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Find the generalized solution to the following heat equation ди a(x)- dt ди t(x)- ar) - B(x)u, 0 0, dx ди aj u(0, t) + B1 dx ди azu(1, t) + B2 -(0, г) %3D 0, t > 0, (1, t) = 0, t > 0, %3D dx u(х, 0) %3D f(x), 0 < x < I, where a(x) > 0, т(х) > 0, and B(x) > 0 for 0 < х <1.

Find the generalized solution to the following heat equation ди a(x)- dt ди t(x)- ar) - B(x)u, 0 0, dx ди aj u(0, t) + B1 dx ди azu(1, t) + B2 -(0, г) %3D 0, t > 0, (1, t) = 0, t > 0, %3D dx u(х, 0) %3D f(x), 0 < x < I, where a(x) > 0, т(х) > 0, and B(x) > 0 for 0 < х <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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Find the generalized solution to the following heat equation ди a(x)- ди T(x)- dx 0 < x < I, t > 0, dt ди ɑ¡ u(0, t) + ß1 (0, t) = 0, dx t > 0, %3D ди azu(l, t) + B2- (1, t) = 0, dx t > 0, u(x, 0) = f(x), 0<x< 1, where a(x) > 0, t(x) > 0, and ß(x) > 0 for 0 < x < 1.
Transcribed Image Text:Find the generalized solution to the following heat equation ди a(x)- ди T(x)- dx 0 < x < I, t > 0, dt ди ɑ¡ u(0, t) + ß1 (0, t) = 0, dx t > 0, %3D ди azu(l, t) + B2- (1, t) = 0, dx t > 0, u(x, 0) = f(x), 0<x< 1, where a(x) > 0, t(x) > 0, and ß(x) > 0 for 0 < x < 1.
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