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Use the method of separation of variables and the superposition principle to solve the PDE 2,0 +u, 0 < x < 6π, t > 0, ² əx² subject to the boundary conditions ux(0,t) = = 0, ux(6π, t) = 0, t > 0, ди = dt and the initial condition 2 u(x,0) = sin²x+cos(5x), 0 < x < 6π. (Hint: Using a trigonometric identity might help.)

Use the method of separation of variables and the superposition principle to solve the PDE 2,0 +u, 0 < x < 6π, t > 0, ² əx² subject to the boundary conditions ux(0,t) = = 0, ux(6π, t) = 0, t > 0, ди = dt and the initial condition 2 u(x,0) = sin²x+cos(5x), 0 < x < 6π. (Hint: Using a trigonometric identity might help.)

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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Use the method of separation of variables and the superposition principle to solve the PDE 2,0 2² ax² + subject to the boundary conditions ux(0,t) = 0, ux(6π, t) = 0, t > 0, du Ət u, 0 < x < 6л, t > 0, and the initial condition 2 u(x,0) = sin²x+cos(5x), 0 < x < 6π. (Hint: Using a trigonometric identity might help.)
Transcribed Image Text:Use the method of separation of variables and the superposition principle to solve the PDE 2,0 2² ax² + subject to the boundary conditions ux(0,t) = 0, ux(6π, t) = 0, t > 0, du Ət u, 0 < x < 6л, t > 0, and the initial condition 2 u(x,0) = sin²x+cos(5x), 0 < x < 6π. (Hint: Using a trigonometric identity might help.)
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