Warnings:

(1) This is NOT a group or team work/test; NO; it is an individual work to do at

home. Any indication of copying someone else will result in zero.

(2) Show your work step-by-step.

(3) Write cleanly and neatly.

Question:

Solve:

1. Find the Laplace transform of the following function(s)

(a) f(t) = 6e−^4t (t^2 + 3t + 5)

(b) f(t) = t^2e ^3t

(c) f(t) = e^2t sin(2t)

2. Find the inverse Laplace transform (zero initial condition(s))

(a) ÿ+ 9y = f(t) where f(t) is a step function.

(b) ÿ+ 2ẏ + y = 3te^−t