test3_07_solutions

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

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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
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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.

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

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