{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

practice1

# practice1 - ν ≥ 0 J ν x = ∞ s n =0-1 n n!Γ(1 ν n p...

This preview shows page 1. Sign up to view the full content.

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 find a recursion formula for the coefficients. 3. Let J ν ( x ) be the Bessel function of the first kind of order
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ν ≥ 0: J ν ( x ) = ∞ s n =0 (-1) n n !Γ(1 + ν + n ) p x 2 P 2 n + ν . Prove that J ν +1 ( x ) = J ν − 1 ( x )-2 J ′ ν ( x ) . 4. ²ind 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....
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online