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Solving Partial Differential Equations : Laplace Transforms, Fourier Transforms and Separation of Variables

Please use: 1.) LaPlace Transform and 2.) Fourier Transforms methods and 3.) our old friend separation of variables with eigenvalues expansion to solve each problem. It is not necessary to evaluate an inverse transform. Where convenient, show any solution as a convolution of two functions and indicate how these functions are determined.

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A PDE is solved by three methods. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.