Consider the differential equation y' (t) + 8y(t) = 6cos(1t)u(t), with initial condition y(0) = 6, Find the Laplace transform of the solution Y(s). Write the solution as a single fraction in s Y(s) = help (formulas) Find the partial fraction decomposition of Y(s). Enter all factors as first order terms in s, that is, all terms should be of the form , where c is a constant and the s-p root p is a constant. Both c and p may be complex. Y(s) = + Find the inverse Laplace transform of Y(s). The solution must consist of all real terms. (Remeber to use u(t).) y(t) = L-1 {Y(s)} = help (formulas)

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