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).
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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F267b756b-4631-45c0-98bc-62ca391f0187%2Febb5c270-96fe-4bcd-bc3a-dab0c807cd28%2Fa48hwoj_processed.jpeg&w=3840&q=75)
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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