his is some (a) Use this

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 54E
icon
Related questions
Question
This is sometimes called the Heaviside expansion theorem.
(a) Use this theorem to write the solution of y" + 3y' + 2y = f(t),
y(0) =y'(0)=0.
(b) Give an explicit evaluation of the solution in (a) for the cases f(t) = e3t
and f(t) = t.
(c) Find the solutions in (b) by using the superposition principle (13).
Transcribed Image Text:This is sometimes called the Heaviside expansion theorem. (a) Use this theorem to write the solution of y" + 3y' + 2y = f(t), y(0) =y'(0)=0. (b) Give an explicit evaluation of the solution in (a) for the cases f(t) = e3t and f(t) = t. (c) Find the solutions in (b) by using the superposition principle (13).
5. When the polynomial z(p) has distinct real zeros a and b, so that
1
1
A
B
2(p)
(р-а)(р-b) р-а р-b
for suitable constants A and B, then
h(t) = Aeat + Bebt
and (15) takes the form
y(t) = [f(t)[Aec-1) + Bebl-=")]dt.
%3D
Transcribed Image Text:5. When the polynomial z(p) has distinct real zeros a and b, so that 1 1 A B 2(p) (р-а)(р-b) р-а р-b for suitable constants A and B, then h(t) = Aeat + Bebt and (15) takes the form y(t) = [f(t)[Aec-1) + Bebl-=")]dt. %3D
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps

Blurred answer
Knowledge Booster
Pyramids
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Elements Of Modern Algebra
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning