2. Consider the equation utt = c²uxx for 0 < x < l, with the boundary conditions ux (0, t) = 0, u(l, t) = 0 (Neumann at the left, Dirichlet at the right). a. Show that the eigenfunctions are cos [(n + 1) πx/l]. b. Write the series expansion for a solution u(x, t).

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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2. Consider the equation utt = c²uxx for 0 < x < l, with the boundary conditions
ux (0, t) = 0, u(l, t) = 0 (Neumann at the left, Dirichlet at the right).
a. Show that the eigenfunctions are cos [(n + 1)πx/l].
b. Write the series expansion for a solution u(x, t).
Пх
Transcribed Image Text:2. Consider the equation utt = c²uxx for 0 < x < l, with the boundary conditions ux (0, t) = 0, u(l, t) = 0 (Neumann at the left, Dirichlet at the right). a. Show that the eigenfunctions are cos [(n + 1)πx/l]. b. Write the series expansion for a solution u(x, t). Пх
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