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2 A. B. C. D. Which of the following can be obtained after substitution of your answer in (1)? X-7 Y X" Y" 11 Y' XY X' X 11 I Y" Y

2 A. B. C. D. Which of the following can be obtained after substitution of your answer in (1)? X-7 Y X" Y" 11 Y' XY X' X 11 I Y" Y

Advanced Engineering Mathematics
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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Answer 2 Only Part 3
Part 3. Use separation of variables to obtain a product solution to the following: ²ud²u + əx² ay² 1. to be the form of the solution u? A. u = X(x)T(t) B. u = xt C. u = X(x)Y(y) D. u = xy 2 A. B. C. D. Using the method of separation of variables, which of the following is assumed Which of the following can be obtained after substitution of your answer in (1)? ***** 3. reduced into A. Two first-order ODES B. Two second-order ODES = 0 X" Y" Y X = Y" Y Y' X=Y C. A first-order ODE and a second-order ODE D. None of these From the correct answer in (2), the given partial differential equation can be Y" Y
Transcribed Image Text:Part 3. Use separation of variables to obtain a product solution to the following: ²ud²u + əx² ay² 1. to be the form of the solution u? A. u = X(x)T(t) B. u = xt C. u = X(x)Y(y) D. u = xy 2 A. B. C. D. Using the method of separation of variables, which of the following is assumed Which of the following can be obtained after substitution of your answer in (1)? ***** 3. reduced into A. Two first-order ODES B. Two second-order ODES = 0 X" Y" Y X = Y" Y Y' X=Y C. A first-order ODE and a second-order ODE D. None of these From the correct answer in (2), the given partial differential equation can be Y" Y
4 A. 1 B.2 C. 3 D. 4 If the correct answer in (2) is equal to -, how many case/s is/are possible? 5 Using the correct answers in (2) and (4), if λ = -a², the solution is A. u = (A₁ cosh ax + A₂ sinh ax) (B₁ cos ay + B₂ sin ay) B. u = (A₁ cos ax + A₂ sin ax) (B₁ cosh ay + B₂ sinh ay) C. u = (A1 cosh ax + A, sinh ax)(B, cosh ay + B2 sinh ay) D. u = (A₁ cos ax + A₂ sin ax) (B₁ cos ay + B₂ sin ay) Using the correct answers in (2) and (4), if λ = 0, the solution is 6 A. u A3x + A4Y B. u (A3 + A4x) (B3 + B4Y) = C. u= A3 + A4x D. u A3 + A4y
Transcribed Image Text:4 A. 1 B.2 C. 3 D. 4 If the correct answer in (2) is equal to -, how many case/s is/are possible? 5 Using the correct answers in (2) and (4), if λ = -a², the solution is A. u = (A₁ cosh ax + A₂ sinh ax) (B₁ cos ay + B₂ sin ay) B. u = (A₁ cos ax + A₂ sin ax) (B₁ cosh ay + B₂ sinh ay) C. u = (A1 cosh ax + A, sinh ax)(B, cosh ay + B2 sinh ay) D. u = (A₁ cos ax + A₂ sin ax) (B₁ cos ay + B₂ sin ay) Using the correct answers in (2) and (4), if λ = 0, the solution is 6 A. u A3x + A4Y B. u (A3 + A4x) (B3 + B4Y) = C. u= A3 + A4x D. u A3 + A4y
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