Solve the one-dimensional Laplace equation for the equilibrium temperature distribution in a finite rod of length \( L \) for the following boundary conditions:1. \( u(0) = -2 \) and \( u(L) = 2 \)2. \( u(0) = A \) and \( u(L) + u_x(L) = 0 \)Please also draw a sketch for each boundary condition.

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Answered: Solve the one-dimensional Laplace…

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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Solve the one-dimensional Laplace equation for the equilibrium temperature distribution in a finite rod of length L for the following boundary conditions: 1. u(0) = −2 and u(L) = 2 2. u(0) = A and u(L) + ux (L) = 0 Please also draw a sketch for each boundary condition.