Using the Laplace transform method, solve for t > 0 the following differential equation: d²x dx +3- + 2x = 6e¯', dt2 dt subject to x = 1 and = 2 at t = 0. Your answer must contain detailed explanation, calculation as well as logical argumentation leading to the result. If you use mathematical theorem(s)/property(-ies) that you have learned par- ticularly in this unit, clearly state them in your answer.

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