Query 32 Differential Equations

Question:  Use Laplace transforms to solve the equation y ' + 2 y = 4 t, with initial condition y(0) = 3.  Verify your solution.

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Question:  Let f(t) = sin(t) for 0 <= t < pi, f(t) = 0 for pi <= t < 2 pi, with f(t + 2 pi) = f(t).

Graph this periodic function and find its Laplace transform.

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Question:  Find the function whose Laplace transform is (s^2 - s) / s^3 + e^(-s) / (s ( 1 - e^(-s) ).

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