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In: Advanced Math

The Bessel equation of order p is t2y" + ty' + (t2 - p2)y = 0....

The Bessel equation of order p is t2y" + ty' + (t2 - p2)y = 0. In this problem, assume that p = 1/2:

a.) Show that y1 = sin(t / sqrt(t)) and y2 = cos(t / sqrt(t)) are linearly independent solutions for 0 < t < infinity.

b.) Use the result from part (a), and the preamble in Exercise 3, to find the general solution of t2y" + ty' + (t2 - (1/4))y = t3/2cos(t). (answer should be: 1/2 sin(t) sqrt(t))

**Preamble of Exercise 3: The formula for a particular solution given in (3.42) applies to the more general problem of solving y" + p(t)y' + q(t)y = f(t). In this case, y1 and y2 are independent solutions of the associated homogeneous equation y" + p(t)y' + q(t)y = 0.

Please show work!

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Expert Solution

Colby Messinger answered 1 month ago
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