Show that the Bessel equation of order one-half x2 y + xy + x2 1 4 y = 0, x > 0 can be
Chapter 5, Problem 6(choose chapter or problem)
Show that the Bessel equation of order one-half x2 y + xy + x2 1 4 y = 0, x > 0 can be reduced to the equation v + v = 0 by the change of dependent variable y = x1/2v(x). From this conclude that y1(x) = x1/2 cos x and y2(x) = x1/2 sin x are solutions of the Bessel equation of order one-half.
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