can't solve in math and elsewhere: put it on the back-burner and work some simpler ones first and then "scale-up" .
    Thanks for your advice, I am away from this subject for years same as u.
    Someone ask me this question, I cann't solve it, and I wont to help him.
    Thank you any way.
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