Given the initial value problem 2 y": y' + 0, y(0) = 19, y'(0) = b, - 9 81 Find the solution as a function of b, and then determine the critical value of b that separates solutions that remain positive for all t > 0 from those that eventually become negative. NOTE: Use t as the independent variable. y(t) The critical value of b is
Given the initial value problem 2 y": y' + 0, y(0) = 19, y'(0) = b, - 9 81 Find the solution as a function of b, and then determine the critical value of b that separates solutions that remain positive for all t > 0 from those that eventually become negative. NOTE: Use t as the independent variable. y(t) The critical value of b is
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 17EQ
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![Given the initial value problem
2
y"-
ay + = 0, y(0) = 19, y'(0) = b,
-
9
81
Find the solution as a function of b, and then determine the critical
value of b that separates solutions that remain positive for all t > 0
from those that eventually become negative.
NOTE: Use t as the independent variable.
y(t)
The critical value of b is](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa19b06ce-ec0f-46d1-9818-e8eb6bd76173%2Fbbff8741-2736-4454-a7bd-974db05a2eca%2Fgriy9th_processed.png&w=3840&q=75)
Transcribed Image Text:Given the initial value problem
2
y"-
ay + = 0, y(0) = 19, y'(0) = b,
-
9
81
Find the solution as a function of b, and then determine the critical
value of b that separates solutions that remain positive for all t > 0
from those that eventually become negative.
NOTE: Use t as the independent variable.
y(t)
The critical value of b is
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