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-cu" = Let the constant c > 0. The boundary value problem 2x, u(0) = u(1) = 0 models the displacement u (x) of a uniform elastic bar with forcing 2x. (a) Directly integrate to find the resulting displacement of the bar. (b) Find the Green's function for the boundary value problem. (c) Use superposition to check your solution from part (a).

-cu" = Let the constant c > 0. The boundary value problem 2x, u(0) = u(1) = 0 models the displacement u (x) of a uniform elastic bar with forcing 2x. (a) Directly integrate to find the resulting displacement of the bar. (b) Find the Green's function for the boundary value problem. (c) Use superposition to check your solution from part (a).

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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6. Let the constant c> 0. The boundary value problem -cu" = 2x, u(0) = u(1) = 0 models the displacement u (x) of a uniform elastic bar with forcing 2x. (a) Directly integrate to find the resulting displacement of the bar. (b) Find the Green's function for the boundary value problem. (c) Use superposition to check your solution from part (a).
Transcribed Image Text:6. Let the constant c> 0. The boundary value problem -cu" = 2x, u(0) = u(1) = 0 models the displacement u (x) of a uniform elastic bar with forcing 2x. (a) Directly integrate to find the resulting displacement of the bar. (b) Find the Green's function for the boundary value problem. (c) Use superposition to check your solution from part (a).
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