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e part 1 2

e part 1 2

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 12T
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pde part 1 2
nsider the following boundary value problem (E) : u ôu + = 0, 0 < x < 1, t > 0. (1) u(0, t) = 0, u(1, t) = 0, t > 0.… (2) %3D u(x,t) → 0, ast → +.. (3), U(x, 0) = x + 1, 0 <x <1•…(4), (1) By using the method of separation of variables, the family of solutions Un(r, t) for equations (1), (2) and (3) is: a. un(r, t) = An cos(nn2)e""t + B, cos(nAx)e¬n#t b. Un(r, t) = Bn sin(nar)e"t c. Un(r,t) = Bn sin(nar)e¬"t d. None of the above +00 Let now u(r, t) =) Un(x, t) be a solution of (E). n=1 (2) By using the initial condition (4), we obtain that 4(-1)" a. Bn Vn > 1. %3D (n7)² 4(-1)7+1 (n7)2 (nx)² b. Bn Vn 2 1. (n7)2 с. В, — 0. d. None of the above
Transcribed Image Text:nsider the following boundary value problem (E) : u ôu + = 0, 0 < x < 1, t > 0. (1) u(0, t) = 0, u(1, t) = 0, t > 0.… (2) %3D u(x,t) → 0, ast → +.. (3), U(x, 0) = x + 1, 0 <x <1•…(4), (1) By using the method of separation of variables, the family of solutions Un(r, t) for equations (1), (2) and (3) is: a. un(r, t) = An cos(nn2)e""t + B, cos(nAx)e¬n#t b. Un(r, t) = Bn sin(nar)e"t c. Un(r,t) = Bn sin(nar)e¬"t d. None of the above +00 Let now u(r, t) =) Un(x, t) be a solution of (E). n=1 (2) By using the initial condition (4), we obtain that 4(-1)" a. Bn Vn > 1. %3D (n7)² 4(-1)7+1 (n7)2 (nx)² b. Bn Vn 2 1. (n7)2 с. В, — 0. d. None of the above
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