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Homework Help: Showing that bessel function satifies differential equation

  1. Feb 14, 2010 #1
    1. The problem statement, all variables and given/known data
    Show that y'' + ((1+2n)/x)y' + y = 0 is satisfied by x-nJn(x)


    2. Relevant equations
    y= x-nJn(x)
    y'=-x-nJn+1(x)
    y''=nx-n-1Jn+1(x) - x-n(dJn+1(x)
    /dx)

    3. The attempt at a solution
    Equation in question becomes:
    x-n(2(n/x)Jn+1 - Jn - ((1+2n)/x)Jn+1 + Jn)

    = x-n(-x-1Jn+1)
    which isn't 0 :confused:?

    Perhaps I made the mistake when I differentiated y?
    Help would be very much appreciated.
     
  2. jcsd
  3. Feb 20, 2010 #2
    Well, when u are going differentiation, Y=X*J(x)
    You see its a product of X and J(X), so u have to used product rules.
    Y'=J(x)D(x)+xD(J(x)).
     
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