A. Find the Laplace Transform F(s) = L{f(t)} of the function f(t) = t(sin t + cost). B. Let y(t) be the solution of the Initial Value Problem y'' − 3y' + 2y = 2t^2 − 6t + 2, y(0) = 3, y0 (0) = 4. Find...

A. Find the Laplace Transform F(s) = L{f(t)} of the function f(t) = t(sin t + cost).

B. Let y(t) be the solution of the Initial Value Problem

y'' − 3y' + 2y = 2t^2 − 6t + 2, y(0) = 3, y0 (0) = 4.

Find the Laplace transform Y (s) = L{y(t)} and the solution y(t) = L^−1{Y (s)} using the Method of Laplace Transforms.