26. What are the roots of the auxiliary equation corresponding to the DE y"-3y+3y-y=0? (A) m = -1 (multiplicity 3) (C) m = -1, 1 (multiplicity 2) (B) m = 1 (multiplicity 3) (D) m = 1, 1 (multiplicity 2) 27. Write the general solution for the homogeneous DE y" + 3y + 3y + y = 0. (A) y = e(a₁ + ₂x + C₂2²) (B) y = e(a₁ + ₂x + ₂x²) 28. Find a linear differential operator (of lowest order) that annihilates the given function: f(x)=r³(1-5x) (A) D³ (B) D¹ (A) D² (D-2)² (B) D(D-2)2 29. Find a linear differential operator (of lowest order) that annihilates the given function: f(x)=x²+3re² (A) D'(D²+1)³(D² +9)² (B) D'(D²+1)(D² +9)² 31. Evaluate W(1-1, 1, 1²) 30. Find a linear differential operator (of lowest order) that annihilates the given function: f(x)= x³ + z³ cos z - 3r sin 3r (A) 2 (B) 2r (C) y = e(c₁+0₂x) + c3e-² (D) y = e(+₂)+c₂e² (A) m = 0,-1,1 (B) m = 0,1 (multiplicity 2) (C) D³ (D) D² (C) D³(D+ 2)² (D) D³(D - 2)² (A) (B) = ce+c₂e-² ce + Gez (C) D'(D² - 1)³(D² +9)² (D) D'(D²+1)³(D² - 9)² 32. The roots of the auxiliary equation corresponding to the associated homogeneous equation of the DE "+2y" -= 10 are (C) -2r (D) -2 33. The complementary solution, ye, of the equation y" + 2y" - y = 10 is (A) yec₁e + c₂e-² +0₂ (C) ce +0₂0² + 0₂ (B) y =ce* +oe to (D) ye ce + ©₂0€¯² +03 (C) m = 0,-1 (multiplicity 2) (D) m = 1,-1 (multiplicity 2) For the next four questions, consider the differential equation: y" - y = r²e²-5 34. Which of the following represents the complementary function for the given DE? (C) y = ₂² +₂² (D) = ₁ + ₂rez
26. What are the roots of the auxiliary equation corresponding to the DE y"-3y+3y-y=0? (A) m = -1 (multiplicity 3) (C) m = -1, 1 (multiplicity 2) (B) m = 1 (multiplicity 3) (D) m = 1, 1 (multiplicity 2) 27. Write the general solution for the homogeneous DE y" + 3y + 3y + y = 0. (A) y = e(a₁ + ₂x + C₂2²) (B) y = e(a₁ + ₂x + ₂x²) 28. Find a linear differential operator (of lowest order) that annihilates the given function: f(x)=r³(1-5x) (A) D³ (B) D¹ (A) D² (D-2)² (B) D(D-2)2 29. Find a linear differential operator (of lowest order) that annihilates the given function: f(x)=x²+3re² (A) D'(D²+1)³(D² +9)² (B) D'(D²+1)(D² +9)² 31. Evaluate W(1-1, 1, 1²) 30. Find a linear differential operator (of lowest order) that annihilates the given function: f(x)= x³ + z³ cos z - 3r sin 3r (A) 2 (B) 2r (C) y = e(c₁+0₂x) + c3e-² (D) y = e(+₂)+c₂e² (A) m = 0,-1,1 (B) m = 0,1 (multiplicity 2) (C) D³ (D) D² (C) D³(D+ 2)² (D) D³(D - 2)² (A) (B) = ce+c₂e-² ce + Gez (C) D'(D² - 1)³(D² +9)² (D) D'(D²+1)³(D² - 9)² 32. The roots of the auxiliary equation corresponding to the associated homogeneous equation of the DE "+2y" -= 10 are (C) -2r (D) -2 33. The complementary solution, ye, of the equation y" + 2y" - y = 10 is (A) yec₁e + c₂e-² +0₂ (C) ce +0₂0² + 0₂ (B) y =ce* +oe to (D) ye ce + ©₂0€¯² +03 (C) m = 0,-1 (multiplicity 2) (D) m = 1,-1 (multiplicity 2) For the next four questions, consider the differential equation: y" - y = r²e²-5 34. Which of the following represents the complementary function for the given DE? (C) y = ₂² +₂² (D) = ₁ + ₂rez
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
CHOOSE THE LETTER OF THE CORRECT ANSWER
Transcribed Image Text:26. What are the roots of the auxiliary equation corresponding to the DE y"-3y+3y-y=0?
(A) m = -1 (multiplicity 3)
(B) m = 1 (multiplicity 3)
27. Write the general solution for the homogeneous DE y" + 3y+3y+y=0.
(C) y = e(c₁ + ₂x) + c3€¯²
(D) y = e(₁+0₂x) + c₂e²
(A) y=e*(₁ + ₂x + 3x²)
(B) y=e¹(₁+₂x+c₂x²)
28. Find a linear differential operator (of lowest order) that annihilates the given function:
f(x)= x³(1-5x)
(A) D
(B) Dª
(A) D²(D-2)²
(B) D(D-2)²
29. Find a linear differential operator (of lowest order) that annihilates the given function:
f(x)=x² + 3re²
(A) D'(D²+1)³(D² +9)²
(B) D'(D²+1)(D² +9)²
31. Evaluate W(1-1, 1, 1²)
30. Find a linear differential operator (of lowest order) that annihilates the given function:
f(x)= x³ + z³ cos z- 3r sin 3r
(A) 2
(C) m = -1, 1 (multiplicity 2)
(D) m = 1, -1 (multiplicity 2)
(B) 2r
(A) m = 0,-1,1
(B) m = 0,1 (multiplicity 2)
(C) D³
(D) D²
(C) D³(D+2)²
(D) D³(D - 2)²
(A)
(B) = ce + Gez
= ce+c₂e-²
(C) D'(D² - 1)³(D² +9)²
(D) D'(D²+1)³(D² - 9)²
32. The roots of the auxiliary equation corresponding to the associated homogeneous equation of the
DE y + 2y" - y = 10 are
(C) -2r
(D) -2
33. The complementary solution, ye, of the equation y" + 2y" - y = 10 is
(A) = ce +0₂0² +0₂
(C) = ce +0₂0² + 0₂
(B) ye ce +0₂x² +03
(D) ycie +0₂0€¯² +03
(C) m = 0,-1 (multiplicity 2)
(D) m = 1,-1 (multiplicity 2)
For the next four questions, consider the differential equation: y" - y = r²e-5
34. Which of the following represents the complementary function for the given DE?
(C) y = ₁² +₂e²
(D) = C₁₂z+c₂rez
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 1 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
