Answered: decide if the given statement is true…

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

decide if the given statement is true or false,and give a brief justiﬁcation for your answer.If true, you can quote a relevant deﬁnition or theorem .
If false,provide an example,illustration,or brief explanation of why the statement is false.
Q.)` The radius of convergence of a power series solution to the differential equation y′′+ 1/x²−1 y′+ 1/x +2 y =0 centered at x =2 is at least 2.

Expert Solution

Step 1

Given differential equation is:

$\begin{array}{rcl} y'' + \frac{1}{x^{2} - 1} y' + \frac{1}{x + 2} y & = & 0 \\ x_{0} & = & 2 \end{array}$

Now, at the singular points,

$\begin{array}{rcl} x^{2} - 1 & = & 0 \\ x & = & 1, - 1 \\ x + 2 & = & 0 \\ x & = & - 2 \end{array}$

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