Given the initial value problem 2 y/" y' + 9. - + 0, y(0) = 24, y'(0) = b, %3D 81 Find the solution as a function of b, and then determine the cri value of b that separates solutions that remain positive for all t from those that eventually become negative.
Given the initial value problem 2 y/" y' + 9. - + 0, y(0) = 24, y'(0) = b, %3D 81 Find the solution as a function of b, and then determine the cri value of b that separates solutions that remain positive for all t from those that eventually become negative.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Given the initial value problem
2
y"
y +
81
= 0, y(0) = 24, y (0) = 6,
-
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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