Suppose we have a bar of length L = 2 and, instead of keeping the ends at a constant 0°C, the bar has insulated ends. We can model this situation with the following boundary conditions: Uz(0, t) = 0 , uz(2, t) = 0 (a) Show that the boundary condition uz (0, t) implies X'(0) = 0 or T(t) = 0. (b) Fill in the blanks: The boundary condition u (2, t) = 0 implies = 0 or = 0. (c) This leads us to the boundary value problem with param ter: X" + XX = 0, X'(0) = ), X'(2) = 0 Find the nontrivial solutions to the BVP for the case w rere A > 0. Assume A = µ?. Recall that sin 0 = 0 for 0 = nr.

Suppose we have a bar of length L = 2 and, instead of keeping the ends at a constant 0°C, the bar has insulated ends. We can model this situation with the following boundary conditions: Uz(0, t) = 0 , uz(2, t) = 0 (a) Show that the boundary condition uz (0, t) implies X'(0) = 0 or T(t) = 0. (b) Fill in the blanks: The boundary condition u (2, t) = 0 implies = 0 or = 0. (c) This leads us to the boundary value problem with param ter: X" + XX = 0, X'(0) = ), X'(2) = 0 Find the nontrivial solutions to the BVP for the case w rere A > 0. Assume A = µ?. Recall that sin 0 = 0 for 0 = nr.

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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Question

1.
Suppose we have a bar of length L
= 2 and, instead of keeping the ends at a constant 0°C,
the bar has insulated ends. We can model this situation with the following boundary conditions:
Uz(0, t) = 0
Uz(2, t) = 0
(a) Show that the boundary condition uz(0, t) implies X'(0) = 0 or T(t) = 0.
(b) Fill in the blanks:
The boundary condition u (2, t) = 0 implies
= 0 or
= 0.
(c) This leads us to the boundary value problem with param ter:
X" + XX = 0, X'(0) = ), X'(2) = 0
Find the nontrivial solutions to the BVP for the case w rere A > 0. Assume A = µ?.
Recall that sin 0 = 0 for 0 = NT.

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1. Suppose we have a bar of length L = 2 and, instead of keeping the ends at a constant 0°C, the bar has insulated ends. We can model this situation with the following boundary conditions: Uz (0, t) = 0 , Uz (2, t) = 0 (a) Show that the boundary condition uz(0, t) implies X'(0) = 0 or T(t) = 0. (b) Fill in the blanks: The boundary condition uz(2, t) = 0 implies or 0. (c) This leads us to the boundary value problem with parameter: X" + AX = 0, X'(0) = 0, X'(2) = 0 Find the nontrivial solutions to the BVP for the case where A> 0. Assume = µ?. Recall that sin 0 = 0 for 0 = na.