M334Su10exam3-solutions

M334Su10exam3-solutions - Math 334-1 (Ordinary Differential...

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Unformatted text preview: Math 334-1 (Ordinary Differential Equations) Exam 3 RED KEY Part I: Multiple Choice . Mark the correct answer on your scantron. Each question is worth 5 points. 1. Find the regular singular points of the differential equation ( t 2- 1) 2 y 00 + ( t 2- 1) cos t t y + t + 1 t- 1 y = 0 a)-1 only b) 0 only c) 1 only d)-1,1 e)-1,0 f) 0,1 g)-1,0,1 h) None of these Solution: e) 2. Solve t 2 y 00 + 5 ty + 4 y = 0 y (1) = 0 , y (1) = 1 . What is y ( e )? a) e- 2 b) e- 1 c) 1 d) e e) e 2 f) None of these Solution: a) 3. What are the exponents at the singularity x = 0 (the roots of the indicial equation) for the differential equation x 2 (1- x ) y 00- (1 + x ) y + 2 xy = 0? a)-2,0 b) 2,1 c)-1,2 d) 0,2 e) 0,-1 f) 0,1 g) 1,1 h) None of these. Solution: h) 4. Which function cannot have a Laplace Transform? a) t 2 sin t b) e 100 t c) sec t d) 1 t + 1 e) e t cosh( t ) f) All of these functions have a Laplace Transform. Solution: c) 5. Let F ( s ) = s + 3 s 2 + 4 s + 5 . Find its inverse Laplace transform, f ( t ). What is f ( )? a)- e- 2 b) e- 2 c)- 2 e- 2 d) 2 e- 2 e)- e- f) e- g) None of these Solution: a) 6. Let f ( t ) = ( t 2 t 2 1 t &gt; 2 and let F ( s ) be its Laplace Transform. What is F (1)?...
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This note was uploaded on 11/29/2011 for the course MATH 334 taught by Professor Dallon during the Fall '08 term at BYU.

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M334Su10exam3-solutions - Math 334-1 (Ordinary Differential...

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