Question: Problem 1. (40 points): The differential equation 22day dy + (12 - n ? ) y = 0 is known as the the Bessel's differential

Problem 1. (40 points): The differential equation 22day dy + (12 - n ? ) y = 0 is known as the the Bessel's differential equation of order n. Show the following function y(x) satisfies the above differential equation y(x) = AJn(x) + BJ_(2) where A and B are constants. The functions J,(a) and Jem(x) are given by: r=DO n+2r In(x) = _ (-1)" r=0 r![(r +n+1) r=00 -n+2r J_n(x) = r!r(r - n+1)

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