(b) ruz – 2yuy + u = eª , for x> 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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Please do 1(b) & 3 (b)
![(b) rug – 2yuy + u = eª , for x> 0
(a) ru, + 2yuy = 0, for x > 0, y > 0
(d) yuz – 4xuy = 2xy, for all (x, y).
(c) ruz – ryuy – u = 0, for all (x, y)
2. Find the particular solution of the PDES in Problem 1 satisfying the following resne
side conditions.
(b) u(1, y) = y?
(d) u(x, 0) = xª.
(a), u(x, 1/2) = x (x > 0)
(c) u(x, x) = x²e²
3. Find the parametric form of the solutions of the PDES in Problem 1, which satisfy the
following respective side conditions. In each case, note the futility of finding an explici
solution u(x, y).
(a) u(s, e-) = sin(8), s > 0
(e) u(s², s) = s³
(b) u(s, sinh(s)) = 0, s > 0
(d) u(s, s') = 1.
%3D
%3D](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc9e98fa3-11a8-4dae-ae94-890fe707821d%2F07753a13-e60b-41bc-a9d9-d6b1ee384a74%2Fau46ue6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(b) rug – 2yuy + u = eª , for x> 0
(a) ru, + 2yuy = 0, for x > 0, y > 0
(d) yuz – 4xuy = 2xy, for all (x, y).
(c) ruz – ryuy – u = 0, for all (x, y)
2. Find the particular solution of the PDES in Problem 1 satisfying the following resne
side conditions.
(b) u(1, y) = y?
(d) u(x, 0) = xª.
(a), u(x, 1/2) = x (x > 0)
(c) u(x, x) = x²e²
3. Find the parametric form of the solutions of the PDES in Problem 1, which satisfy the
following respective side conditions. In each case, note the futility of finding an explici
solution u(x, y).
(a) u(s, e-) = sin(8), s > 0
(e) u(s², s) = s³
(b) u(s, sinh(s)) = 0, s > 0
(d) u(s, s') = 1.
%3D
%3D
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