Question

(a) [5 points] using only the definition, find the laplace transform y (s) of y(t) = e a t where a is a constant. for what values of s does the laplace transform y (s) exist? (b) [10 points] solve, using laplace transforms, the initial value problem: y 00 − 4y 0 + 4y = 3, y(0) = 0, y0 (0) = 1.

Answer 1

Find the Laplace transform y (s) of y (t) = e a t. Here, a is a constant. Which value of s exists for the Laplace transform y (s)? (0) = 0, y 0 (0) = 0, y (0) = 0,