Use laplace transforms to solve the following initial value problem: x"+8x'+15x = 0; x(0) = 2, x'(0) = -3 show all work, or risk losing all x')=sx (s) - x(0) x"(t) = sº x(s) - sx(0) - x'(0)

Taking the transform of both sides gives

where denotes the Laplace transform of , . Solve for to get

Split the right side into partial fractions:

If , then ; if , then . So

Finally, take the inverse transform of both sides to solve for :

answer: the answer for that is 22/3