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21. Which of the following statements is(are) true? (A) y = e³ is a solution of the DE y"+y' - 12y = 0. (B) y"-6y' + 5y = -9 ln 2x is a nonhomogeneous linear DE which can be solved by undetermined coefficients. (C) The roots of the auxiliary equation of the DE y" + 5y +6y= 0 are distinct imaginary. (D) The roots of the auxiliary equation of the DE y" + 3y" - 4y = 0 are both real and distinct.

21. Which of the following statements is(are) true? (A) y = e³ is a solution of the DE y"+y' - 12y = 0. (B) y"-6y' + 5y = -9 ln 2x is a nonhomogeneous linear DE which can be solved by undetermined coefficients. (C) The roots of the auxiliary equation of the DE y" + 5y +6y= 0 are distinct imaginary. (D) The roots of the auxiliary equation of the DE y" + 3y" - 4y = 0 are both real and distinct.

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...
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Pls. answer 21 and 22 thank you.

21. Which of the following statements is (are) true? (A) y = e³ is a solution of the DE y"+y' - 12y = 0. (B) y"-6y'+ 5y = -9 In 2x is a nonhomogeneous linear DE which can be solved by undetermined coefficients. (C) The roots of the auxiliary equation of the DE y" + 5y + 6y = 0 are distinct imaginary. (D) The roots of the auxiliary equation of the DE y" + 3y" - 4y = 0 are both real and distinct. 22. Which of the following describes the nature of roots of the auxiliary equation corresponding to the DE y(4) + 3y" + 6y" + 5y + 3y = 0? (A) real - repeated; imaginary - distinct (B) real - distinct; imaginary - distinct (C) real - distinct; real-repeated; imaginary - distinct (D) imaginary - repeated
Transcribed Image Text:21. Which of the following statements is (are) true? (A) y = e³ is a solution of the DE y"+y' - 12y = 0. (B) y"-6y'+ 5y = -9 In 2x is a nonhomogeneous linear DE which can be solved by undetermined coefficients. (C) The roots of the auxiliary equation of the DE y" + 5y + 6y = 0 are distinct imaginary. (D) The roots of the auxiliary equation of the DE y" + 3y" - 4y = 0 are both real and distinct. 22. Which of the following describes the nature of roots of the auxiliary equation corresponding to the DE y(4) + 3y" + 6y" + 5y + 3y = 0? (A) real - repeated; imaginary - distinct (B) real - distinct; imaginary - distinct (C) real - distinct; real-repeated; imaginary - distinct (D) imaginary - repeated
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