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Solve the problem: u – kuxx = e-t sin x , 0< x < n, t> 0; satisfying the conditions u(0,t) = 2n, u(t, t) = 4n, t > 0,u(x,0) = 2x + 2n, 0 < x < TI

Solve the problem: u – kuxx = e-t sin x , 0< x < n, t> 0; satisfying the conditions u(0,t) = 2n, u(t, t) = 4n, t > 0,u(x,0) = 2x + 2n, 0 < x < TI

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. Solve the problem: \( u_t - ku_{xx} = e^{-t} \sin x \), for \( 0 < x < \pi \), \( t > 0 \); satisfying the conditions \( u(0, t) = 2\pi \), \( u(\pi, t) = 4\pi \), \( t > 0 \), \( u(x, 0) = 2x + 2\pi \), \( 0 < x < \pi \).
Transcribed Image Text:8. Solve the problem: \( u_t - ku_{xx} = e^{-t} \sin x \), for \( 0 < x < \pi \), \( t > 0 \); satisfying the conditions \( u(0, t) = 2\pi \), \( u(\pi, t) = 4\pi \), \( t > 0 \), \( u(x, 0) = 2x + 2\pi \), \( 0 < x < \pi \).
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