Question 4 Given one-dimensional Heat equation as shown below u, = 6u. u(0,t) = u(27,1) = 0, t>0 u(x,0) = 2 sin (2x), 00 is an eigenvalue for X"+kX = 0. nx c) Show that the series solution of the Heat equation is u(x,1)=Eb,e": sin d) Based on your understanding, what will happen to X(x), if k = -10?

Question 4 Given one-dimensional Heat equation as shown below u, = 6u. u(0,t) = u(27,1) = 0, t>0 u(x,0) = 2 sin (2x), 00 is an eigenvalue for X"+kX = 0. nx c) Show that the series solution of the Heat equation is u(x,1)=Eb,e": sin d) Based on your understanding, what will happen to X(x), if k = -10?

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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