Answer the following items on a clean sheet of paper. Upload photos of your answer sheets showing your solutions. D² f – Df = 0 mm f(0) = Df(0) = 1 2. Solve the initial value problem, with
Answer the following items on a clean sheet of paper. Upload photos of your answer sheets showing your solutions. D² f – Df = 0 mm f(0) = Df(0) = 1 2. Solve the initial value problem, with
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section: Chapter Questions
Problem 5T
Related questions
Question
The second image is a reference.
Transcribed Image Text:Answer the following items on a clean sheet of paper. Upload photos of your answer sheets showing your solutions.
D² ƒ – Df = 0 wm
f (0) = Df(0) = 1
2. Solve the initial value problem,
with
![Solve the initial-value problem:
Df – D²f = 0; f(0) = Df (0) = D²f(0) = 3
Solution:
We apply L to both sides of our ODE
L[D®f] – L[D²f] = L[0] = 0
%3D
By Theorem 1.2,
L[D³f] = s³L[f] – s²f(0) – sDf(0) – D²f(0)
= s³L[f] – 3s² – 3s – 3
L[D²f] = s?L[f] - sf(0) – Df (0)
= s?L[f]– 3s – 3
%D
Substituting into the transformed ODE,
(s°L[f] – 3s? – 3s – 3) – (s²L[f] – 3s – 3) = 0
s³ L[f] – s²L[f] – 3s² = 0
3s2
L[f] =
3
s3 - s2
S- 1
f(x) = L-1
S -
= 3e*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F639a7ef1-f4e6-4fee-a616-51c4d4cf8a40%2F584709f8-341c-40b7-a033-c99905f56572%2Fgd77mp_processed.png&w=3840&q=75)
Transcribed Image Text:Solve the initial-value problem:
Df – D²f = 0; f(0) = Df (0) = D²f(0) = 3
Solution:
We apply L to both sides of our ODE
L[D®f] – L[D²f] = L[0] = 0
%3D
By Theorem 1.2,
L[D³f] = s³L[f] – s²f(0) – sDf(0) – D²f(0)
= s³L[f] – 3s² – 3s – 3
L[D²f] = s?L[f] - sf(0) – Df (0)
= s?L[f]– 3s – 3
%D
Substituting into the transformed ODE,
(s°L[f] – 3s? – 3s – 3) – (s²L[f] – 3s – 3) = 0
s³ L[f] – s²L[f] – 3s² = 0
3s2
L[f] =
3
s3 - s2
S- 1
f(x) = L-1
S -
= 3e*
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage