Question 1Consider the homogeneousдиJ²uƏt Ər²¹heat problem with boundary conditionди(0, t) = 0 = u(1, t) ;u (x,0) = f(x)ərwhere t > 0, 0 ≤ x ≤ 1 and f is a piecewise smooth function on [0,1].(a) Find the eigenvalues An and the eigenfunctions X₁ (x) for this problem.Write the formal solution of the problem (a), and express the constantcoefficients as integrals involving f(x).=(b) Find a series solution in the case that f(x) = uo, uo a constant. Find anapproximate solution good for large times.

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Answered: Question 1 Consider the homogeneous du…

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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