II J (X) = g(r), r = [X], and n ≥ 3, show that 8²f 0х12 V²f= + + for x = 0. (b) Deduce from (a) that, if V²ƒ = 0, then f(x) = 8²f n 2 axn² X a n - 2 - + b₂ r 1 - g'(r) + g″(r) x = 0,

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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3.11 (a) Iff(x) = g(r), r = |x|, and n ≥ 3, show that
2² f
V²f=
əx₁
2
+
+
f(x) =
2²f
2
Əxn²
for x = 0.
(b) Deduce from (a) that, if V²ƒ= 0, then
a
x"
n 1
"=² 'g'(r) + g″(r)
Y
+ b₂
x = 0,
Transcribed Image Text:3.11 (a) Iff(x) = g(r), r = |x|, and n ≥ 3, show that 2² f V²f= əx₁ 2 + + f(x) = 2²f 2 Əxn² for x = 0. (b) Deduce from (a) that, if V²ƒ= 0, then a x" n 1 "=² 'g'(r) + g″(r) Y + b₂ x = 0,
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