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solutions2-test2

# solutions2-test2 - MATH 3705A Test 2 Solutions[Marks...

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MATH 3705A Test 2 Solutions February 16, 2007 Questions 1-5 are multiple choice. Circle the correct answer. Only the answer will be marked. [Marks] 1. The general solution of x 2 y 00 - 2 xy 0 + 3 y = 0 for x 6 = 0 is [3] (a) | x | 3 2 + 3 2 [ c 1 + c 2 ln | x | ] (b) | x | 3 2 h c 1 cos ± 3 2 ln | x | ² + c 2 sin ± 3 2 ln | x | ²i (c) c 1 | x | 3 2 + c 2 | x | 3 2 (d) c 1 | x | 3 2 + 3 2 + c 2 | x | 3 2 - 3 2 (e) None of these Solution: (b) 2. The general solution of x 2 y 00 - 3 xy 0 + 4 y = 0 for x 6 = 0 is [3] (a) c 1 x 2 + c 2 x 2 (b) x 2 [ c 1 + c 2 ln | x | ] (c) x 2 [ c 1 cos(ln | x | ) + c 2 sin(ln | x | )] (d) x 2 [ c 1 cos(2 ln | x | ) + c 2 sin(2 ln | x | )] (e) None of these Solution: (b) 3. The general solution of 2 x 2 y 00 - xy 0 + y = 0 for x 6 = 0 is [3] (a) | x | 1 2 " c 1 cos 7 2 ln | x | ! + c 2 sin 7 2 ln | x | !# (b) c 1 | x | 1 2 + c 2 x (c) x 2 [ c 1 cos(2 ln | x | ) + c 2 sin(2 ln | x | )] (d) x 2 [ c 1 cos(ln | x | ) + c 2 sin(ln | x | )] (e) None of these

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solutions2-test2 - MATH 3705A Test 2 Solutions[Marks...

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