Consider the DE y"(x) + p(x)y'(x) + q(x) y(x) = 0. %3D The corresponding "normal form" DE is 1 1 u"(x) + Q(x)u(x) = 0, where Q(x) = q(x) – p(x)' P(x)? %3D %3D (a) The Bessel DE of order 1 is x y" + xy'+ (x-1) y = 0. %3D Find its normal form DE. (b) Explain why the distance between successive zeros of any nontrivial solution of this DE must be greater than T. (Refer to one of the Sturm theorems.)

Consider the DE y"(x) + p(x)y'(x) + q(x) y(x) = 0. %3D The corresponding "normal form" DE is 1 1 u"(x) + Q(x)u(x) = 0, where Q(x) = q(x) – p(x)' P(x)? %3D %3D (a) The Bessel DE of order 1 is x y" + xy'+ (x-1) y = 0. %3D Find its normal form DE. (b) Explain why the distance between successive zeros of any nontrivial solution of this DE must be greater than T. (Refer to one of the Sturm theorems.)

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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