test2_09_solutions

# test2_09_solutions - MATH 3705 B Test 2 Solutions February...

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MATH 3705 * B Test 2 - Solutions. February 2009 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 II 8 xy I +9 y =0for x W =0is ( 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 ± C 1 cos p 7ln | x | Q + C 2 sin p 7ln | x | Q= (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 II +4 xy I 10 y =0for x W =0is ( 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. [2 marks] The equation 3 xy II + x 2 y I + 1 5 y =0has (a) one regular singular point x =5 . (b)

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test2_09_solutions - MATH 3705 B Test 2 Solutions February...

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