Exam2004

Exam2004 - MATH 3705 Final Examination April 2004 1. Lfe2t...

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MATH 3705 Final Examination April 2004 1. Lf e 2 t cos(3 t ) g = (a) s ¡ 2 ( s ¡ 2) 2 +9 (b) s ( s ¡ 2) 2 (c) s ¡ 2 s 2 (d) e ¡ 2 s s 2 (e) None of the above. 2. Lf t sin(2 t ) g = (a) s ( s 2 +4) 2 (b) ¡ s ( s 2 2 (c) 2 ( s ¡ 1) 2 +4 (d) 4 s ( s 2 2 (e) None of the above. 3. L ¡ 1 ½ 3 e ¡ 2 s s 2 + s ¡ 2 ¾ = (a) u ( t ¡ 2) [ e t ¡ e ¡ 2 t ] (b) u ( t ¡ 2) [ e t ¡ 2 ¡ e ¡ 2 t +4 ] (c) e t ¡ 2 ¡ e ¡ 2( t ¡ 2) (d) u ( t ) e t ¡ u ( t ¡ 2) e t ¡ 2 (e) None of the above. 1

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4. L ¡ 1 ½ s s 2 +2 s +10 ¾ = (a) e ¡ t cos(3 t ) (b) e ¡ t sin(3 t ) (c) e ¡ t cos(3 t ) ¡ e ¡ t sin(3 t ) (d) e ¡ t [cos(3 t ) ¡ 1 3 sin(3 t )] (e) None of the above. 5. The general solution of the di®erential equation 2 x 2 y 00 ¡ 5 xy 0 +3 y = 0, valid for x 6 =0 ,i s given by (a) c 1 j x j 3 + c 2 j x j 1 2 (b) j x j 3 [ c 1 + c 2 ln j x j ] (c) j x j 3 c 1 cos μ 1 2 ln j x j + c 2 sin μ 1 2 ln j x j ¶¸ (d) c 1 j x j 1 2 + c 2 j x j 3 ln j x j (e) None of the above. 6. The general solution of the di®erential equation x 2 y 00 xy 0 + 1 4 y = 0, valid for x 6 ,isg iven by (a) j x j ¡ 1 " c 1 cos Ã p 3 2 ln j x j ! + c 2 sin Ã p 3 2 ln j x j !# (b) c 1 j x j ¡ 1 + c 2 j x j p 3 2 (c) c 1 j x j ¡ 1 2 + c 2 j x j ¡ 1 2 (d) j x j ¡ 1 2 ( c 1 + c 2 ln j x j ) (e) None of the above. 2
7. The general solution of the di®erential equation x 2 y 00 + xy 0 +(7 x 2 ¡ 4) y = 0, valid for x> 0, is given by (a) c 1 J 2 ( p 7 x )+ c 2 J ¡ 2 ( p 7 x ) (b) c 1 J p 7 (2 x c 2 J ¡ p 7 (2 x ) (c) c 1 J 2 ( p 7 x c 2 Y 2 ( p 7 x ) (d) c 1 J p 7 (2 x c 2 Y p 7 (2 x ) (e) None of the above.

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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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Exam2004 - MATH 3705 Final Examination April 2004 1. Lfe2t...

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