SW Consider the equation 2x2y" - xy' + (x - 5)y=0 in some interval 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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SOS DE
Consider the equation 2x2y" - xy' + (x - 5)y=0 in some interval 0 < x < R.
(a) verify that x = 0 is a regular singular point.
(b) There are two values of r such that y = Σno Cnxn+ (co 0) is a solution of the equation for
0<x< R. Find the two values of r.
(c) Given that y₁ and y2 are two solutions of the equation corresponding to the two values of r
found in (b) using the (Frobenius) method given in the class/book, show that y₁ and y2 are linearly
independent.
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