28. Using the method of reduction of order, show that if 7₁ is a repeated root of r(r-1) +ar+ 3 = 0, then x²¹ and x¹ In x are solutions of x²y"+axy+3y=0 for x > 0.
28. Using the method of reduction of order, show that if 7₁ is a repeated root of r(r-1) +ar+ 3 = 0, then x²¹ and x¹ In x are solutions of x²y"+axy+3y=0 for x > 0.
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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Transcribed Image Text:28. Using the method of reduction of order, show that if 7₁ is a
repeated root of
r(r-1) +ar+ 3 = 0,
then x¹ and x¹ In x are solutions of x²y"+axy+3y=0 for x > 0.
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