Consider the parametric Bessel equation of order n xy" + xy + (a²x-n²)y=0, (1) where a is a postive constant. 1.1. Show that the parametric Bessel equation (1) takes the Sturm-Liouville form [1] d - (²x - 4y -0. (2) dx 1.2. By multiplying equation (2) by 2xy and integrating the subsequent equation from 0 to c show that for n=0 [18] (3) [xlo(ax)1²dx = (1₂(ac)l² + 1/₁(ac)1³). Hint: x(x) = nJn(x) -x/n+1- 1 27

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