test2_08_solutions

test2_08_solutions - MATH 3705 Test 2 Answers and Solutions...

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MATH 3705 Test 2 - Answers and Solutions February 2008 LAST NAME: ––––––––––––––––— ID#: ––––––– Questions 1-7 are multiple choice. Circle the correct answer. Only the answer will be marked. 1. [3 marks] The general solution of x 2 y II +2 xy I + y =0for x W =0is ( a ) c 1 | x | 1 2 + c 2 | x | 3 2 ( b ) c 1 | x | 1 2 + 3 2 + c 2 | x | 1 2 3 2 ( c ) | x | 1 2 + 3 2 [ c 1 + c 2 ln | x | ] ( d ) | x | 1 2 ^ c 1 cos X 3 2 ln | x | ~ + c 2 sin X 3 2 ln | x | (e) None of the above Solution: This is an Euler equation with A =2 , B = 1. The indicial equation is r 2 + r + 1 = 0 with r 1 , 2 = 1 2 ± i 3 2 Euler Equation, case (iii) ( d ) . 2. [3 marks] The general solution of 4 x 2 y II +8 xy I + y = 0 for x W =0is ( a ) c 1 | x | 1 2 + c 2 | x | 1 2 ( b ) | x | 1 2 [ c 1 + c 2 ln | x | ]( c ) | x | 1 2 [ c 1 cos (ln | x | )+ c 2 sin (ln | x | )] ( d ) | x | 1 2 c 1 cos w 1 2 ln | x | W + c 2 sin w 1 2 ln | x | W] (e) None of the above Solution: This is an Euler equation with A = 8 4 =2 , B = 1 4 . The indicial equation is r 2 +(2 1) r + 1 4 =0 , or4 r 2 +4 r +1=(2 r +1) 2 = 0. The roots are r 1 = r 2 = 1 2 Euler Equation, case (ii) ( b )
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This note was uploaded on 02/12/2011 for the course MATH 3705 taught by Professor Jaberabdualrahman during the Spring '08 term at Carleton CA.

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test2_08_solutions - MATH 3705 Test 2 Answers and Solutions...

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