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QUESTION 2 a²u If consider the problem 2- = 00 Əx² with boundary conditions u(0, t) = 0 and u(1, t)=0 and initial condition u(x,0) = 3. If X(x) = A cos(xx) + B sin(ax) and T(t) = Ce-2a²t are the solutions of separated equations when separation of variable constant is λ = a² > 0. Then the general solution is: 8 u(x, t) = Σ n=1 u(x,t)= Σ n=1 8 u(x, t) = [ n=1 Ou(x, t) = E n=1 8 u(x, t) = Σ n=1 2(1-(-1)") 3nπ -e-2n²π²tsin(nπx) 6(1 + (-1)")-2n²r²tsin(ntx) e nπ 6(1-(-1)") -2n²²¹sin(nπx) nπt 6(1-(-1)")e-3ntsin(nπx) nπ e 3(1+(-1)") 2nπ -e-3n²π²tsin(nπx)

QUESTION 2 a²u If consider the problem 2- = 00 Əx² with boundary conditions u(0, t) = 0 and u(1, t)=0 and initial condition u(x,0) = 3. If X(x) = A cos(xx) + B sin(ax) and T(t) = Ce-2a²t are the solutions of separated equations when separation of variable constant is λ = a² > 0. Then the general solution is: 8 u(x, t) = Σ n=1 u(x,t)= Σ n=1 8 u(x, t) = [ n=1 Ou(x, t) = E n=1 8 u(x, t) = Σ n=1 2(1-(-1)") 3nπ -e-2n²π²tsin(nπx) 6(1 + (-1)")-2n²r²tsin(ntx) e nπ 6(1-(-1)") -2n²²¹sin(nπx) nπt 6(1-(-1)")e-3ntsin(nπx) nπ e 3(1+(-1)") 2nπ -e-3n²π²tsin(nπx)

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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QUESTION 2 a²u ди If consider the problem 2- = Əx² 0<x< 1, t>0 with boundary conditions u(0, t) = 0 and u(1, t)=0 and initial condition u(x,0) = 3. EES If X(x) = A cos(xx) + B sin(ax) and T(t) = Ce-2a²1 are the solutions of separated equations when separation of variable constant is λ = x² > 0. Then the general solution is: 8 u(x, t) = Σ n=1 u(x, t) = [ n=1 8 u(x, t) = [ n=1 u(x, t) = Σ n=1 8 u(x, t) = Σ n=1 2(1-(-1)") 3nπ 15 -e-2n²π²tsin(nπx) 6(1 + (-1)")-2n²r²tsin(ntx) e nπ 6(1-(-1)") nπt nπt -e-2n²π²tsin(nπtx) 6(1-(-1)")e-3ntsin(nπx) 3(1+(-1)") 2nπ -e-3n²π²tsin(nπx)
Transcribed Image Text:QUESTION 2 a²u ди If consider the problem 2- = Əx² 0<x< 1, t>0 with boundary conditions u(0, t) = 0 and u(1, t)=0 and initial condition u(x,0) = 3. EES If X(x) = A cos(xx) + B sin(ax) and T(t) = Ce-2a²1 are the solutions of separated equations when separation of variable constant is λ = x² > 0. Then the general solution is: 8 u(x, t) = Σ n=1 u(x, t) = [ n=1 8 u(x, t) = [ n=1 u(x, t) = Σ n=1 8 u(x, t) = Σ n=1 2(1-(-1)") 3nπ 15 -e-2n²π²tsin(nπx) 6(1 + (-1)")-2n²r²tsin(ntx) e nπ 6(1-(-1)") nπt nπt -e-2n²π²tsin(nπtx) 6(1-(-1)")e-3ntsin(nπx) 3(1+(-1)") 2nπ -e-3n²π²tsin(nπx)
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