Obtain the eigenvalues and eigenfunctions of the following homogeneous boundary value prot + a*xy = 0, y(0) is finite, y(L) = 0 dx dx. Use the results of part (i) to find the solution of the following non-homogeneous problem dy +2²xy x, y(0) is finite, y(L) = 0 %3D dx

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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5
(b)
i. Obtain the eigenvalues and eigenfunctions of the following homogeneous boundary value problem:
+ a*xy = 0, x0) is finite, y(L) = 0
%3D
ii. Use the results of part (i) to find the solution of the following non-homogeneous problem
+2xy x, y(0) is finite, y(L) = 0
in the form
1 Jo(Anx)
22- 22 AnL J1(„L)'
y =
n=1
where Jo(A,L) = 0 (n = 1,2, ...), if Jo(AL) # 0. Hint: Use eigenfunction expansion.
Transcribed Image Text:(b) i. Obtain the eigenvalues and eigenfunctions of the following homogeneous boundary value problem: + a*xy = 0, x0) is finite, y(L) = 0 %3D ii. Use the results of part (i) to find the solution of the following non-homogeneous problem +2xy x, y(0) is finite, y(L) = 0 in the form 1 Jo(Anx) 22- 22 AnL J1(„L)' y = n=1 where Jo(A,L) = 0 (n = 1,2, ...), if Jo(AL) # 0. Hint: Use eigenfunction expansion.
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