test3_07_solutions

# test3_07_solutions - MATH 3705 B Test 3 Answers and...

This preview shows pages 1–2. Sign up to view the full content.

MATH 3705* B Test 3 Answers and solutions March 2007 Questions 1-3 are multiple choice. Circle the correct answer. Only the answer will be marked. 1. [3 marks] The general solution of xy II + y I +7 xy =0for x> 0is ( a ) c 1 J 0 ( 7 x )+ c 2 J 0 ( 7 x )ln( x )( b ) c 1 J 0 ( 7 x )+ c 2 Y 0 ( 7 x ) ( c ) c 1 J 7 ( x )+ c 2 J 7 ( x )( d ) c 1 J 7 ( x )+ c 2 Y 7 ( x )( e ) None of the above 2. [2 marks] At x = 17, the Fourier cosine series of f ( x )= F 1 , 0 x< 2 0 , 2 x< 3 k converges to (a) 0 (b) 1 2 (c) 1 2 (d) 1 (e) None of these 3. [3 marks] The solution of the wave equation u xx = 1 9 u tt , 0 <x< 2, which satis f es the boundary conditions u (0 ,t )= u (2 ,t ) = 0, is given by u ( x, t )= 3 n =1 sin p n π x 2 Q F a n cos w 3 n π t 2 W + b n sin w 3 n π t 2 Wk . If u ( x, t )sat is f es the initial conditions u ( x, 0) = 0 and u t ( x, 0) = 3 sin( π x ) sin(3 π x ), the coe cients a n and b n are given by (a) b 2 =3 ,b 6 = 1 ,b n = 0 otherwise, and a n

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 07/16/2009 for the course MATH 3705 taught by Professor Jaberabdualrahman during the Winter '08 term at Carleton CA.

### Page1 / 4

test3_07_solutions - MATH 3705 B Test 3 Answers and...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online