Problem. Suppose that p() is a differentiable function with d'(1) s ko(1) (k > 0) for t2 a. Multiply both sides by eki, then transpose to show that for i2a. Then apply the mean value theorem to conclude that (1) s pla)eku-a) for t2a.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Problem.
Suppose that p() is a differentiable function with
d'(1) s ko(1)
(k > 0)
for t2 a. Multiply both sides by eki, then transpose to
show that
for i2a. Then apply the mean value theorem to conclude
that
(1) s pla)eku-a)
for t2a.
Transcribed Image Text:Problem. Suppose that p() is a differentiable function with d'(1) s ko(1) (k > 0) for t2 a. Multiply both sides by eki, then transpose to show that for i2a. Then apply the mean value theorem to conclude that (1) s pla)eku-a) for t2a.
Expert Solution
Step 1

Given : ϕ'tkϕt   for k>0

To show : for ta    ddtϕte-kt0   and ϕtϕaekt-a

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