Solve the following problems (a) Find the eigenvalues and eigen-functions for the problem ƒ” (x) + λƒ(x) = 0, (b) Discuss the orthogonality relation for the eigen-functions in part (a) f(0) = 0, f'(2) = 0
Solve the following problems (a) Find the eigenvalues and eigen-functions for the problem ƒ” (x) + λƒ(x) = 0, (b) Discuss the orthogonality relation for the eigen-functions in part (a) f(0) = 0, f'(2) = 0
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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![**Solve the following problems**
(a) **Find the eigenvalues and eigen-functions for the problem**
\[ f''(x) + \lambda f(x) = 0, \quad f(0) = 0, \quad f'(2) = 0 \]
(b) **Discuss the orthogonality relation for the eigen-functions in part (a)**
(c) **Find the general solution of the problem**
\[ u_t(x, t) = 9u_{xx}(x, t), \quad 0 \leq x \leq 2, \quad t > 0 \]
\[ u(0, t) = 0, \quad u_x(2, t) = 0 \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc8134ebd-8b7f-4dc9-a03c-a1e30fa7cac5%2Fcd4666a0-f18a-4e4d-aa45-c8412ffbe034%2F0wc71x_processed.png&w=3840&q=75)
Transcribed Image Text:**Solve the following problems**
(a) **Find the eigenvalues and eigen-functions for the problem**
\[ f''(x) + \lambda f(x) = 0, \quad f(0) = 0, \quad f'(2) = 0 \]
(b) **Discuss the orthogonality relation for the eigen-functions in part (a)**
(c) **Find the general solution of the problem**
\[ u_t(x, t) = 9u_{xx}(x, t), \quad 0 \leq x \leq 2, \quad t > 0 \]
\[ u(0, t) = 0, \quad u_x(2, t) = 0 \]
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