Verify that if c is a constant, then the function defined piecewise by if x

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter1: Functions
Section1.3: Properties Of Functions
Problem 17E
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Verify that if c is a constant, then the function defined
piecewise by
if x <c,
y(x) = {cos(x – c) if c <x < c +x,
if x 2c+1
(+1
-1
satisfies the differential equation y' = -VI- y² for all x.
(Perhaps a preliminary sketch with c = 0 will be helpful.)
Sketch a variety of such solution curves. Then determine
(in terms of a and b) how many different solutions the ini-
tial value problem y' = -V1- y2, y(a) = b has.
Transcribed Image Text:Verify that if c is a constant, then the function defined piecewise by if x <c, y(x) = {cos(x – c) if c <x < c +x, if x 2c+1 (+1 -1 satisfies the differential equation y' = -VI- y² for all x. (Perhaps a preliminary sketch with c = 0 will be helpful.) Sketch a variety of such solution curves. Then determine (in terms of a and b) how many different solutions the ini- tial value problem y' = -V1- y2, y(a) = b has.
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