Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
1- Explain the the difference between DE with Ordinary points and DE with singular points Find two power series solutions of the given differential equation about the ordinary point x = 0. y" - 4xy + y = 0 We are asked to find two power series solutions to the following homogenous linear second-order differential equation. y" – 4xy' + y = 0 By Theorem 6.2.1, we know two such solutions exist about the ordinary point x= 0. In fact, the differential equation has no singular points as each of the coefficient functions are (very simple) polynomials. Therefore, they are trivially represented as power series at any point and are therefore analytic. This means the power series solution will converge for Ixl < o. Let y = . We substitute this series and its derivatives into the given differential equation. We will n=0 solve for two sets of cn to find the two solutions. The differential equation includes non-zero terms for the first and second derivative of y. These derivatives always have the same form, so we refer to equation (1) of section 6.1. Y = C,nx" -1 n-1 E ,m(n - 1)x - 2 n- 2 Substitute the power series into the given differential equation. y" - 4xy + y = - 4

1- Explain the the difference between DE with Ordinary points and DE with singular points Find two power series solutions of the given differential equation about the ordinary point x = 0. y" - 4xy + y = 0 We are asked to find two power series solutions to the following homogenous linear second-order differential equation. y" – 4xy' + y = 0 By Theorem 6.2.1, we know two such solutions exist about the ordinary point x= 0. In fact, the differential equation has no singular points as each of the coefficient functions are (very simple) polynomials. Therefore, they are trivially represented as power series at any point and are therefore analytic. This means the power series solution will converge for Ixl < o. Let y = . We substitute this series and its derivatives into the given differential equation. We will n=0 solve for two sets of cn to find the two solutions. The differential equation includes non-zero terms for the first and second derivative of y. These derivatives always have the same form, so we refer to equation (1) of section 6.1. Y = C,nx" -1 n-1 E ,m(n - 1)x - 2 n- 2 Substitute the power series into the given differential equation. y" - 4xy + y = - 4

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
1- Explain the the difference between DE with Ordinary points and DE with singular points Find two power series solutions of the given differential equation about the ordinary point x = 0o. y" - 4xy' + y = 0 We are asked to find two power series solutions to the following homogenous linear second-order differential equation. y" - 4xy' + y = 0 By Theorem 6.2.1, we know two such solutions exist about the ordinary point x = 0. In fact, the differential equation has no singular points as each of the coefficient functions are (very simple) polynomials. Therefore, they are trivially represented as power series at any point and are therefore analytic. This means the power series solution will converge for |x| < oo. Let y = 5C". We substitute this series and its derivatives into the given differential equation. We will n = 0 solve for two sets of cn to find the two solutions. The differential equation includes non-zero terms for the first and second derivative of y. These derivatives always have the same form, so we refer to equation (1) of section 6.1. Y = ) C,nxn - 1 n = 1 y" = E on(n – 1)x" - 2 n = 2 Substitute the power series into the given differential equation. y" - 4xy' + y = - 4 - n = 1 n = 0
Transcribed Image Text:1- Explain the the difference between DE with Ordinary points and DE with singular points Find two power series solutions of the given differential equation about the ordinary point x = 0o. y" - 4xy' + y = 0 We are asked to find two power series solutions to the following homogenous linear second-order differential equation. y" - 4xy' + y = 0 By Theorem 6.2.1, we know two such solutions exist about the ordinary point x = 0. In fact, the differential equation has no singular points as each of the coefficient functions are (very simple) polynomials. Therefore, they are trivially represented as power series at any point and are therefore analytic. This means the power series solution will converge for |x| < oo. Let y = 5C". We substitute this series and its derivatives into the given differential equation. We will n = 0 solve for two sets of cn to find the two solutions. The differential equation includes non-zero terms for the first and second derivative of y. These derivatives always have the same form, so we refer to equation (1) of section 6.1. Y = ) C,nxn - 1 n = 1 y" = E on(n – 1)x" - 2 n = 2 Substitute the power series into the given differential equation. y" - 4xy' + y = - 4 - n = 1 n = 0
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 5 steps with 5 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Laplace Transformation
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,
SEE MORE TEXTBOOKS