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a²u If consider the problem 3- -du 00 ax² with boundary conditions u(0, t)=0 and u(2, t) = 0 and initial condition u(x,0) = 5. If x(x) = A cos(xx) + B sin(ax) and T(t) = Ce-3at are the solutions of separated equations when separation of variable constant is λ=a² > 0. Then the general solution is: O u(x,t) = Σ n = 1 u(x,t)= Σ n = 1 u(x,t) = Σ n=1 5(1 − (− 1)") nπ u(x,t) = Σ n=1 10(1-(-1)") ηπ 2(1-(-1)") 5nπ e u(x,t)= Σ 5(1 + (−1)″) n=1 2nπ -2n²x², 9 e e 10(1-(-1)") nπ 4n² ²₁² 3 e "sin(x) -3n²π²₁ 2 e ηπ =sin(x) -3n²π²₁ 4 cos(x) "sin (1 x) -3n²² 4 * sin(x)

a²u If consider the problem 3- -du 00 ax² with boundary conditions u(0, t)=0 and u(2, t) = 0 and initial condition u(x,0) = 5. If x(x) = A cos(xx) + B sin(ax) and T(t) = Ce-3at are the solutions of separated equations when separation of variable constant is λ=a² > 0. Then the general solution is: O u(x,t) = Σ n = 1 u(x,t)= Σ n = 1 u(x,t) = Σ n=1 5(1 − (− 1)") nπ u(x,t) = Σ n=1 10(1-(-1)") ηπ 2(1-(-1)") 5nπ e u(x,t)= Σ 5(1 + (−1)″) n=1 2nπ -2n²x², 9 e e 10(1-(-1)") nπ 4n² ²₁² 3 e "sin(x) -3n²π²₁ 2 e ηπ =sin(x) -3n²π²₁ 4 cos(x) "sin (1 x) -3n²² 4 * sin(x)

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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a²u If consider the problem 3- 24.c 0<x<2,t>0 дх2 with boundary conditions u(0, t) = 0 and u(2, 1) = 0 and initial condition u(x,0)=5. If x(x) = A cos(xx) + B sin(ax) and T(t) = Ce-3at are the solutions of separated equations when separation of variable constant is λ=a² >0. Then the general solution is: O u(x,t) = Σ n = 1 u(x,t)= Σ n=1 u(x,t) = Σ n=1 5(1 − (− 1)″) nπ u(x,t) = Σ n=1 e 10(1-(-1)") nπt 2(1-(-1)) 5nπ -2n²x², 9 e 10(1-(-1)") nπ u(x,t)= Σ 5(1 + (−1)″) - e n=1 2nπ ²² 3 e "sin(x) -3n²π²₁ 2 e -3n²π²₁ 4 sin(x) cos(x) -3n²² 4 * sin(x) * sin(x)
Transcribed Image Text:a²u If consider the problem 3- 24.c 0<x<2,t>0 дх2 with boundary conditions u(0, t) = 0 and u(2, 1) = 0 and initial condition u(x,0)=5. If x(x) = A cos(xx) + B sin(ax) and T(t) = Ce-3at are the solutions of separated equations when separation of variable constant is λ=a² >0. Then the general solution is: O u(x,t) = Σ n = 1 u(x,t)= Σ n=1 u(x,t) = Σ n=1 5(1 − (− 1)″) nπ u(x,t) = Σ n=1 e 10(1-(-1)") nπt 2(1-(-1)) 5nπ -2n²x², 9 e 10(1-(-1)") nπ u(x,t)= Σ 5(1 + (−1)″) - e n=1 2nπ ²² 3 e "sin(x) -3n²π²₁ 2 e -3n²π²₁ 4 sin(x) cos(x) -3n²² 4 * sin(x) * sin(x)
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