practice1 - 0: J ( x ) = s n =0 (-1) n n !(1 + + n ) p x 2...

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Practice Exam 1: MAP 4305 * 1. Does 5 xy ′′ + 4(1 - x 2 ) y + y = 0 , x > 0 , have a solution which is bounded near zero? Notice that to answer this question, you only need to consider the indicial equation. 2. Determine the form of a series expansion about x = 0 of 2 linearly independent solutions to: x 2 y ′′ - xy + (1 - x 2 ) y = 0 , x > 0 . Do not Fnd a recursion formula for the coe±cients. 3. Let J ν ( x ) be the Bessel function of the Frst kind of order
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Unformatted text preview: 0: J ( x ) = s n =0 (-1) n n !(1 + + n ) p x 2 P 2 n + . Prove that J +1 ( x ) = J 1 ( x )-2 J ( x ) . 4. ind the Frst three non-zero terms in a series expansion about x = 0 of 2 linearly independent solutions to: 3 xy + (2-x ) y -y = 0 , x > . * Instructor: Patrick De Leenheer....
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This note was uploaded on 09/12/2011 for the course MAP 4305 taught by Professor Deleenheer during the Summer '06 term at University of Florida.

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