determine the roots of the indicial equa- tion of the given differential equation. Also obtain the general form of two linearly independent solutions to the differen- tial equation on an interval (0, R). Finally, if r1 -r2 equals a positive integer, obtain the recurrence relation and determine whether the constant A in y2(x) = Ayı (x) In x +x2 bnx" n=0 is zero or nonzero.

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

Q.x2y′′+x(x −3)y′+(4−x)y =0.

determine the roots of the indicial equa-
tion of the given differential equation. Also obtain the general
form of two linearly independent solutions to the differen-
tial equation on an interval (0, R). Finally, if r1 -r2 equals a
positive integer, obtain the recurrence relation and determine
whether the constant A in
y2(x) = Ayı (x) In x +x2
bnx"
n=0
is zero or nonzero.
Transcribed Image Text:determine the roots of the indicial equa- tion of the given differential equation. Also obtain the general form of two linearly independent solutions to the differen- tial equation on an interval (0, R). Finally, if r1 -r2 equals a positive integer, obtain the recurrence relation and determine whether the constant A in y2(x) = Ayı (x) In x +x2 bnx" n=0 is zero or nonzero.
Expert Solution
Introduction

As per the question we are given the following 2nd order linear differential equation as :

x2y′′ + x(x −3)y′ + (4−x)y = 0

And we have to find the roots of the indicial equation of this ODE then find the two independent series solutions.

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