Check whether the following Sturm-Liouville eigenvalue problems are regular or singular; and whether the eigenvalues are positive or not. If the problem is singular, where is the singularity? (a). ((1+x²)y')' + Ay = 0, y(0) = 0, y(3) = 0. (b). ry" + y' + Ay = 0, y(a) = 0, y(b) = 0, 0

Check whether the following Sturm-Liouville eigenvalue problems are regular or singular; and whether the eigenvalues are positive or not. If the problem is singular, where is the singularity? (a). ((1+x²)y')' + Ay = 0, y(0) = 0, y(3) = 0. (b). ry" + y' + Ay = 0, y(a) = 0, y(b) = 0, 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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Question

Check whether the following Sturm-Liouville eigenvalue problems are regular
or singular; and whether the eigenvalues are positive or not. If the problem is
singular, where is the singularity?
(a). ((1+x²)y')' + Ay = 0, y(0) = 0, y(3) = 0.
(b). xy" + y' + Ay = 0, y(a) = 0, y(b) = 0, 0<a < b.
(c). xry" + 2y' + Xy = 0, y(1) = 0, y'(2) = 0. Hint: Multiply by r.
(d). xy" – y' + Axy= 0, y(0) = 0, y'(5) = 0. Hint: Divide by x².
(e). ((1 – x²)y')' – 2æy' + (1 + Aæ)y = 0, y(-1) = 0, y(1) = 0.

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