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Exercise 6: (10 points) Solve the following initial value problem using Laplace transform: If necessary; use convolution integral to express its solution or part of...

Question

Exercise 6: (10 points) Solve the following initial value problem using Laplace transform: If necessary; use convolution integral to express its solution or part of its solution: + 2y' + 2y = e-t _ 8(t - 4), y(0) = 2, y(0) = -5Note: do not use partial fractions

Exercise 6: (10 points) Solve the following initial value problem using Laplace transform: If necessary; use convolution integral to express its solution or part of its solution: + 2y' + 2y = e-t _ 8(t - 4), y(0) = 2, y(0) = -5 Note: do not use partial fractions



Answers

Use the Laplace transform to solve the given initial value problem. $$ y^{\prime \prime}+2 y^{\prime}+5 y=0 ; \quad y(0)=2, \quad y^{\prime}(0)=-1 $$

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