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 + 9 (c) s ¡ 2 s 2 + 9 (d) e ¡ 2 s s 2 + 9 (e) None of the above. 2. Lf t sin(2 t ) g = (a) s ( s 2 + 4) 2 (b) ¡ s ( s 2 + 4) 2 (c) 2 ( s ¡ 1) 2 + 4 (d) 4 s ( s 2 + 4) 2 (e) None of the above. 3. L ¡ 1 ½ 3 e ¡ 2 s s 2 + s ¡ 2 ¾ = 1
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4. L ¡ 1 ½ s s 2 + 2 s + 10 ¾ = 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, is given by 6. The general solution of the di®erential equation x 2 y 00 + 2 xy 0 + 1 4 y = 0, valid for x 6 = 0, is given by (a) j x j ¡ 1 " c 1 cos à p 3 2 ln j x j ! + c 2 sin à 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
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