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Help with frobenius

  1. May 8, 2005 #1
    Somebody please help, I'm not sure I know what is going on with this.

    My problem: find the first solution and use it to find the second solution for

    x^2*y"-x*y'+(x^2+1)y=0

    assuming y=summation from n=0 to infinity for An*x^n+r

    substituting and solving gives me r=1 and a general equation: An=A(n-2)/((n+r)*(n+r-2)+1) for n >= 2

    plugging r into my general equation gives An=A(n-2)/((n+1)*(n-1)+1) for n >= 2

    plugging n into this I get y=A0*x+(1/4)A0*x^3+(1/64)A0*x^5+(1/2304)A0*x^7........ this is y1

    now y2=y1*v

    I'm not entirely sure what to do after this because I'm unable to reduce y1 to a simple summation which is the only way I've seen this problem done before
     
    Last edited: May 8, 2005
  2. jcsd
  3. May 8, 2005 #2
    Maybe you could try to write A_n in product form to see if something more manageable pops out with a nice selection* of A_0.

    *You know, the kind of selections people who already know the answer to the problem always do just to mock us mere mortals.
     
  4. May 8, 2005 #3
    Using the reduction formula I came up with this solution:

    y2=y1*integral(x*(y1)^(-2)*dx)

    I don't know how to write math symbols in here so I attached a picture that is easier to understand.

    does this seem like the correct solution? I'm also concerned about my answer for y1. The index value and power particularly.
     

    Attached Files:

  5. May 8, 2005 #4

    Hurkyl

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