(a) Use the Laplace transform to solve the initial value problem. Here you must use unit step functions. Any other method will not earn credit. Please show all steps. dy + y = f(t), y (0) = -1, dt where ƒ (t) = { -2 if 0

(a) Use the Laplace transform to solve the initial value problem. Here you must use unit step functions. Any other method will not earn credit. Please show all steps. dy + y = f(t), y (0) = -1, dt where ƒ (t) = { -2 if 0

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter2: Graphical And Tabular Analysis

Section2.1: Tables And Trends

Problem 1TU: If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per...

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Question

(a) Use the Laplace transform to solve the initial value problem. Here you must
use unit step functions. Any other method will not earn credit. Please
show all steps.
dy
+ y = f(t),
y (0)
= -1,
dt
where ƒ (t) = {
-2
if 0<t<4
t
if t≥4

(b) Compute each of the following. Please show all work.
(i) L(e-tu(t4))
(ii) L-1
3s-8
s2 2s+5

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