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
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Chapter1: Functions And Models
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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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F52e723cb-7ef7-4ac5-81ec-4d30aaafb8c8%2F29f86025-0c0e-4682-a5ed-4e49fb815c61%2Fp17y_processed.png&w=3840&q=75)
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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