Given the following BVP: r>1, 0<0< v²u = 0, u(r,0) = ug = 0 u(1,0) = f(0) and Ju(r,0)| < M Let u(r,0) = R(r)Ø(8), (Hint: The eigenvalues and eigenfunctions of the SLP y" + ly = 0, y(0) = 0, y'(L) = 0 A, = (E) and y, = sin ( ), n EN (2n-1)m ((2n-1)mx' are 2L 2L The form of R, (r) must be: A. -(2n-1)2 4 В. r-(2n-1)2 С. (2n-1)2 4 D. r(2n-1)2 E. None
Given the following BVP: r>1, 0<0< v²u = 0, u(r,0) = ug = 0 u(1,0) = f(0) and Ju(r,0)| < M Let u(r,0) = R(r)Ø(8), (Hint: The eigenvalues and eigenfunctions of the SLP y" + ly = 0, y(0) = 0, y'(L) = 0 A, = (E) and y, = sin ( ), n EN (2n-1)m ((2n-1)mx' are 2L 2L The form of R, (r) must be: A. -(2n-1)2 4 В. r-(2n-1)2 С. (2n-1)2 4 D. r(2n-1)2 E. None
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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Transcribed Image Text:Given the following BVP:
r>1, 0<0<
- (r.) = 0 ,r>1
vu = 0,
u(r,0) = ug
u(1,0) = f(0)
and Ju(r,0)| < M
Let u(r, 0) = R(r)Ø(8),
(Hint: The eigenvalues and eigenfunctions of the SLP
y" + ly = 0,
y(0) = 0,
y'(L) = 0
A, = (eD) and y, = sin (nD, neN
(2n-1)m
((2n-1)mxY
are
%3D
2L
2L
The form of R, (r) must be:
А.
-(2n-1)2
4
В.
r-(2n-1)2
(2n-1)2
4
D.
r(2n-1)²
E.
None
C.
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