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Let us consider the following problem for the heat equation ôu ô’u = 0 in (0,1) × (0,+00), ốt u(x,0) = u,(x),Vx e (0,1), ди (0,t) = %3D (1) ди -(1,t) = 0, Vt > 0. Use the method of separation of variables to compute the solution of problem (1) if 1) u, (x) = 1, Vx e(0,1).

Let us consider the following problem for the heat equation ôu ô’u = 0 in (0,1) × (0,+00), ốt u(x,0) = u,(x),Vx e (0,1), ди (0,t) = %3D (1) ди -(1,t) = 0, Vt > 0. Use the method of separation of variables to compute the solution of problem (1) if 1) u, (x) = 1, Vx e(0,1).

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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Let us consider the following problem for the heat equation ди = 0 in (0,1) × (0,+∞), ốt u(x,0) = u,(x),Vx E (0,1), ди (0,t): (1) ди -(1,t) = 0, Vt > 0. Use the method of separation of variables to compute the solution of problem (1) if 1) и,(х) %3D1, Vx € (0,1). 2) u,(x)= cos77x, Vx e (0,1). 3) u,(x) = 3+2 cos7x,Vx € (0,1). 4) u,(x) = sin x, Vx e (0,1).
Transcribed Image Text:Let us consider the following problem for the heat equation ди = 0 in (0,1) × (0,+∞), ốt u(x,0) = u,(x),Vx E (0,1), ди (0,t): (1) ди -(1,t) = 0, Vt > 0. Use the method of separation of variables to compute the solution of problem (1) if 1) и,(х) %3D1, Vx € (0,1). 2) u,(x)= cos77x, Vx e (0,1). 3) u,(x) = 3+2 cos7x,Vx € (0,1). 4) u,(x) = sin x, Vx e (0,1).
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