3.4.1 Example A An easy calculation shows that (1) Yk (3.77) Yk = 1 are solutions to the homogeneous equation Yk+2 – 3yk+1 + 2yk = 0. (3.78) Furthermore, their Casoratian is given by the following expression: C(k + 1) = 2k+1 1 2k+2 1 -2k+1. (3.79) Let us use these results to calculate a particular solution to the inhomo- geneous equation Yk+2 – 3yk+1 + 2yk = 4k + 3k². (3.80) Let Y be the particular solution, where Yk = C1(k)2* + C2(k). (3.81) The functions C1(k) and C2(k) satisfy the following equations: 2k+1AC1(k) + AC2(k) = 0, (3.82) 2*+2AC1 (k) + AC2(k) = 4* + 3k?.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Topic Video
Question

Explain the determaine

3.4.1 Example A
An easy calculation shows that
(1)
Yk
2k,
.(2)
= 1
Yk
(3.77)
are solutions to the homogeneous equation
Yk+2 – 3yk+1 + 2yk = 0.
(3.78)
Furthermore, their Casoratian is given by the following expression:
2k+1
2k+2 1
1
C(k + 1)
1--2*+1
(3.79)
Let us use these results to calculate a particular solution to the inhomo-
geneous equation
Yk+2
3yk+1 + 2yk
4k + 3k?.
(3.80)
Let Yk be the particular solution, where
Yk = C1 (k)2* + C2(k).
(3.81)
The functions C1(k) and C2(k) satisfy the following equations:
2*+1AC1 (k) + AC2(k) = 0,
(3.82)
2*+2AC1 (k) + AC2(k) = 4* + 3k².
Transcribed Image Text:3.4.1 Example A An easy calculation shows that (1) Yk 2k, .(2) = 1 Yk (3.77) are solutions to the homogeneous equation Yk+2 – 3yk+1 + 2yk = 0. (3.78) Furthermore, their Casoratian is given by the following expression: 2k+1 2k+2 1 1 C(k + 1) 1--2*+1 (3.79) Let us use these results to calculate a particular solution to the inhomo- geneous equation Yk+2 3yk+1 + 2yk 4k + 3k?. (3.80) Let Yk be the particular solution, where Yk = C1 (k)2* + C2(k). (3.81) The functions C1(k) and C2(k) satisfy the following equations: 2*+1AC1 (k) + AC2(k) = 0, (3.82) 2*+2AC1 (k) + AC2(k) = 4* + 3k².
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Discrete Probability Distributions
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
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,