Given the initial value problem 1 y" – y' + = 0, y(0) = 21, y'(0) = b, 16 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

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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Given the initial value problem
1
y" -
y' +
16
= 0, y(0) =
21, y'(0) = b,
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
Transcribed Image Text:Given the initial value problem 1 y" - y' + 16 = 0, y(0) = 21, y'(0) = b, 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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