solutions1-test1

# solutions1-test1 - MATH 3705A Test 1 Solutions Questions...

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MATH 3705A Test 1 Solutions January 26, 2007 Questions 1-4 are multiple choice. Circle the correct answer. Only the answer will be marked. [Marks] 1. L{ t 1 2 e 3 t } = [2] (a) Γ ( 1 2 ) 2 s 3 2 (b) Γ ( 1 2 ) ( s + 3) 3 2 (c) Γ ( 1 2 ) ( s - 3) 3 2 (d) Γ ( 1 2 ) 2( s - 3) 3 2 (e) None of these Solution: (d) 2. L{ t cos(4 t ) } = [2] (a) s 2 s 2 + 16 (b) - s 2 + 16 ( s 2 + 16) 2 (c) s 2 - 16 ( s 2 + 16) 2 (d) s 2 ( s 2 + 16) 2 (e) None of these Solution: (c) 3. L - 1 ± e - 2 s s 2 - 9 ² = [3] (a) 1 6 u ( t - 2) ³ e 3( t - 2) - e - 3( t - 2) ´ (b) u ( t - 2) ³ e 3( t - 2) - e - 3( t - 2) ´ (c) u ( t - 2) ³ e 3( t - 2) + e - 3( t - 2) ´ (d) 1 6 u ( t - 2) ³ e 3 t - e - 3 t ´ (e) None of the above Solution: (a) 4. L ±Z t 0 e x - 1 cos ( t - x ) dx ² = [3] (a) s - 1 ( s + 1)( s 2 + 1) (b) e - 1 s ( s + 1)( s 2 + 1) (c) e - 1 s ( s - 1)( s 2 + 1) (d) s - 1 ( s - 1) 2 + 1 (e) None of the above Solution: (c) 5. Solve the initial-value problem y 00 + 4 y = 1 , y (0) = 0 , y 0 (0) = 0. [5] Solution: [ s 2 Y ( s ) - sy (0) - y 0 (0)] + 4 Y ( s ) = 1 s ( s

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solutions1-test1 - MATH 3705A Test 1 Solutions Questions...

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