a. Show that the given differential equation has a regular singular point at x = 0. b. Determine the indicial equation, the recurrence relation, and the roots of the indicial equation. c. Find the series solution (x > 0) corresponding to the larger root. d. If the roots are unequal and do not differ by an integer, find the series solution corresponding to the smaller root also.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
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x²y" + xy' + (x − 2) y = 0
Transcribed Image Text:x²y" + xy' + (x − 2) y = 0
a. Show that the given differential equation has a regular
singular point at x = 0.
b. Determine the indicial equation, the recurrence relation, and
the roots of the indicial equation.
c. Find the series solution (x > 0) corresponding to the larger
root.
d. If the roots are unequal and do not differ by an integer, find
the series solution corresponding to the smaller root also.
Transcribed Image Text:a. Show that the given differential equation has a regular singular point at x = 0. b. Determine the indicial equation, the recurrence relation, and the roots of the indicial equation. c. Find the series solution (x > 0) corresponding to the larger root. d. If the roots are unequal and do not differ by an integer, find the series solution corresponding to the smaller root also.
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