Final test_April2004

# Final test_April2004 - MATH 3705 Final Examination April...

This preview shows pages 1–4. Sign up to view the full content.

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 = (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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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 +2 xy 0 + 1 4 y = 0, valid for x 6 =0 ,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
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 09/21/2009 for the course MATH 3705 taught by Professor Dr.e.devdariani during the Winter '09 term at Carleton.

### Page1 / 9

Final test_April2004 - MATH 3705 Final Examination April...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online