(a) Verify that if c is a constant, then the function defined piecewise by So y(x) = (x - c)? for x > c for x

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
1st Edition
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
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Chapter8: Graphing Quadratic Functions
Section: Chapter Questions
Problem 16CT
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(a) Verify that if c is a constant, then the function defined
piecewise by
So
y(x) =
(x - c)? for x > c
for x <c,
satisfies the differential equation y = 2,F for all x (in-
cluding the point x = c). Construct a figure illustrating the
fact that the initial value problem y' = 2./ỹ, y(0) = 0 has
infinitely many different solutions. (b) For what values of
b does the initial value problem y' = 2,y, y(0) = b have
(i) no solution, (ii) a unique solution that is defined for all
x?
Transcribed Image Text:(a) Verify that if c is a constant, then the function defined piecewise by So y(x) = (x - c)? for x > c for x <c, satisfies the differential equation y = 2,F for all x (in- cluding the point x = c). Construct a figure illustrating the fact that the initial value problem y' = 2./ỹ, y(0) = 0 has infinitely many different solutions. (b) For what values of b does the initial value problem y' = 2,y, y(0) = b have (i) no solution, (ii) a unique solution that is defined for all x?
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