4038T2 - m =0 a m x m + r to 4 xy + 2 y + y = 0. a. Find...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Name: Instructions. Show all work in the space provided. Indicate clearly if you continue on the back side, and write your name at the top of the scratch sheet if you will turn it in for grading. No books or notes are allowed, but a scientifc calculator is ok - though unnecessary . All work must be shown to receive credit. Please do not give decimal approximations For square roots, For trigonometric or exponential Functions, or For π . Maximum score = 100 points. A list oF useFul Formulas appears below. Legendre’s Equation: (1 - x 2 ) y 0 - 2 xy 0 + n ( n +1) y =0 Bessel’s Equation: x 2 y 0 + xy 0 +( x 2 - ν 2 ) y =0 1. (20) ±ind a non-trivial polynomial solution to (9 - x 2 ) y 0 - 2 xy 0 +20 y =0 . (H in t : substitute x
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
2. (30) There are solutions of the form y =
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: m =0 a m x m + r to 4 xy + 2 y + y = 0. a. Find all values of r which yield a solution. b. Find a recursion formula for a m +1 in terms of a m , m , and r . c. Now set r equal to its smallest possible value from part (a), and nd a formula for a m in terms of m . 2 3. (25) (1 + x ) x 2 y-(1 + 2 x ) xy + (1 + 2 x ) y = 0 has a solution y 1 = x + C . a. Find the value of C which makes y 1 a solution. b. Find a solution y 2 = y 1 u which is independent of y 1 . (Hint: What must the sum of all the terms which have an undierentiated u as a factor?) 3 4. (25) Find the general solution for y in terms of x using Bessel functions: x 2 y + xy + (4 x 4-1 4 ) y = 0 (Hint: Substitute z = x 2 .) 4...
View Full Document

Page1 / 4

4038T2 - m =0 a m x m + r to 4 xy + 2 y + y = 0. a. Find...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online