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8. A rod has length / = 1 and constant k = 1. Its temperature satisfies the heat equation. Its left end is held at temperature o, its right end at temperature 1. Initially (at t = 0) the temperature is given by 5x 2 for 0 < x < 1/3 (x) = 3 −2x for ¾½/ < x < 1. Find the solution, including the coefficients. (Hint: First find the equilibrium solution U(x), and then solve the heat equation with initial condition u (x, 0) = 0 (x) – U (x)

8. A rod has length / = 1 and constant k = 1. Its temperature satisfies the heat equation. Its left end is held at temperature o, its right end at temperature 1. Initially (at t = 0) the temperature is given by 5x 2 for 0 < x < 1/3 (x) = 3 −2x for ¾½/ < x < 1. Find the solution, including the coefficients. (Hint: First find the equilibrium solution U(x), and then solve the heat equation with initial condition u (x, 0) = 0 (x) – U (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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8. A rod has length / = 1 and constant k = 1. Its temperature satisfies the heat equation. Its left end is held at temperature o, its right end at temperature 1. Initially (at t = 0) the temperature is given by 5x 2 for 0 < x < 1/3 (x) = 3 −2x for ¾½/ < x < 1. Find the solution, including the coefficients. (Hint: First find the equilibrium solution U(x), and then solve the heat equation with initial condition u (x, 0) = 0 (x) – U (x)
Transcribed Image Text:8. A rod has length / = 1 and constant k = 1. Its temperature satisfies the heat equation. Its left end is held at temperature o, its right end at temperature 1. Initially (at t = 0) the temperature is given by 5x 2 for 0 < x < 1/3 (x) = 3 −2x for ¾½/ < x < 1. Find the solution, including the coefficients. (Hint: First find the equilibrium solution U(x), and then solve the heat equation with initial condition u (x, 0) = 0 (x) – U (x)
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