Homework Help is Here – Start Your Trial Now!
Math
Calculus
Solve the following ordinary differential equations using the power series method: (x+1) y' - (x+2) = 0 Example solutions is in the picture.

Solve the following ordinary differential equations using the power series method: (x+1) y' - (x+2) = 0 Example solutions is in the picture.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
See similar textbooks
icon
Related questions
Question
Solve the following ordinary differential equations using the power series method: (x+1) y' - (x+2) = 0 Example solutions is in the picture.
The power series method is a method of solving differential equations SOLUTION OF DIFFERENTIAL EQUATIONS USING THE POWER SERIES METHOD which yields solutions in the form of power series. It is a very effective standard procedure in connection with linear differential equation whose coefficients are variable. The basic idea of the power series method for solving differential equa- tion is very simple and natural. Given differential equation, first represent given functions in the equation by power series in powers of x. Then, assume a solution in the form of a power series, say y = Co + C,x + C,x2 + C3x + and insert this series and the series obtained by termwise differentiation, y' C, + 2C2X + 3C,x? + y" = 2C, + 3(2)C,x + 4(3)C,x2 + ... %3D %3D into the equation. Collecting like powers of x, write the resulting equation in the form Ko + K,x + K2x² + = 0 ... ... are expressions containing the unknown where the constants Ko, K, K2 coefficients Co, C, etc. So that Ko = 0, K, = 0, K2 = 0, .. %3D %3D From these equations, determine the coefficients Co, C, C,, Then substitute these coefficients into the assumed power series solution and simplify. successively. PROBLEM: Solve the differential equation y'-y 0 using the power series method. %3D Salution:
Transcribed Image Text:The power series method is a method of solving differential equations SOLUTION OF DIFFERENTIAL EQUATIONS USING THE POWER SERIES METHOD which yields solutions in the form of power series. It is a very effective standard procedure in connection with linear differential equation whose coefficients are variable. The basic idea of the power series method for solving differential equa- tion is very simple and natural. Given differential equation, first represent given functions in the equation by power series in powers of x. Then, assume a solution in the form of a power series, say y = Co + C,x + C,x2 + C3x + and insert this series and the series obtained by termwise differentiation, y' C, + 2C2X + 3C,x? + y" = 2C, + 3(2)C,x + 4(3)C,x2 + ... %3D %3D into the equation. Collecting like powers of x, write the resulting equation in the form Ko + K,x + K2x² + = 0 ... ... are expressions containing the unknown where the constants Ko, K, K2 coefficients Co, C, etc. So that Ko = 0, K, = 0, K2 = 0, .. %3D %3D From these equations, determine the coefficients Co, C, C,, Then substitute these coefficients into the assumed power series solution and simplify. successively. PROBLEM: Solve the differential equation y'-y 0 using the power series method. %3D Salution:
Encc, 53 y'-y = 0 (C, + 2Cx + 3C,x + ..)- (C, + C,x + Cx? + ...) = 0 Collecting like powers of x: (C) - Co) + (2C, - C,)x + (3C, - C)x? + ... = 0 Then, C, - C, 0 C, = Co : 20- C, = 0 %3D 3C,- C, 0 C, = 3 2. C, = 3. C; = Therefore, y = C, + C, + C,x? + C,x' + .. y = C, + Cyx + C,x? + C+ x2 y = Co(l + x + 2! + ...) 3! y = Coe PROBLEM: I Solve the differential equation y" + y = 0 using the power series method. Tolu
Transcribed Image Text:Encc, 53 y'-y = 0 (C, + 2Cx + 3C,x + ..)- (C, + C,x + Cx? + ...) = 0 Collecting like powers of x: (C) - Co) + (2C, - C,)x + (3C, - C)x? + ... = 0 Then, C, - C, 0 C, = Co : 20- C, = 0 %3D 3C,- C, 0 C, = 3 2. C, = 3. C; = Therefore, y = C, + C, + C,x? + C,x' + .. y = C, + Cyx + C,x? + C+ x2 y = Co(l + x + 2! + ...) 3! y = Coe PROBLEM: I Solve the differential equation y" + y = 0 using the power series method. Tolu
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS