Answer
See below
Work Step by Step
Given: $x^2y''+x(1-x)y'-7y=0$
We can notice that $p=1-x, q=-7$
and $p(0)=1, q(0)=-7$
Obtain: $r(r-1)+r-7=0\\
r^2-7=0\\
r=\pm 7$
Differential Equations and Linear Algebra (4th Edition)
by Goode, Stephen W.; Annin, Scott A.
Published by
Pearson
ISBN 10:
0-32196-467-5
ISBN 13:
978-0-32196-467-0
Chapter 11 - Series Solutions to Linear Differential Equations - 11.4 Series Solutions about a Regular Singular Point - Problems - Page 758: 6
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