m251_problem_set1[sp11] - MATH 251.4/5/6 Problem set #1...

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Unformatted text preview: MATH 251.4/5/6 Problem set #1 Due: 4-7-2011 1. Find the general solution of (a) y (6)- 5 y (4)- 36 y = 0 (b) y (6)- 2 y (4) + y = 0 2. Find the Laplace transform of (a) u /4 ( t ) e 3 t cos t . (b) u 2 ( t ) ( t 3 t + 4) (c) ( t 3) t 2 cos( t ) 3. Find the Laplace transform of (a) e-5 t sin(2 t ) cos(2 t ). (b) 6sin(8 t ) sin(2 t ) 4. Find the inverse Laplace transform of each given function: (a) F ( s ) = e- s (7 - 3 s ) / ( s 2- 8 s + 20) (b) F ( s ) = 5 e-3 s s / ( s 4- 16) (c) F ( s ) = e- s / ( s 3 + 9 s ) 5. Use the method of Laplace transform to solve the following 1st order linear IVP. y + 6 y = e-5 t + u 8 ( t ), y (0) = 3 6. Use the method of Laplace transform to solve the following 3rd order linear IVP. y - y - 2 y = 0, y (0) = 0, y (0) = 1, y (0) = 5 7. Find the general solution for each system. Then classify the type and stability of the critical point at (0,0)....
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This note was uploaded on 07/16/2011 for the course MATH 251 taught by Professor Chezhongyuan during the Spring '08 term at Pennsylvania State University, University Park.

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m251_problem_set1[sp11] - MATH 251.4/5/6 Problem set #1...

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