Show, using the application of Laplace Transforms, that the solution x(t) to the differential equation x(t)...

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Show, using the application of Laplace Transforms, that the solution x(t) to the differential equation x"(t) – 2x'(t)+10x(t) = e", with initial conditions x(0) = 0, x'(0) = 1, is x(1) =e'le' - cos(3t) + 3sin(31)]. 10 Show, using the application of Laplace Transforms, that the solution x(t) to the differential equation x"(t) – 2x'(t)+10x(t) = e", with initial conditions x(0) = 0, x'(0) = 1, is x(1) =e'le' - cos(3t) + 3sin(31)]. 10