Explanation Procedure used: “ Method of undetermined coefficients: 1) Choose a trial form for the particular solution y p ( x ) from the following table. G ( x ) Trial form for y p ( x ) G ( x ) = e k x P ( x ) y p ( x ) = e k x Q ( x ) G ( x ) = e k x P ( x ) cos m x or G ( x ) = e k x P ( x ) sin m x y p ( x ) = e k x Q ( x ) cos m x + e k x R ( x ) sin m x 2) Substitute y p ′ ′ ( x ) , y p ′ ( x ) and y p ( x ) into a y ″ + b y ′ + c y = G ( x ) and solve for the coefficients of Q ( x ) and if appropriate, R ( x ) . 3) Check to see whether y p ( x ) solves the complementary equation a y ″ + b y ′ + c y = 0 . 4) If none of the individual terms of y p ( x ) are solutions to the complementary equation, use y p as the particular solution. If any term of y p ( x ) is a solution to the complementary equation and y p and x y p are solutions to the complementary equation, use x 2 y p as the particular solution.” Calculation: Given that, the equation is y ″ − 6 y ′ + 5 y = − 6 e 2 x . The general solution is given by y ( x ) = y c ( x ) + y p ( x ) , where y c ( x ) is the general solution and y p ( x ) is a particular solution. Obtain the general solution to y ″ − 6 y ′ + 5 y = − 6 e 2 x as follows. The auxiliary equation to the complementary equation y ″ − 6 y ′ + 5 y = 0 is r 2 − 6 r + 5 = 0 . Factor the auxiliary equation r 2 − 6 r + 5 = 0 as, r 2 − 6 r + 5 = 0 r 2 − r − 5 r + 5 = 0 r ( r − 1 ) − 5 ( r − 1 ) = 0 ( r − 5 ) ( r − 1 ) = 0 r = 5 , 1 Thus, the solutions r 1 = 1 and r 2 = 5 are real and unequal

Study Guide for Stewart's Multivariable Calculus, 8th

8th Edition

ISBN: 9781305271845

Author: Stewart, James

Publisher: Brooks Cole

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Chapter 17.2, Problem 4PT

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To choose: The appropriate option for the statement “Use the method of undetermined coefficients to solve y″−6y′+5y=−6e2x”.

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Study Guide for Stewart's Multivariable Calculus, 8th

Ch. 17.1 - True or False: (x + y)y + (x 10)y + xy + 10 = 0...Ch. 17.1 - Prob. 2PT Ch. 17.1 - Prob. 3PT Ch. 17.1 - The solution to y 10y + 25y = 0, y(0) = 5, y(1) =...Ch. 17.1 - True or False: An initial-value problem specifies...Ch. 17.1 - Prob. 6PT Ch. 17.2 - Prob. 1PT Ch. 17.2 - Prob. 2PT Ch. 17.2 - Prob. 3PT Ch. 17.2 - Prob. 4PT

Ch. 17.2 - Prob. 5PT Ch. 17.3 - A series circuit has a resistor with R = 15 , an...Ch. 17.3 - Prob. 2PT Ch. 17.4 - Prob. 1PT Ch. 17.4 - Prob. 2PT

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To choose: The appropriate option for the statement “Use the method of undetermined coefficients to solve y ″ − 6 y ′ + 5 y = − 6 e 2 x ”.

Solution Summary: The author explains the correct option for the statement "Use the method of undetermined coefficients to solve y

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To choose: The appropriate option for the statement “Use the method of undetermined coefficients to solve y″−6y′+5y=−6e2x”.

Chapter 17 Solutions