5. Knowing that (2" J,(x))' = x" J,-1(x) (x-" J,(x))' = -x=" Jp+1(x) 2v Jy-1(x) + Jp+1(x) = Jy-1(x) – Jy+1(x) = 2J',(x) %3D (x)"S - x Verify that d ((=)) = (-1(2) – Ji+1(x)) . (1(2) – J1(#)) . dx 2n

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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5. Knowing that
(x" J„(x))' = x" Jy-1(x)
(x-" J,(x))' = -x=" Jy+1(x)
2v
Jy-1(x) + Jy+1(x) =
-Ju(x)
J„-1(x) – Jµ+1(x) = 2.J',(x)
Verify that
d
((x)) = (J-1(x) – Ji+1(x) .
dx
2n
Transcribed Image Text:5. Knowing that (x" J„(x))' = x" Jy-1(x) (x-" J,(x))' = -x=" Jy+1(x) 2v Jy-1(x) + Jy+1(x) = -Ju(x) J„-1(x) – Jµ+1(x) = 2.J',(x) Verify that d ((x)) = (J-1(x) – Ji+1(x) . dx 2n
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