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Unformatted text preview: MATH 251.4/5/6 Problem set #1 Due: 472011 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) e5 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 e3 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 = e5 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.
 Spring '08
 CHEZHONGYUAN
 Math, Differential Equations, Equations, Partial Differential Equations

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