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Solved: In 15–24, x = 0 is a regular singular point of the
Chapter 6, Problem 15E(choose chapter or problem)
In Problems 15–24, x = 0 is a regular singular point of the given differential equation. Show that the indicial roots of the singularity do not differ by an integer. Use the method of Frobenius to obtain two linearly independent series solutions about x = 0. Form the general solution on \((0, \infty)\).
\(2 x y^{\prime \prime}-y^{\prime}+2 y=0\)
Text Transcription:
(0,infty)
2xy^prime\prime-y^prime+2 y=0
Questions & Answers
QUESTION:
In Problems 15–24, x = 0 is a regular singular point of the given differential equation. Show that the indicial roots of the singularity do not differ by an integer. Use the method of Frobenius to obtain two linearly independent series solutions about x = 0. Form the general solution on \((0, \infty)\).
\(2 x y^{\prime \prime}-y^{\prime}+2 y=0\)
Text Transcription:
(0,infty)
2xy^prime\prime-y^prime+2 y=0
ANSWER:Step 1 of 4
In this problem, we have to show that the indicial roots of the singularity do not differ by an integer.