Consider applying the method of separation of variables with u(x, t) = X(a)T' (t) to the partial differential equation 8²u Jau du +U= 82:² 8t² Ot Select the option that gives the resulting pair of ordinary differential equations (where is a non-zero separation constant). Select one: ⒸX" (2) - X¹ (2) = AX (2), F(t) + 1 = T (t) X" (x) - X'(x)=14, Ï(t) + 1 = μ X" (a)+1, (t) - T (t) = μ X" (x) + X(x) = μX(x), F(t)-(t) = µT(t)
Consider applying the method of separation of variables with u(x, t) = X(a)T' (t) to the partial differential equation 8²u Jau du +U= 82:² 8t² Ot Select the option that gives the resulting pair of ordinary differential equations (where is a non-zero separation constant). Select one: ⒸX" (2) - X¹ (2) = AX (2), F(t) + 1 = T (t) X" (x) - X'(x)=14, Ï(t) + 1 = μ X" (a)+1, (t) - T (t) = μ X" (x) + X(x) = μX(x), F(t)-(t) = µT(t)
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:Consider applying the method of separation of variables with u(x, t) = X(x) T(t) to the partial
differential equation
8²u
8²u
дче
+2=
6212
8t² Ot
fl
Select the option that gives the resulting pair of ordinary differential equations (where is a non-zero
separation constant).
Select one:
ⒸX" (x) - X¹ (2) = µμX(x), Ï(t)+1= µT(t)
OX" (x) - X'(x) = μ Ï(t) + 1 = μ
X" () +1=,
(t)-Ï(t) = μ
X" (x) + X(x) = μX(x), Ï(t)-Ï(t) = µT(t)
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