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  1. #1
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    Bessel equation

    the question says 'use the result to solve bessel's equation of index n=1/2'.
    i wasn't sure what it means by index n=1/2?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by panda View Post
    the question says 'use the result to solve bessel's equation of index n=1/2'.
    i wasn't sure what it means by index n=1/2?
    Compute \frac{dy}{dx} and \frac{d^2y}{dx^2} in terms of x and \nu using the suggested y(x)=x^{-1/2}\nu(x). It is labourious but it does give the quoted equation.

    Now if we put n=1/2 in the final equation it reduces to:

     <br />
\frac{d^2\nu}{dx^2}+\nu=0<br />

    which has general solution \nu(x)=A\cos(x)+B\sin(x), so the solution of the Bessel equation with n=1/2 (that is of order n=1/2) is:

     <br />
y(x)=x^{-1/2}[A\cos(x)+B\sin(x)]<br />

    RonL
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