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Math Help - Series Solutions to 2nd Order DEs HELP!

  1. #1
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    Series Solutions to 2nd Order DEs HELP!

    x^2 y" + 2 x^2 y' -2y = 0

    I need to find the indicial equation and find the values of k but I don't understand how to find po and qo.

    Thanks
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  2. #2
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    To calculate the indicial equation, write it as:

    y''+p(x)y'+q(x)y=0

    If it's a regular singular point, p(x) cannot have it its denominator the factor x to a power higher than 1.

    Write p(x)=\frac{p_0}{x}+p_1+p_2x+\cdots

    q(x)=\frac{q_0}{x^2}+\frac{q_1}{x}+q_2+q_3x+\cdots

    Then it's simple, the indicial equation is:

    c^2+(p_0-1)c+q_0

    In your case, it's c^2-c-2=0
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  3. #3
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    Sorry I still don't understand how you've got that
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  4. #4
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    Ok, your equation is: x^2y''+2x^2y'-2y=0 or y''+2y'-\frac{2}{x^2}y=0

    That means p(x)=\frac{0}{x}+2+0x+0x^2+\cdots

    and q(x)=-\frac{2}{x^2}+\frac{0}{x}+0+\cdots

    That is p_0=0 and q_0=-2. Now just plug it into the indicial equation:

    c^2-c-2=0
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  5. #5
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    Please look here : http://www.mathhelpforum.com/math-he...s-problem.html for a similar problem (with a rough method)
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  6. #6
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    Thanks, shawsend is it the same for q(x), it also cannot have its denominator the factor x to a power higher than 1.
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