5. (a) Find the Laplace transform of e-2t + 5t[u(t 2) u(t)] where u(t...

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5. (a) Find the Laplace transform of e-2t + 5t[u(t – 2) – u(t)] where u(t – 2) and u(t) are the unit step functions (include proper justification by stating any non-trivial formulae/theorems used in the process). (b) Find the particular solution of the following differential equation by the operator method (only using partial fractions decompositions): y" – 3y + 2y = xe". [4+4] 5. (a) Find the Laplace transform of e-2t + 5t[u(t – 2) – u(t)] where u(t – 2) and u(t) are the unit step functions (include proper justification by stating any non-trivial formulae/theorems used in the process). (b) Find the particular solution of the following differential equation by the operator method (only using partial fractions decompositions): y" – 3y + 2y = xe". [4+4]