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Consider the partial differential equation 8²u Du 8x² It' with boundary conditions u(0, t) = 0 and u(2x, t) = 0 for t≥ 0. Applying the method of separation of variables with u(x, t) = X(x) T(t) gives the ordinary differential equations X" = μ.Χ, Υ = μT, = where is a non-zero separation constant. You may assume that μ-², where k is a positive constant. Select the options that gives a family of non-trivial solutions for u(x, t) that satisfy the partial differential equation and boundary conditions. Select one: un (x, t) An sin(kx) et, where kand n=1,2,... Un (x, t) = An cos(kx) e-t, where k = and n = 1, 2,... un (x, t) = An sin(kx) e-t, where un (x, t) An cos(kx) e, where = and n =1,2,... and n=1,2,...

Consider the partial differential equation 8²u Du 8x² It' with boundary conditions u(0, t) = 0 and u(2x, t) = 0 for t≥ 0. Applying the method of separation of variables with u(x, t) = X(x) T(t) gives the ordinary differential equations X" = μ.Χ, Υ = μT, = where is a non-zero separation constant. You may assume that μ-², where k is a positive constant. Select the options that gives a family of non-trivial solutions for u(x, t) that satisfy the partial differential equation and boundary conditions. Select one: un (x, t) An sin(kx) et, where kand n=1,2,... Un (x, t) = An cos(kx) e-t, where k = and n = 1, 2,... un (x, t) = An sin(kx) e-t, where un (x, t) An cos(kx) e, where = and n =1,2,... and n=1,2,...

Advanced Engineering Mathematics
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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Consider the partial differential equation 8²μ Ou 8x² Ət' with boundary conditions (0, t) = 0 and u(2π, t) = 0 for t > 0. Applying the method of separation of variables with u(x, t) = X(x) T(t) gives the ordinary differential equations X" = µX, Ï = µT, where is a non-zero separation constant. You may assume that μ = -², where k is a positive fub constant. Select the options that gives a family of non-trivial solutions for u(x, t) that satisfy the partial differential equation and boundary conditions. Select one: =1,2,... un (x, t) = An sin(kx) et, where k = un (x, t) = An cos(kx) e-t, where k = un (x, t) = An sin(kx) e-k²t, where k = un (x, t) = An cos(kx) e-*t, where k = and n = and n =1,2,... and n=1,2,... -and n =1 1,2,...
Transcribed Image Text:Consider the partial differential equation 8²μ Ou 8x² Ət' with boundary conditions (0, t) = 0 and u(2π, t) = 0 for t > 0. Applying the method of separation of variables with u(x, t) = X(x) T(t) gives the ordinary differential equations X" = µX, Ï = µT, where is a non-zero separation constant. You may assume that μ = -², where k is a positive fub constant. Select the options that gives a family of non-trivial solutions for u(x, t) that satisfy the partial differential equation and boundary conditions. Select one: =1,2,... un (x, t) = An sin(kx) et, where k = un (x, t) = An cos(kx) e-t, where k = un (x, t) = An sin(kx) e-k²t, where k = un (x, t) = An cos(kx) e-*t, where k = and n = and n =1,2,... and n=1,2,... -and n =1 1,2,...
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