Consider the second order linear ODE (1 − x²)y" — xy' + X²y = 0 0 ≤ x ≤1/2, with boundary conditions (a) form: - y(0) = 0 y(1/2) = 0. Demonstrate that this ODE can be rewritten in Sturm-Liouville dy d dx (p(x) d²/2) + q(x)y — X²r(x)y = 0, (b) (c) and identify p(x), q(x), and r(x). Characterize this boundary value problem as a regular or singular Sturm-Liouville problem. Solve for the eigenvalues and eigenfunctions (Hint: Consider the change of variable x = cos(0).)
Consider the second order linear ODE (1 − x²)y" — xy' + X²y = 0 0 ≤ x ≤1/2, with boundary conditions (a) form: - y(0) = 0 y(1/2) = 0. Demonstrate that this ODE can be rewritten in Sturm-Liouville dy d dx (p(x) d²/2) + q(x)y — X²r(x)y = 0, (b) (c) and identify p(x), q(x), and r(x). Characterize this boundary value problem as a regular or singular Sturm-Liouville problem. Solve for the eigenvalues and eigenfunctions (Hint: Consider the change of variable x = cos(0).)
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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help me with part c please
Transcribed Image Text:Consider the second order linear ODE
(1 − x²)y" — xy' + X²y = 0 0 ≤ x ≤1/2,
with boundary conditions
(a)
form:
-
y(0) = 0 y(1/2) = 0.
Demonstrate that this ODE can be rewritten in Sturm-Liouville
dy
d
dx
(p(x) d²/2) + q(x)y — X²r(x)y = 0,
(b)
(c)
and identify p(x), q(x), and r(x).
Characterize this boundary value problem as a regular or singular
Sturm-Liouville problem.
Solve for the eigenvalues and eigenfunctions (Hint: Consider the
change of variable x = cos(0).)
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