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Exam2004Solutions

# Exam2004Solutions - MATH 3705 Final Examination Solutions...

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MATH 3705 Final Examination Solutions April 2004 1. Lf e 2 t cos(3 t ) g =(a) (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 =(d) 3. L ¡ 1 ½ 3 e ¡ 2 s s 2 + s ¡ 2 ¾ =(b)

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2 4. L ¡ 1 ½ s s 2 + 2 s + 10 ¾ =(d) 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 (a) (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 + 2 xy 0 + 1 4 y = 0, valid for x 6 = 0, is given by (d)
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