(b) Argue that the graph of is decreasing for x near zero and that as x increases from zero, (x) decreases until it crosses the line y = x, where its derivative is zero. (c) Let x* be the abscissa of the point where the solution curve y = $(x) crosses the line y = x. Consider the sign of o"(x*) and argue that o has a relative minimum at x*.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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(b) Argue that the graph of is decreasing for x
near zero and that as x increases from zero, (x)
decreases until it crosses the line y = x, where its
derivative is zero.
(c) Let x* be the abscissa of the point where the solution
curve y = $(x) crosses the line y = x. Consider
the sign of o"(x*) and argue that o has a relative
minimum at x*.
Transcribed Image Text:(b) Argue that the graph of is decreasing for x near zero and that as x increases from zero, (x) decreases until it crosses the line y = x, where its derivative is zero. (c) Let x* be the abscissa of the point where the solution curve y = $(x) crosses the line y = x. Consider the sign of o"(x*) and argue that o has a relative minimum at x*.
9. Let ø (x) denote the solution to the initial value problem
dy
= x- y,
dx
y(0) = 1.
(a) Show that d"(x) = 1– 4'(x) = 1- x+ ¢(x).
Transcribed Image Text:9. Let ø (x) denote the solution to the initial value problem dy = x- y, dx y(0) = 1. (a) Show that d"(x) = 1– 4'(x) = 1- x+ ¢(x).
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