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Unformatted text preview: b 9 , ≤ t < 3 , t 2 , t ≥ 3 . (b) Find the Laplace transform of f ( t ) = e t sin( √ 2 t ) . (c) Find the inverse Laplace transform of F ( s ) = s2 s 2 + 2 s + 10 . 3. Solve the following initial value problem using Laplace transform, y (4)16 y = 0 , y (0) = 1 , y ′ (0) = 2 , y ′′ (0) = 0 , y (3) (0) = 0 . 4. Solve the following initial value problem, y ′′ + 6 y ′ + 13 y = g ( t ) , where g ( t ) = b t1 , ≤ t < 1 , , t ≥ 1 . sketch the solution in time. 5. Solve the following initial value problem. y ′′2 y = 4 e − 2 t δ ( t1) , y (0) = 0 , y ′ (0) = 1 . Sketch the solution....
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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 Penn State.
 Spring '08
 CHEZHONGYUAN
 Math, Differential Equations, Equations, Partial Differential Equations

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