- In Problems 25-30, x = 0 is a regular singular point of the given differential equation. Show that the indicial roots of the singularity differ by an integer. Use the method of Frobenius to obtain at least one series solution about x = 0. Use (21) where necessary and a CAS, if instructed, to find a second solution. Form the general solution on the interval (0, ∞). 25. xy" +2y' - xy = 0 26. x²y" + xy' + (x² - y = 0 27. xy" - xy' + y = 0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Question
-
In Problems 25-30, x = 0 is a regular singular point of the
given differential equation. Show that the indicial roots of the
singularity differ by an integer. Use the method of Frobenius
to obtain at least one series solution about x = 0. Use (21)
where necessary and a CAS, if instructed, to find a second
solution. Form the general solution on the interval (0, ∞).
25. xy" +2y' - xy = 0
26. x²y" + xy' + (x² - y = 0
27. xy" - xy' + y = 0
Transcribed Image Text:- In Problems 25-30, x = 0 is a regular singular point of the given differential equation. Show that the indicial roots of the singularity differ by an integer. Use the method of Frobenius to obtain at least one series solution about x = 0. Use (21) where necessary and a CAS, if instructed, to find a second solution. Form the general solution on the interval (0, ∞). 25. xy" +2y' - xy = 0 26. x²y" + xy' + (x² - y = 0 27. xy" - xy' + y = 0
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