1. Suppose that f : [0, 0) → R is continuous and f(x) # 0 for all x > 0. If we have (f(x))? = 2 f(t)dt for all x> 0, Show that f(x) = x for all x > 0.
1. Suppose that f : [0, 0) → R is continuous and f(x) # 0 for all x > 0. If we have (f(x))? = 2 f(t)dt for all x> 0, Show that f(x) = x for all 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:1. Suppose that f : [0, ∞) → R is continuous and f(x) # 0 for all x > 0. If
we have
(f(x))² = 2 f(t)dt for all r > 0,
Show that f(x) = x for all x > 0.
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how can I show this using the Fundamental Theory of Calc?
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