Preliminaries on Problems associated with Different = 0, 0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Find Values of Lemda ( eigenvalues ) for which the given problem has a non trivial solution. Also determine the corresponding nontrivial solutions ( eigen function )

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Chapter 1. Preliminaries on Problems associated with Different
4. y" + Ay = 0, 0<x<T/2, y (0) = 0, y'(T /2) = 0.
0 < x < T/2, y'(0) =
0, y'(T/2) =0.
%3D
%3D
5. y" = Ay = 0, 0<x < T, y(0) – y'(0) = 0, y(T) = 0.
3Xy%3D0,
%3D
6. y" – 2y' + Ay = 0, 0<x < T, y(0) = 0, y(T) = 0.
y(0)% 3D0,
7. Discuss why the following PDES can not be solved by the
ration of variables.
(a) uz + Uy =1
(b)
Ugr + Uxy + Uyy = 0
%3D
8. Show that the PDE
Urp + (1/r) u
, + (1/r²) uoo = 0
3D0
Transcribed Image Text:Chapter 1. Preliminaries on Problems associated with Different 4. y" + Ay = 0, 0<x<T/2, y (0) = 0, y'(T /2) = 0. 0 < x < T/2, y'(0) = 0, y'(T/2) =0. %3D %3D 5. y" = Ay = 0, 0<x < T, y(0) – y'(0) = 0, y(T) = 0. 3Xy%3D0, %3D 6. y" – 2y' + Ay = 0, 0<x < T, y(0) = 0, y(T) = 0. y(0)% 3D0, 7. Discuss why the following PDES can not be solved by the ration of variables. (a) uz + Uy =1 (b) Ugr + Uxy + Uyy = 0 %3D 8. Show that the PDE Urp + (1/r) u , + (1/r²) uoo = 0 3D0
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