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).)

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter9: Multivariable Calculus

Section9.2: Partial Derivatives

Problem 33E

See similar textbooks