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Exam2003Solutions - 1 MATH 3705 Final Examination Solutions...

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1 MATH 3705 Final Examination Solutions April 2003 1. Lf t 3 e 2 t g = (d) (a) 6 ( s + 2) 3 (b) 6 e ¡ 2 s s 3 (c) 6 ( s ¡ 2) 3 (d) 6 ( s ¡ 2) 4 (e) None of the above. 2. Lf e ¡ 3 t cos(4 t ) g = (b) 3. L ¡ 1 ½ e ¡ 3 s s 2 ¡ 2 s + 5 ¾ = (a) 4. L ¡ 1 ½ 3 s ( s 2 + 9) 2 ¾ = (c)
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2 5. The general solution of 4 x 2 y 00 ¡ 8 xy 0 + 9 y = 0, valid for x 6 = 0, is given by (d) (a) c 1 j x j 3 = 2 + c 2 j x j 3 = 2 (b) j x j " c 1 cos à p 5 2 ln j x j ! + c 2 sin à p 5 2 ln j x j !# (c) c 1 j x j + c 2 j x j p 5 = 2 (d) c 1 j x j 3 = 2 + c 2 j x j 3 = 2 ln j x j (e) None of the above. 6. The general solution of x 2 y 00 + xy 0 + (5 x 2 ¡ 9) y = 0 near x 0 = 0, valid for x > 0, is given by (b) (a) c 1 J 3 ( p 5 x ) + c 2 J ¡ 3 ( p 5 x ) (b) c 1 J 3 ( p 5 x ) + c 2 Y 3 ( p 5 x ) (c) c 1 J p 5 (3 x ) + c 2 J ¡ p 5 (3 x ) (d) c 1 J p 5 (3 x ) + c 2 Y p 5 (3 x ) (e) None of the above.
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