Given the differential equation: y (4)_2y"+y=xe* Choose All Correct Answers Below A There is duplication with the complementary function. The complimentary function is given by: y = A e + Bx e* (B) D (E) F There is no duplication with the complementary function. A patrticular solution is given by: y = - P 24 The complementary function is given by: y = P A patrticular solution is given by: 1 24 1 --x 8 y = (A + Bx) e¯* + (C+Dx) e* x³ et 1
Given the differential equation: y (4)_2y"+y=xe* Choose All Correct Answers Below A There is duplication with the complementary function. The complimentary function is given by: y = A e + Bx e* (B) D (E) F There is no duplication with the complementary function. A patrticular solution is given by: y = - P 24 The complementary function is given by: y = P A patrticular solution is given by: 1 24 1 --x 8 y = (A + Bx) e¯* + (C+Dx) e* x³ et 1
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![Given the differential equation:
\[ y^{(4)} - 2y'' + y = x \, e^x \]
**Choose All Correct Answers Below**
A) There is duplication with the complementary function.
B) The complementary function is given by:
\[ y_c = A \, e^{-x} + B \, e^x \]
C) There is no duplication with the complementary function.
D) A particular solution is given by:
\[ y_p = \frac{1}{24} x^2 e^x - \frac{1}{8} x \, e^x \]
E) The complementary function is given by:
\[ y_c = (A + Bx) \, e^{-x} + (C + Dx) \, e^x \]
F) A particular solution is given by:
\[ y_p = \frac{1}{24} x^3 e^x - \frac{1}{8} x^2 e^x \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3490bf33-1a76-4540-9d98-23dec986ea0c%2Fcf42b63c-a2af-4dc7-9872-57eca17aaf04%2F9jq1m3a_processed.png&w=3840&q=75)
Transcribed Image Text:Given the differential equation:
\[ y^{(4)} - 2y'' + y = x \, e^x \]
**Choose All Correct Answers Below**
A) There is duplication with the complementary function.
B) The complementary function is given by:
\[ y_c = A \, e^{-x} + B \, e^x \]
C) There is no duplication with the complementary function.
D) A particular solution is given by:
\[ y_p = \frac{1}{24} x^2 e^x - \frac{1}{8} x \, e^x \]
E) The complementary function is given by:
\[ y_c = (A + Bx) \, e^{-x} + (C + Dx) \, e^x \]
F) A particular solution is given by:
\[ y_p = \frac{1}{24} x^3 e^x - \frac{1}{8} x^2 e^x \]
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