test2_07_solutions_CORRECTED

test2_07_solutions_CORRECTED - MATH 3705 * B Test 2 -...

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MATH 3705 * B Test 2 - Solutions. February 2007 Questions 1-4 are multiple choice. Circle the correct answer. Only the answer will be marked. 1. [3 marks] The general solution of 4 x 2 y 00 - 8 xy 0 + 9 y = 0 for x 6 = 0 is ( a ) C 1 | x | - 3 2 + C 2 | x | 3 2 ( b ) | x | 3 2 ( C 1 + C 2 ln | x | ) ( c ) | x | 4+ 7 ( C 1 + C 2 ln | x | ) ( d ) | x | 4 h C 1 cos ± 7 ln | x | ² + C 2 sin ± 7 ln | x | ²i (e) None of the above Solution: The indicial equation is 4 r ( r - 1) - 8 r + 9 = 0, or 4 r 2 - 12 r + 9 = 0, with r 1 = r 2 = 12 8 = 3 2 , Euler Equation, case (ii) ( b ) . 2. [3 marks] The general solution of x 2 y 00 + 4 xy 0 - 10 y = 0 for x 6 = 0 is ( a ) C 1 | x | 2 + C 2 | x | - 5 ( b ) C 1 | x | - 2 + C 2 | x | 5 ( c ) | x | - 2 ( C 1 + C 2 ln | 5 x | ) ( d ) | x | - 2 [ C 1 cos (5 ln | x | ) + C 2 sin (5 ln | x | )] (e) None of the above Solution: The indicial equation is r ( r - 1) + 4 r - 10 = 0, or r 2 + 3 r - 10 = 0, with r 1 = 2 , r 2 = - 5 , Euler equation, case (i) ( a ) . 3. [3 marks] The equation 3 xy 00 + x 2 y 0 + 1 5 y = 0 has (a) one regular singular point x = 5. (b) one regular singular point x = 0. (c)
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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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test2_07_solutions_CORRECTED - MATH 3705 * B Test 2 -...

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