{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

MAP 4305 Exam Practice 4

# MAP 4305 Exam Practice 4 - ˙ r = sin r ˙ θ =-1 Are there...

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

Practice Exam 3: MAP 4305 * 1. Does 5 xy 00 + 4(1 - x 2 ) y 0 + 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 00 - xy 0 + (1 - x 2 ) y = 0 , x > 0 . Do not find a recursion formula for the coefficients. 3. Find the first three non-zero terms in a series expansion about x = 0 of 2 linearly independent solutions to: 3 xy 00 + (2 - x ) y 0 - y = 0 , x > 0 . 4. Draw solutions in the ( x, y ) plane of the following system in polar coordinates:
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ˙ r = sin r ˙ θ =-1 Are there any non-trivial periodic solutions? If yes, are they limit cycles? If there are non-trivial periodic solutions, how many are there, and what can be said about their stability? 5. The Legendre polynomials P n ( x ) satisfy the following recurrence relation: ( n + 1) P n +1 ( x ) = (2 n + 1) xP n ( x )-nP n-1 ( x ) . Given that P ( x ) = 1 and P 1 ( x ) = x , determine P 2 ( x ), P 3 ( x ) and P 4 ( x ). * Instructor: Patrick De Leenheer....
View Full Document

{[ snackBarMessage ]}