For armodrillo1

MAT 275 Written Homework #8

6.1, 6.2, 6.3 Due: November 18

Solve the following problems, showing any necessary work.

1. [1 point] Solve the following initial value problem, using Laplace Transforms.

9y′′ − 8y′ − y = 10et

y(0) = −4 y′(0) = −3

(If it looks familiar, it should. It’s problem #2 from Homework #7.)

2. [1 point] The function f is defined piecewise:

f(t) =

 

0 if t < 1 t − 1 if 1 ≤ t ≤ 2 3 − t if 2 < t < 3 0 if 3 ≤ t

Write f(t) in terms of the Heaviside (step) function u∗, and then solve the following initial value problem using Laplace Transforms:

y′(t) = f(t)

y(0) = 0